Jet&planet

Page 1

Jet&Planet Astroscitheo


Contents 1

2

Jet Propulsion Laboratory

1

1.1

History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1.2

Location . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

1.3

Employees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

1.4

Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

1.4.1

Internships and fellowships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

1.4.2

Museum Alliance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

1.4.3

Educator Resource Center . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

1.5

Open house . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

1.6

Other works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

1.7

Funding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

1.8

Peanuts tradition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

1.9

Missions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

1.10 List of directors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

1.11 Team X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

1.12 Controversies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

1.12.1 Employee background check lawsuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

1.12.2 Coppedge v Jet Propulsion Laboratory . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

1.13 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

1.14 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

1.15 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

Voyager program

7

2.1

History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

2.2

Spacecraft design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

2.2.1

ScientiďŹ c instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

2.2.2

Computers and data processing

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

2.2.3

Communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2.2.4

Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

2.3

Voyager Interstellar Mission

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10

Mission details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

2.4

Telemetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

2.5

Voyager Golden Record . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

2.3.1

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ii

3

CONTENTS 2.6

Pale blue dot

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

2.7

In popular culture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

2.8

See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

2.9

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

2.10 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14

Pioneer program

16

3.1

Naming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

3.2

Early Pioneer missions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

3.2.1

Able space probes (1958–1960) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

3.2.2

Juno II lunar probes (1958–1959) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

Later Pioneer missions (1965–1978) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

3.3.1

Pioneer 6, 7, 8, and 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

3.3.2

Outer Solar System missions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

3.3.3

Pioneer Venus project

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

3.4

See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

3.5

References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

3.6

External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

3.3

4

5

Copernican Revolution

20

4.1

Historical overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20

4.1.1

Nicolaus Copernicus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20

4.1.2

Tycho Brahe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4.1.3

Johannes Kepler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

4.1.4

Galileo Galilei . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22

4.1.5

Sphere of the fixed stars

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23

4.1.6

Isaac Newton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

4.2

Metaphorical use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

4.3

See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

4.4

References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

4.5

Works cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

Celestial spheres

25

5.1

History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

5.1.1

Early ideas of spheres and circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

5.1.2

Emergence of the planetary spheres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

5.1.3

Middle Ages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

5.1.4

Renaissance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28

5.2

Literary and symbolic expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

5.3

See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

5.4

Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

5.5

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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CONTENTS

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5.6

33

6

7

8

External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Firmament

35

6.1

Biblical use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

6.2

Etymology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

6.3

History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

6.4

ScientiďŹ c development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36

6.5

See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36

6.6

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36

6.7

External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

Primum Mobile

38

7.1

Appearance and rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38

7.2

Spherical variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38

7.3

Copernicus and after . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38

7.4

Literary references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38

7.5

See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

7.6

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

7.7

Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

Geocentric model

40

8.1

Ancient Greece . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

40

8.2

Ptolemaic model

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41

8.2.1

Ptolemaic system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

42

8.2.2

Islamic astronomy and geocentrism

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

Copernican system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

8.3

Geocentrism and rival systems 8.3.1

8.4

Gravitation

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8.5

Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46

8.6

Religious and contemporary adherence to geocentrism . . . . . . . . . . . . . . . . . . . . . . . .

46

8.6.1

Historical positions of the Roman Catholic hierarchy . . . . . . . . . . . . . . . . . . . . .

47

8.6.2

Orthodox Judaism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

8.6.3

Islam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

8.7

Planetariums

8.8

Geocentric models in ďŹ ction

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

8.9

See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

8.10 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

8.11 References

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51

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53

8.13 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

Geocentric orbit

54

9.1

54

8.12 Bibliography

9

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

List of terms and concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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iv

CONTENTS 9.2

Geocentric orbit types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

9.2.1

Altitude classifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

9.2.2

Inclination classifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

9.2.3

Eccentricity classifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

9.2.4

Directional classifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

9.2.5

Geosynchronous classifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

9.2.6

Special classifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

9.2.7

Non-geocentric classifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

9.3

Tangential velocities at altitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

9.4

See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

9.5

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

9.6

External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

10 Goddard Space Flight Center 10.1 History

58

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

58

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

10.2.1 Testing chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

10.2.2 High Energy Astrophysics Science Archive Research Center

. . . . . . . . . . . . . . . .

59

10.2.3 Software Assurance Technology Center . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

10.2.4 Goddard Visitor Center

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

10.2.5 External facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

10.2 Facilities

10.3 Employees

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

10.4.1 Past . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

10.4.2 Present . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

10.4.3 Future

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

10.5 Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

10.6 Spinoff technologies

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

62

10.7 Community . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

10.8 Queen Elizabeth II’s visit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

10.9 References

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63

10.10External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

10.4 Missions

11 Moon

65

11.1 Name and etymology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65

11.2 Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66

11.3 Physical characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67

11.3.1 Internal structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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11.3.2 Surface geology

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68

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

11.3.4 Magnetic field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

11.3.5 Atmosphere

71

11.3.3 Gravitational field

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


CONTENTS

v

11.3.6 Seasons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

11.4 Relationship to Earth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

11.4.1 Orbit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72

11.4.2 Relative size

72

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11.4.3 Appearance from Earth

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72

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73

11.4.5 Eclipses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

74

11.4.4 Tidal effects

11.5 Observation and exploration

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

75

11.5.1 Ancient and medieval studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

75

11.5.2 By spacecraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

76

11.6 Astronomy from the Moon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

79

11.7 Legal status . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

79

11.8 In culture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

80

11.8.1 Mythology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

80

11.8.2 Calendar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

80

11.8.3 Modern art and literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

80

11.8.4 Lunacy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81

11.9 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81

11.10References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81

11.10.1 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81

11.10.2 Citations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81

11.10.3 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89

11.11Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89

11.12External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

90

11.12.1 Cartographic resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

90

11.12.2 Observation tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

90

11.12.3 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

90

12 Space Network

91

12.1 Satellite generations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

12.2 Coverage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

12.3 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

92

12.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

92

12.5 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

92

13 NASA

93

13.1 Creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

93

13.2 Space flight programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

94

13.2.1 Manned programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

94

13.2.2 Unmanned programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 13.2.3 Recent and planned activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 13.3 Scientific research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102


vi

CONTENTS 13.4 Sta and leadership . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 13.5 Facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 13.6 Budget . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 13.7 Environmental impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 13.8 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 13.9 Spacecraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 13.10Examples of missions by target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 13.11See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 13.12Footnotes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 13.13References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 13.14External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

14 Solar System

110

14.1 Discovery and exploration

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

14.2 Structure and composition

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

14.2.1 Distances and scales 14.3 Formation and evolution

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

14.4 Sun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 14.5 Interplanetary medium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 14.6 Inner Solar System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 14.6.1 Inner planets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 14.6.2 Asteroid belt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 14.7 Outer Solar System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 14.7.1 Outer planets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 14.7.2 Centaurs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 14.8 Comets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 14.9 Trans-Neptunian region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 14.9.1 Kuiper belt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 14.9.2 Scattered disc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 14.10Farthest regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 14.10.1 Heliosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 14.10.2 Detached objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 14.10.3 Oort cloud

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

14.10.4 Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 14.11Galactic context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 14.11.1 Neighbourhood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 14.11.2 Comparison with other planetary systems

. . . . . . . . . . . . . . . . . . . . . . . . . . 122

14.12Visual summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 14.13See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 14.14Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 14.15References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 14.16External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129


CONTENTS 15 Sun

vii 130

15.1 Name and etymology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 15.1.1 Religious aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 15.2 Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 15.3 Sunlight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 15.4 Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 15.4.1 Singly ionized iron-group elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 15.4.2 Isotopic composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 15.5 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 15.5.1 Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 15.5.2 Radiative zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 15.5.3 Tachocline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 15.5.4 Convective zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 15.5.5 Photosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 15.5.6 Atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 15.5.7 Photons and neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 15.6 Magnetism and activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 15.6.1 Magnetic field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 15.6.2 Variation in activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 15.6.3 Long-term change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 15.7 Life phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 15.7.1 Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 15.7.2 Main sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 15.7.3 After core hydrogen exhaustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 15.8 Motion and location . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 15.8.1 Orbit in Milky Way . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 15.9 Theoretical problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 15.9.1 Coronal heating problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 15.9.2 Faint young Sun problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 15.10History of observation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 15.10.1 Early understanding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 15.10.2 Development of scientific understanding . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 15.10.3 Solar space missions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 15.11Observation and effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 15.12See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 15.13Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 15.14References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 15.15Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 15.16External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 16 Nicolaus Copernicus

152

16.1 Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152


viii

CONTENTS 16.1.1 Father’s family . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 16.1.2 Mother’s family . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 16.1.3 Languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 16.1.4 Name . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 16.1.5 Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 16.1.6 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 16.1.7 Heliocentrism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 16.1.8 The book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 16.1.9 Death . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 16.2 Copernican system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 16.2.1 Predecessors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 16.2.2 Copernicus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 16.2.3 Successors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 16.3 Controversy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 16.3.1 Tolosani . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 16.3.2 Theology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 16.3.3 Ingoli . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 16.3.4 Galileo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 16.4 Nationality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 16.5 Commemoration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 16.5.1 Copernicium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 16.5.2 55 Cancri A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 16.5.3 Veneration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 16.5.4 Influence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 16.6 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 16.7 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 16.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 16.9 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 16.10External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

17 Ptolemy

178

17.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 17.2 Astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 17.3 The Geography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 17.4 Astrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 17.5 Music . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 17.6 Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 17.7 Named after Ptolemy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 17.8 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 17.9 Footnotes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 17.10References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 17.10.1 Texts and translations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184


CONTENTS

ix

17.11External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 17.11.1 Primary sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 17.11.2 Secondary material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 18 Galileo Galilei

186

18.1 Early life and family

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

18.1.1 Name . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 18.1.2 Children

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

18.2 Career as a scientist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 18.2.1 Galileo, Kepler and theories of tides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 18.2.2 Controversy over comets and The Assayer . . . . . . . . . . . . . . . . . . . . . . . . . . 188 18.2.3 Controversy over heliocentrism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 18.3 Death . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 18.4 Scientific methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 18.5 Astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 18.5.1 Kepler’s supernova . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 18.5.2 Jupiter’s moons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 18.5.3 Venus, Saturn, and Neptune . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 18.5.4 Sunspots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 18.5.5 Moon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 18.5.6 Milky Way and stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 18.6 Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 18.7 Physics

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

18.7.1 Falling bodies

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

18.8 Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 18.9 Writings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 18.9.1 Published written works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 18.10Legacy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 18.10.1 Later Church reassessments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 18.10.2 Impact on modern science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 18.10.3 In artistic and popular media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 18.11Timeline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 18.12See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 18.13Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 18.14References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 18.15External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 18.15.1 By Galileo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 18.15.2 On Galileo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 19 Heliocentrism

212

19.1 Early developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 19.1.1 Greek and Hellenistic world . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213


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CONTENTS 19.1.2 Medieval Europe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 19.1.3 India . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 19.1.4 Medieval Islamic world . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 19.2 Copernican revolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 19.2.1 Astronomical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 19.2.2 Religious attitudes to Heliocentrism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 19.3 The view of modern science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 19.3.1 Modern use of geocentric and heliocentric . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 19.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 19.5 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 19.6 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 19.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

20 Johannes Kepler 20.1 Early years

226 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

20.2 Graz (1594–1600)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

20.2.1 Mysterium Cosmographicum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 20.2.2 Marriage to Barbara Müller

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228

20.2.3 Other research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 20.3 Prague (1600–1612)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

20.3.1 Work for Tycho Brahe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 20.3.2 Advisor to Emperor Rudolph II

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230

20.3.3 Astronomiae Pars Optica . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 20.3.4 The Supernova of 1604

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

20.3.5 Astronomia nova . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 20.3.6 Dioptrice, Somnium manuscript, and other work . . . . . . . . . . . . . . . . . . . . . . . 232 20.3.7 Work in mathematics and physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 20.3.8 Personal and political troubles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 20.4 Linz and elsewhere (1612–1630) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 20.4.1 Second marriage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 20.4.2 Epitome of Copernican Astronomy, calendars, and the witch trial of his mother . . . . . . . 234 20.4.3 Harmonices Mundi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 20.4.4 Rudolphine Tables and his last years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 20.5 Reception of his astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 20.6 Historical and cultural legacy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 20.6.1 History of science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 20.6.2 Editions and translations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 20.6.3 Popular science and historical fiction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 20.6.4 Veneration and eponymy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 20.7 Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 20.8 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 20.9 Notes and references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240


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20.10Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 20.11External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 21 De revolutionibus orbium coelestium

247

21.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 21.2 Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 21.3 Ad lectorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 21.4 Reception . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 21.5 Census of copies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 21.6 Editions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 21.7 Translations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 21.8 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 21.9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 21.10External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 22 Kepler’s laws of planetary motion

255

22.1 Comparison to Copernicus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 22.2 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 22.3 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 22.4 Formulary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 22.4.1 First law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 22.4.2 Second law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 22.4.3 Third law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 22.5 Planetary acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 22.5.1 Acceleration vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 22.5.2 The inverse square law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 22.5.3 Newton’s law of gravitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 22.6 Position as a function of time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 22.6.1 Mean anomaly, M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 22.6.2 Eccentric anomaly, E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 22.6.3 True anomaly, θ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 22.6.4 Distance, r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 22.7 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 22.8 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 22.9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 22.10Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 22.11External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 23 Giordano Bruno

265

23.1 Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 23.1.1 Early years, 1548–1576 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 23.1.2 First years of wandering, 1576–1583 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266


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CONTENTS 23.1.3 England, 1583–1585 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 23.1.4 Last years of wandering, 1585–1592 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 23.1.5 Imprisonment, trial and execution, 1593–1600 . . . . . . . . . . . . . . . . . . . . . . . . 268 23.1.6 Physical appearance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 23.2 Cosmology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 23.2.1 Contemporary cosmological beliefs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 23.2.2 Bruno’s cosmological claims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 23.3 Retrospective views of Bruno . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 23.3.1 Late Vatican position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 23.3.2 A martyr of science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 23.3.3 Theological heresy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 23.4 Artistic depictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 23.5 References in poetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 23.6 Appearances in fiction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 23.7 Giordano Bruno Foundation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 23.8 Giordano Bruno Memorial Award . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 23.9 Astronomical objects named after Bruno . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 23.10Other remembrances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 23.11Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 23.12Collections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 23.13See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 23.14Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 23.15References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 23.16External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278

24 Copernican heliocentrism

280

24.1 Earlier theories with the Earth in motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 24.2 Anticipations of Copernicus’s models for planetary orbits . . . . . . . . . . . . . . . . . . . . . . . 281 24.3 The Ptolemaic system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 24.4 Copernican theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 24.4.1 De revolutionibus orbium coelestium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 24.5 Acceptance of Copernican heliocentrism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 24.6 Modern opinion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 24.7 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 24.8 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 24.9 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 24.10Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 24.11External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 25 Aristarchus of Samos

288

25.1 Heliocentrism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 25.2 Distance to the Sun (lunar dichotomy) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289


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25.3 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 25.4 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 25.5 References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289

25.6 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 25.7 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 26 Ellipse

291

26.1 Elements of an ellipse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 26.2 Drawing ellipses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 26.2.1 Pins-and-string method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 26.2.2 The gardener’s ellipse: worked example . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 26.2.3 Trammel method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 26.2.4 Parallelogram method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 26.3 Mathematical definitions and properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 26.3.1 In Euclidean geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 26.3.2 In projective geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 26.3.3 In analytic geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 26.3.4 In trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298 26.3.5 As a parametric rational polynomial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 26.3.6 Degrees of freedom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 26.4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 26.4.1 Ellipses in physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 26.4.2 Ellipses in statistics and finance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 26.4.3 Ellipses in computer graphics

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301

26.4.4 Ellipses in optimization theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 26.5 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 26.6 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 26.7 References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304

26.8 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 27 Elliptic orbit

305

27.1 Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 27.2 Orbital period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 27.3 Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 27.4 Flight path angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 27.5 Equation of motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 27.6 Orbital parameters

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307

27.7 Solar System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 27.8 Radial elliptic trajectory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 27.9 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 27.10See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 27.11References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307


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CONTENTS 27.12Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 27.13External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308

28 Astronomia nova

309

28.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 28.2 Structure and Summary of the Astronomia nova . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 28.3 Kepler’s laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310 28.4 The “third law” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 28.5 Kepler’s knowledge of gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 28.6 Commemoration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 28.7 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 28.8 References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313

28.9 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 29 Aristotelian physics 29.1 Concepts

314

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314

29.1.1 Terrestrial change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 29.1.2 Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 29.1.3 Four causes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 29.1.4 Biology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 29.1.5 Natural place . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 29.1.6 Natural motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 29.1.7 Unnatural motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 29.1.8 Continuum and vacuum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 29.1.9 Speed, weight and resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 29.2 Medieval commentary

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319

29.3 Life and death of Aristotelian physics

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320

29.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 29.5 Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 29.6 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 29.7 References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321

29.8 Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 29.9 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 30 Gravity

323

30.1 History of gravitational theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 30.1.1 Earlier Concepts of Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 30.1.2 Scientific revolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 30.1.3 Newton’s theory of gravitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 30.1.4 Equivalence principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 30.1.5 General relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 30.1.6 Gravity and quantum mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326


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30.2 SpeciďŹ cs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 30.2.1 Earth’s gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 30.2.2 Equations for a falling body near the surface of the Earth . . . . . . . . . . . . . . . . . . 327 30.2.3 Gravity and astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 30.2.4 Gravitational radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328 30.2.5 Speed of gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328 30.3 Anomalies and discrepancies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328 30.4 Alternative theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 30.4.1 Historical alternative theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 30.4.2 Modern alternative theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 30.5 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 30.6 Footnotes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330 30.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 30.8 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 30.9 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 31 Planet 31.1 History

334 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334

31.1.1 Babylon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 31.1.2 Greco-Roman astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 31.1.3 India

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336

31.1.4 Medieval Muslim astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 31.1.5 European Renaissance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 31.1.6 19th century

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336

31.1.7 20th century

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336

31.1.8 21st century

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337

31.1.9 Objects formerly considered planets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 31.2 Mythology and naming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 31.3 Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340 31.4 Solar System

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341

31.4.1 Planetary attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342 31.5 Exoplanets

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342

31.6 Planetary-mass objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 31.6.1 Rogue planets

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343

31.6.2 Sub-brown dwarfs 31.6.3 Former stars

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343

31.6.4 Satellite planets and belt planets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 31.6.5 Captured planets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 31.7 Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344 31.7.1 Dynamic characteristics

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344

31.7.2 Physical characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 31.7.3 Secondary characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347


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CONTENTS 31.8 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 31.9 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348 31.10References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348

31.11External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 32 Ecliptic

354

32.1 Sun’s apparent motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354 32.2 Relationship to the celestial equator

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354

32.3 Obliquity of the ecliptic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355 32.4 Plane of the Solar System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356 32.5 Celestial reference plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356 32.6 Eclipses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 32.7 Equinoxes and solstices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 32.8 In the constellations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 32.9 Astrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 32.10See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 32.11Notes and references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 32.12External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 33 Orbital eccentricity

359

33.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 33.2 Etymology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 33.3 Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 33.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 33.5 Mean eccentricity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 33.6 Climatic effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 33.7 Exoplanets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 33.8 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 33.9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 33.10External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362


Chapter 1

Jet Propulsion Laboratory “JPL” redirects here. For other uses, see JPL (disambiguation). The Jet Propulsion Laboratory (JPL) is a federally funded research and development center and NASA field center located in La Cañada Flintridge, California and Pasadena, California, United States. The JPL is managed by the nearby California Institute of Technology (Caltech) for NASA. The laboratory’s primary function is the construction and operation of planetary robotic spacecraft, though it also conducts Earthorbit and astronomy missions. It is also responsible for operating NASA’s Deep Space Network. Among the laboratory’s current major active projects are the Mars Science Laboratory mission (which includes the Curiosity rover), the Cassini–Huygens mission orbiting Saturn, the Mars Exploration Rover Opportunity, the Mars Reconnaissance Orbiter, the Dawn mission to the dwarf planet Ceres and asteroid Vesta, the Juno spacecraft orbiting Jupiter, the NuSTAR X-ray telescope, and the Spitzer Space Telescope. They are also responsible for managing the JPL Small-Body Database, and provides physical data and lists of publications for all known small Solar System bodies.

The control room at JPL

Martin Summerfield, and pilot Homer Bushey demonstrated the first JATO rockets to the Army. In 1943, von Kármán, Malina, Parsons, and Forman established the Aerojet Corporation to manufacture JATO motors. The project took on the name Jet Propulsion Laboratory in November 1943, formally becoming an Army facility operated under contract by the university.[1][2][3][4]

During JPL’s Army years, the laboratory developed two The JPL’s Space Flight Operations Facility and Twenty- deployed weapon systems, the MGM-5 Corporal and Five-Foot Space Simulator are designated National His- MGM-29 Sergeant intermediate range ballistic missiles. toric Landmarks. These missiles were the first US ballistic missiles developed at JPL.[5] It also developed a number of other weapons system prototypes, such as the Loki anti-aircraft missile system, and the forerunner of the Aerobee sound1.1 History ing rocket. At various times, it carried out rocket testJPL traces its beginnings to 1936 in the Guggenheim ing at the White Sands Proving Ground, Edwards Air Aeronautical Laboratory at the California Institute of Force Base, and Goldstone, California. A lunar lander design Technology (GALCIT) when the first set of rocket ex- was also developed in 1938-39 which influenced [4] of the Apollo Lunar Module in the 1960s. periments were carried out in the Arroyo Seco. Caltech graduate students Frank Malina, Qian Xuesen, Weld Arnold, and Apollo M. O. Smith, along with Jack Parsons and Edward S. Forman, tested a small, alcoholfueled motor to gather data for Malina’s graduate thesis. Malina’s thesis advisor was engineer/aerodynamicist Theodore von Kármán, who eventually arranged for U.S. Army financial support for this “GALCIT Rocket Project” in 1939. In 1941, Malina, Parsons, Forman,

In 1954, JPL teamed up with Wernher von Braun's rocketeers at the Army Ballistic Missile Agency's Redstone Arsenal in Huntsville, Alabama, to propose orbiting a satellite during the International Geophysical Year. The team lost that proposal to Project Vanguard, and instead embarked on a classified project to demonstrate ablative re-entry technology using a Jupiter-C rocket. They carried out three successful sub-orbital flights in 1956 and 1


2

CHAPTER 1. JET PROPULSION LABORATORY

1957. Using a spare Juno I (a modified Jupiter-C with a fourth stage), the two organizations then launched the United States’ first satellite, Explorer 1, on February 1, 1958.[2][3]

MSL mockup compared with the Mars Exploration Rover and Sojourner rover by the Jet Propulsion Laboratory on May 12, 2008

JPL was transferred to NASA in December 1958,[6] becoming the agency’s primary planetary spacecraft center. JPL engineers designed and operated Ranger and Surveyor missions to the Moon that prepared the way for Apollo. JPL also led the way in interplanetary exploration with the Mariner missions to Venus, Mars, and Mercury.[2] In 1998, JPL opened the Near-Earth Object Program Office for NASA.[7] As of 2013, it has found 95% of asteroids that are a kilometer or more in diameter that cross Earth’s orbit.[8]

Research rockets on display at JPL.

on the northwest border of Pasadena, with a Pasadena address (4800 Oak Grove Drive, Pasadena, CA 91011), which is also the official mailing address. The city of La Cañada Flintridge, California was incorporated in 1976, well after JPL attained international recognition with a Pasadena address. There has been an occasional conflict JPL was early to employ women mathematicians. In the between the two cities over the issue of which should be 1940s and 1950s, using mechanical calculators, women mentioned in the media as the home of the laboratory. in an all-female computations group performed trajectory calculations.[9][10] In 1961, JPL hired Dana Ulery as their first woman engineer to work alongside male engineers as part of the Ranger and Mariner mission tracking 1.3 Employees teams.[11] JPL has been recognized four times by the Space Foun- There are approximately 5,000 full-time Caltech employdation: with the Douglas S. Morrow Public Outreach ees, and typically a few thousand additional contractors Award, which is given annually to an individual or orga- working on any given day. NASA also has a resident ofnization that has made significant contributions to public fice at the facility staffed by federal managers who overawareness of space programs, in 1998; and with the John see JPL’s activities and work for NASA. There are also L. “Jack” Swigert, Jr., Award for Space Exploration on some Caltech graduate students, college student interns three occasions – in 2009 (as part of NASA’s Phoenix and co-op students. Mars Lander Team[12] ), 2006 and 2005.

1.2 Location When founded, JPL’s site was a rocky flood-plain just outside the city limits of Pasadena. Almost all of the 177 acres (72 ha) of the U.S. federal government/NASA owned property that makes up the JPL campus is today located in the city of La Cañada Flintridge, California,[13]

1.4 Education The JPL Education Office serves educators and students by providing them with activities, resources, materials and opportunities tied to NASA missions and science. The mission of its programs is to introduce and further students’ interest in pursuing STEM (science, technology, engineering and mathematics) careers.[14]


1.5. OPEN HOUSE

3

1.4.2 Museum Alliance JPL created the NASA Museum Alliance in 2003 out of a desire to provide museums, planetariums, visitor centers and other kinds of informal educators with exhibit materials, professional development and information related to the upcoming landing of the Mars rovers Spirit and Opportunity.[18] The Alliance now has more than 500 members, who get access to NASA displays, models, educational workshops and networking opportunities through the program. Staff at educational organizations that meet the Museum Alliance requirements can register to participate online.[19] The Museum Alliance is a subset of the JPL Education Office’s Informal Education group, which also serves after-school and summer programs, parents and other kinds of informal educators.[20]

1.4.3 Educator Resource Center

A 1960s advert, it reads: “When you were a kid, science fiction gave you a sense of wonder. Now you feel the same just by going to work.”

The NASA/JPL Educator Resource Center, which is moving from its location at the Indian Hill Mall in Pomona, Calif. at the end of 2013,[21] offers resources, materials and free workshops for formal and informal educators covering science, technology, engineering and science topics related to NASA missions and science.

1.5 Open house 1.4.1

Internships and fellowships

JPL offers research, internship and fellowship opportunities in the summer and throughout the year to high school through postdoctoral and faculty students. (In most cases, students must be U.S. citizens or legal permanent residents to apply, although foreign nationals studying at U.S. universities are eligible for limited programs.) Interns are sponsored through NASA programs, university partnerships and JPL mentors for research opportunities at the laboratory in areas including technology, robotics, planetary science, aerospace engineering, and astrophysics.[15] In August 2013, JPL was named one of “The 10 Most Awesome College Labs of 2013” by Popular Science, A display at the Open House on May 19, 2007. which noted that about 100 students who intern at the laboratory are considered for permanent jobs at JPL af- The lab has an open house once a year on a Saturday and ter they graduate.[16] Sunday in May or June, when the public is invited to tour The JPL Education Office also hosts the Planetary Sci- the facilities and see live demonstrations of JPL science ence Summer School (PSSS), an annual week-long work- and technology. More limited private tours are also availshop for graduate and postdoctoral students. The pro- able throughout the year if scheduled well in advance. gram involves a one-week team design exercise develop- Thousands of schoolchildren from Southern California ing an early mission concept study, working with JPL’s and elsewhere visit the lab every year.[22] Due to fedAdvanced Projects Design Team (“Team X”) and other eral spending cuts mandated by budget sequestration, the open house has been previously cancelled.[23] JPL open concurrent engineering teams.[17]


4

CHAPTER 1. JET PROPULSION LABORATORY

house for 2014 was October 11 and 12 and 2015 was October 10 and 11. Starting from 2016, JPL replaced annual Open House with “Ticket to Explore JPL”, which features the same exhibits but requires tickets and advance reservation.[24]

1.6 Other works In addition to its government work, JPL has also assisted the nearby motion picture and television industries, by advising them about scientific accuracy in their productions. Science fiction shows advised by JPL include Babylon 5 and its sequel series, Crusade. JPL also works with the Department of Homeland Security Science and Technology Directorate (DHSSTD). JPL and DHSSTD developed a search and rescue tool for first responders called FINDER. First responders can use FINDER to locate people still alive who are buried in rubble after a disaster or terrorist attack. FINDER uses microwave radar to detect breathing and pulses.[25]

• Pioneer 3 & 4 • Viking program • Voyager program • Magellan probe • Galileo probe • Wide Field and Planetary Camera 2 • Deep Space 1 & 2 • Mars Global Surveyor • Mars Climate Orbiter • Cassini–Huygens • Stardust • Mars Odyssey • Mars Pathfinder • Mars Exploration Rover Mission • Spitzer Space Telescope

1.7 Funding JPL is a federally funded research and development center (FFRDC) managed and operated by Caltech under a contract from NASA. In fiscal year 2012, the laboratory’s budget was slightly under $1.5 billion, with the largest share going to Earth Science and Technology development.[26]

1.8 Peanuts tradition There is a tradition at JPL to eat “good luck peanuts" before critical mission events, such as orbital insertions or landings. As the story goes, after the Ranger program had experienced failure after failure during the 1960s, the first successful Ranger mission to impact the Moon occurred while a JPL staff member was eating peanuts. The staff jokingly decided that the peanuts must have been a good luck charm, and the tradition persisted.[27][28]

• Mars Reconnaissance Orbiter • Gravity Recovery (GRACE)

and

Climate

Experiment

• CloudSat • Phoenix (spacecraft) • Ocean Surface Topography Mission (OSTM/Jason2) • Orbiting Carbon Observatory • Mars Science Laboratory • Wide-field Infrared Survey Explorer • Shuttle Radar Topography Mission

1.10 List of directors • Theodore von Kármán, 1938 – 1944 • Frank Malina, 1944 – 1946

1.9 Missions These are some of the missions partially sponsored by JPL:[29]

• Louis Dunn, 1946 – October 1, 1954 • William Hayward Pickering, October 1, 1954 – March 31, 1976 • Bruce C. Murray, April 1, 1976 – June 30, 1982

• Explorer program

• Lew Allen, Jr., July 22, 1982 – December 31, 1990

• Ranger program

• Edward C. Stone, January 1, 1991 – April 30, 2001

• Surveyor program

• Charles Elachi, May 1, 2001 – June 30, 2016[30]

• Mariner program

• Michael M. Watkins, July 1, 2016[31] – present


1.13. SEE ALSO

1.11 Team X

5

1.12.2 Coppedge v Jet Propulsion Laboratory

The JPL Advanced Projects Design Team, also known as Team X, is an interdisciplinary team of engineers that utilizes “concurrent engineering methodologies to complete rapid design, analysis and evaluation of mission concept designs”.[32]

On March 12, 2012, Los Angeles Superior Court took opening statements on the case in which former-JPL employee David Coppedge brought suit against the lab due to workplace discrimination and wrongful termination. In the suit, Coppedge alleges that he first lost his “team lead” status on JPL’s Cassini-Huygens mission in 2009 and then was fired in 2011 because of his evangelical Christian beliefs and specifically his belief in intelligent design. Conversely, JPL, through the Caltech lawyers representing the laboratory, allege that Coppedge’s termination was simply due to budget cuts and his demotion from team lead was because of harassment complaints and from on1.12 Controversies going conflicts with his co-workers.[39] Superior Court Judge Ernest Hiroshige issued a final ruling in favor of [40] 1.12.1 Employee background check law- JPL on January 16, 2013.

suit

1.13 See also Main article: NASA v. Nelson • Jet Propulsion Laboratory Science Division On February 25, 2005, the Homeland Security Presidential Directive 12 was approved by the Secretary of Commerce.[33] This was followed by the Federal Information Processing Standards 201 (FIPS 201), which specified how the federal government should implement personal identity verification. New specifications led to a need for rebadging to meet the updated requirements. On August 30, 2007, a group of JPL employees filed suit in federal court against NASA, Caltech, and the Department of Commerce, claiming their Constitutional rights were being violated by new, overly invasive background investigations.[34] 97% of JPL employees were classified at the low-risk level and would be subjected to the same clearance procedures as those obtaining moderate/high risk clearance. Under HSPD12 and FIPS 201, investigators have the right to obtain any information on employees, which includes questioning acquaintances on the status of the employee’s mental, emotional, and financial stability. Additionally, if employees depart JPL before the end of the two-year validity of the background check, no investigation ability gets terminated; former employees can still be legally monitored. Employees were told that if they did not sign an unlimited waiver of privacy,[35] they would be deemed to have “voluntarily resigned”.[36] The rebadging rules were designed to make JPL compliant with FIPS 201. The United States Court of Appeals for the Ninth Circuit found the process violated the employees’ privacy rights and has issued a preliminary injunction.[37] NASA appealed and the US Supreme Court granted certiorari on March 8, 2010. On January 19, 2011, the Supreme Court overturned the Ninth Circuit decision, ruling that the background checks did not violate any constitutional privacy right that the employees may have had.[38]

• Mars rovers • NASA DEVELOP at Jet Propulsion Laboratory

1.14 References [1] “Early Years”. JPL. [2] Koppes, Clayton (1982). “JPL and the American Space Program”. New Haven: Yale University Press. [3] Conway, Erik M. “From Rockets to Spacecraft: Making JPL a Place for Planetary Science”. Engineering and Science. pp. 2–10. [4] Launius, Roger (2002). To Reach High Frontier, A History of U.S. Launch Vehicles. University of Kentucky. pp. 39– 42. ISBN 0-813-12245-7. [5] Keymeulen, Didier; Myers, John; Newton, Jason; Csaszar, Ambrus; et al. (2006). Humanoids for Lunar and Planetary Surface Operations. Jet Propulsion Laboratory, National Aeronautics and Space Administration. Pasadena, CA: JPL TRS 1992+. hdl:2014/39699. [6] Bello, Francis (1959). “The Early Space Age”. Fortune. Retrieved June 5, 2012. [7] Whalen, Mark; Murrill, Mary Beth (24 July 1998). “JPL will establish Near-Earth Object Program Office for NASA”. Jet Propulsion Laboratory. NASA. Retrieved 19 February 2013. [8] “NASA scrambles for better asteroid detection”. France 24. 18 February 2013. Retrieved 19 February 2013. [9] Women Made Early Inroads at JPL - NASA Jet Propulsion Laboratory. Jpl.nasa.gov. Retrieved on 2013-07-21.


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[10] Archived November 7, 2010, at the Wayback Machine. [11] http://pub-lib.jpl.nasa.gov/docushare/dsweb/Get/ Document-697/Bibliography39-03_1961-1962.pdf [12] [13] . Local Agency Formation Commission for the County of Los Angeles [14] Jpl.Nasa.Gov. “About Us - JPL Education - NASA Jet Propulsion Laboratory”. Jpl.nasa.gov. Retrieved 201404-30. [15] Jpl.Nasa.Gov. “Student Programs, Internships & Fellowships at JPL - JPL Education - NASA Jet Propulsion Laboratory”. Jpl.nasa.gov. Retrieved 2014-04-30. [16] 0 <! (2013-08-20). “The 10 Most Awesome College Labs Of 2013 | Popular Science”. Popsci.com. Retrieved 201404-30. [17] “Planetary Science Summer School”. Retrieved May 14, 2008. [18] Jpl.Nasa.Gov (2012-05-23). “JPL Education - NASA Jet Propulsion Laboratory”. Jpl.nasa.gov. Retrieved 201404-30.

[32] “JPL Team X”. Jplteamx.jpl.nasa.gov. August 31, 2007. Retrieved August 18, 2010. [33] HSPD-12 and JPL Rebadging Overview. HSPD12 JPL. Retrieved on 2013-07-21. [34] Overview. HSPD12 JPL. Retrieved on 2013-07-21. [35] US Office of Personnel Management. “Questionnaire for Non-Sensitive Positions” (PDF). Retrieved August 26, 2010. [36] “Declaration of Cozette Hart, JPL Human Resources Director” (PDF). October 1, 2007. Retrieved August 26, 2010. [37] “Nelson v. NASA -- Preliminary Injunction issued by the United States Court of Appeals for the Ninth Circuit” (PDF). Jan 11, 2008. Retrieved August 26, 2010. [38] National Aeronautics and Space Administration et al. v. Nelson et al., No. 09-530 (U.S. January 19, 2011). [39] “Former NASA specialist claims he was fired over intelligent design”. Fox News. March 11, 2012. [40] “Judge confirms earlier ruling, sides with JPL in 'intelligent design' case”. La Canada Valley Sun. January 17, 2013.

[19] “About Us | Museum Alliance”. Informal.jpl.nasa.gov. Retrieved 2014-04-30. [20] Jpl.Nasa.Gov. “Inspire - JPL Education - NASA Jet Propulsion Laboratory”. Jpl.nasa.gov. Retrieved 201404-30. [21] Jpl.Nasa.Gov. “Educator Resource Center - JPL Education - NASA Jet Propulsion Laboratory”. Jpl.nasa.gov. Retrieved 2014-04-30. [22] “JPL Open House”. Archived from the original on January 18, 2009. Retrieved January 2, 2009. [23] “Open House At JPL Closed To Public Over Sequestration « CBS Los Angeles”. Losangeles.cbslocal.com. 2013-04-22. Retrieved 2014-04-30. [24] Ticket to Explore JPL Public Events [25] Cohen, Bryan. “DHS staff members attend annual Day on the Hill”. BioPrepWatch. February 10, 2014 (Retrieved 02-10-2014). [26] http://www.jpl.nasa.gov/annualreport/2012-report.pdf [27] “NPR All Things Considered interview referring to peanuts tradition”. Retrieved January 3, 2009. [28] “Planetary Society chat log for Phoenix referring to peanuts tradition”. Archived from the original on November 21, 2008. Retrieved January 3, 2009. [29] JPL. “NASA Jet Propulsion Laboratory: Jpl.nasa.gov. Retrieved August 26, 2010.

Missions”.

[30] “JPL Directors”. JPL. Retrieved August 26, 2010. [31] “News | Michael Watkins Named Next JPL Director”. May 2, 2016. Retrieved August 24, 2016.

1.15 External links • Official website


Chapter 2

Voyager program This article is about the space probes launched in 1977. stellar space, traveling “further than anyone, or anything, For other uses, see Voyager. in history”.[1] As of 2013, Voyager 1 was moving with The Voyager program is a continuing American scien- a velocity of 17 kilometers per second (11 mi/s) relative to the Sun.[2] Voyager 2 is expected to enter interstellar space by 2016, and its plasma spectrometer should provide the first direct measurements of the density and temperature of the interstellar plasma.[3] Data and photographs collected by the Voyagers’ cameras, magnetometers, and other instruments revealed previously unknown details about each of the giant planets and their moons. Close-up images from the spacecraft charted Jupiter’s complex cloud forms, winds, and storm systems and discovered volcanic activity on its moon Io. Saturn’s rings were found to have enigmatic braids, kinks, and spokes and to be accompanied by a myriad of “ringlets.” At Uranus Voyager 2 discovered a substantial magnetic field around the planet and 10 additional moons. Its flyby of Neptune uncovered three complete rings and six hitherto unknown moons as well as a planetary magnetic field and complex, widely distributed auroras. Voyager 2 is still the only spacecraft to have visited the ice giants. The Voyager spacecraft were built at the Jet Propulsion Laboratory in Southern California, and they were paid for by the National Aeronautics and Space Administration (NASA), which also paid for their launchings from Cape Canaveral, Florida, their tracking, and everything else concerning the space probes.

Montage of planets and some moons the two Voyager spacecraft have visited and studied

tific program that employs two robotic probes, Voyager 1 and Voyager 2, to study the outer Solar System. They were launched in 1977 to take advantage of a favorable alignment of Jupiter, Saturn, Uranus, and Neptune, and are now exploring the outer boundary of the heliosphere in interstellar space. Although their original mission was to study only the planetary systems of Jupiter and Saturn, Voyager 2 continued on to Uranus and Neptune, and both Voyagers are now tasked with exploring interstellar space. Their mission has been extended three times, and both probes continue to collect and relay useful scientific data. Neither Uranus nor Neptune has been visited by any probe other than Voyager 2.

2.1 History

Neptune

Pioneer-10

Voyager II

Uranus

Saturn

Pioneer-11

Pluto

Outer Solar System Probes Pioneer-10: 3 March 1972 Pioneer 11: 6 April, 1973 Voyager 2: 20 August 1977 Voyager I: 5 September 1977

Voyager I

Trajectories and expected location of Pioneer and Voyager

On August 25, 2012, data from Voyager 1 indicated that spacecraft in April 2007 it had become the first human-made object to enter inter7


8

CHAPTER 2. VOYAGER PROGRAM Titan.[9] During the 1990s, Voyager 1 overtook the slower deepspace probes Pioneer 10 and Pioneer 11 to become the most distant human made object from Earth, a record that it will keep for the foreseeable future. The New Horizons probe, which had a higher launch velocity than Voyager 1, is traveling more slowly due to the extra speed Voyager 1 gained from its flybys of Jupiter and Saturn. Voyager 1 and Pioneer 10 are the most widely separated human made objects anywhere, since they are traveling in roughly opposite directions from the Solar System.

The trajectories that enabled Voyager spacecraft to visit the outer planets and achieve velocity to escape the Solar System

The two Voyager space probes were originally conceived as part of the Mariner program, and they were thus initially named Mariner 11 and Mariner 12. They were then moved into a separate program named Mariner JupiterSaturn, later renamed the Voyager Program because it was thought that the design of the two space probes had progressed sufficiently beyond that of the Mariner family to merit a separate name.[4] The Voyager Program was similar to the Planetary Grand Tour planned during the late 1960s and early 70s. The Grand Tour would take advantage of an alignment of the outer planets discovered by Gary Flandro, an aerospace engineer at the Jet Propulsion Laboratory. This alignment, which occurs once every 175 years,[5] would occur in the late 1970s and make it possible to use gravitational assists to explore Jupiter, Saturn, Uranus, Neptune, and Pluto. The Planetary Grand Tour was to send several pairs of probes to fly by all the outer planets (including Pluto, then still considered a planet) along various trajectories, including Jupiter-Saturn-Pluto and JupiterUranus-Neptune. Limited funding ended the Grand Tour program, but elements were incorporated into the Voyager Program, which fulfilled many of the flyby objectives of the Grand Tour except a visit to Pluto. Voyager 2 was the first to launch. Its trajectory was designed to allow flybys of Jupiter, Saturn, Uranus, and Neptune. Voyager 1 was launched after Voyager 2, but along a shorter and faster trajectory that was designed to provide an optimal flyby of Saturn’s moon Titan,[6] which was known to be quite large and to possess a dense atmosphere. This encounter sent Voyager 1 out of the plane of the ecliptic, ending its planetary science mission.[7] Had Voyager 1 been unable to perform the Titan flyby, the trajectory of Voyager 2 could have been altered to explore Titan, forgoing any visit to Uranus and Neptune.[8] Voyager 1 was not launched on a trajectory that would have allowed it to continue to Uranus and Neptune, but could have continued from Saturn to Pluto without exploring

In December 2004, Voyager 1 crossed the termination shock, where the solar wind is slowed to subsonic speed, and entered the heliosheath, where the solar wind is compressed and made turbulent due to interactions with the interstellar medium. On December 10, 2007, Voyager 2 also reached the termination shock, about 1 billion miles closer to the sun than from where Voyager 1 first crossed it, indicating that the Solar System is asymmetrical.[10] In 2010 Voyager 1 reported that the outward velocity of the solar wind had dropped to zero, and scientists predicted it was nearing interstellar space.[11] In 2011, data from the Voyagers determined that the heliosheath is not smooth, but filled with giant magnetic bubbles, theorized to form when the magnetic field of the Sun becomes warped at the edge of the Solar System.[12] On 15 June 2012, scientists at NASA reported that Voyager 1 was very close to entering interstellar space, indicated by a sharp rise in high-energy particles from outside the Solar System.[13][14] In September 2013, NASA announced that Voyager 1 had crossed the heliopause on August 25, 2012, making it the first spacecraft to enter interstellar space.[15][16][17] As of 2015 Voyager 1 and Voyager 2 continue to monitor conditions in the outer expanses of the Solar System. The Voyager spacecraft are expected to be able to operate science instruments through 2020, when limited power will require instruments to be deactivated one by one. Sometime around 2025, there will no longer be sufficient power to operate any science instruments.

2.2 Spacecraft design The Voyager spacecraft weigh 773 kilograms. Of this, 105 kilograms are scientific instruments.[18] The identical Voyager spacecraft use three-axis-stabilized guidance systems that use gyroscopic and accelerometer inputs to their attitude control computers to point their high-gain antennas towards the Earth and their scientific instruments towards their targets, sometimes with the help of a movable instrument platform for the smaller instruments and the electronic photography system. The diagram at the right shows the high-gain antenna (HGA) with a 3.7 m diameter dish attached to the hollow


2.2. SPACECRAFT DESIGN

9 eight filters in a commandable Filter Wheel mounted in front of the vidicons. One has a low resolution 200 mm focal length wide-angle lens with an aperture of f/3 (the wide angle camera), while the other uses a higher resolution 1500 mm narrow-angle f/8.5 lens (the narrow angle camera).

2.2.1 Scientific instruments 2.2.2 Computers and data processing There are three different computer types on the Voyager spacecraft, two of each kind, sometimes used for redundancy. They are proprietary, custom-built computers built from CMOS and TTL medium scale integrated circuits and discrete components. Total number of words among the six computers is about 32K. Voyager 1 and Voyager 2 have identical computer systems.[22][23]

Voyager spacecraft structure

The Computer Command System (CCS), the central controller of the spacecraft, is two 18-bit word, interrupt type processors with 4096 words each of plated wire, nonvolatile memory. During most of the Voyager mission the two CCS computers on each spacecraft were used non-redundantly to increase the command and processing capability of the spacecraft. The CCS is nearly identical to the system flown on the Viking spacecraft.[24]

decagonal electronics container. There is also a spherical The Flight Data System (FDS) is two 16-bit word matank that contains the hydrazine monopropellant fuel. chines with modular memories and 8198 words each. The Voyager Golden Record is attached to one of the bus sides. The angled square panel to the right is the optical calibration target and excess heat radiator. The three radioisotope thermoelectric generators (RTGs) are mounted end-to-end on the lower boom.

The Attitude and Articulation Control System (AACS) is two 18-bit word machines with 4096 words each.

Unlike the other on-board instruments, the operation of the cameras for visible light is not autonomous, but rather it is controlled by an imaging parameter table contained The scan platform comprises: the Infrared Interferome- in one of the on-board digital computers, the Flight Data ter Spectrometer (IRIS) (largest camera at top right); the Subsystem (FDS). More recent space probes, since about Ultraviolet Spectrometer (UVS) just above the UVS; the 1990, usually have completely autonomous cameras. two Imaging Science Subsystem (ISS) vidicon cameras The computer command subsystem (CCS) controls the to the left of the UVS; and the Photopolarimeter System cameras. The CCS contains fixed computer programs (PPS) under the ISS. such as command decoding, fault detection, and correcOnly five investigation teams are still supported, though data is collected for two additional instruments.[19] The Flight Data Subsystem (FDS) and a single eight-track digital tape recorder (DTR) provide the data handling functions.

tion routines, antenna pointing routines, and spacecraft sequencing routines. This computer is an improved version of the one that was used in the Viking orbiter.[25] The hardware in both custom-built CCS subsystems in the Voyagers is identical. There is only a minor software The FDS configures each instrument and controls instru- modification for one of them that has a scientific subsysment operations. It also collects engineering and science tem that the other lacks. data and formats the data for transmission. The DTR is The Attitude and Articulation Control Subsystem used to record high-rate Plasma Wave Subsystem (PWS) (AACS) controls the spacecraft orientation (its attitude). data. The data is played back every six months. It keeps the high-gain antenna pointing towards the The Imaging Science Subsystem, made up of a wide an- Earth, controls attitude changes, and points the scan gle and a narrow angle camera, is a modified version of platform. The custom-built AACS systems on both craft the slow scan vidicon camera designs that were used in are identical. the earlier Mariner flights. The Imaging Science Subsys- It has been erroneously reported [26] on the Internet tem consists of two television-type cameras, each with that the Voyager space probes were controlled by a ver-


10

CHAPTER 2. VOYAGER PROGRAM

sion of the RCA 1802 (RCA CDP1802 “COSMAC” microprocessor), but such claims are not supported by the primary design documents. The CDP1802 microprocessor was used later in the Galileo space probe, which was designed and built years later. The digital control electronics of the Voyagers were not based on a microprocessor integrated circuit chip.

2.2.3

Communications

The uplink communications are executed via S-band microwave communications. The downlink communications are carried out by an X-band microwave transmitter on board the spacecraft, with an S-band transmitter as a back-up. All long-range communications to and from the two Voyagers have been carried out using their 3.7-meter high-gain antennas. Because of the inverse-square law in radio communications, the digital data rates used in the downlinks from the Voyagers have been continually decreasing the farther that they get from the Earth. For example, the data rate used from Jupiter was about 115,000 bits per second. That was halved at the distance of Saturn, and it has gone down continually since then.[27] Some measures were taken on the ground along the way to reduce the effects of the inverse-square law. In between 1982 and 1985, the diameters of the three main parabolic dish antennas of the Deep Space Network was increased from 64 m to 70 m, dramatically increasing their areas for gathering weak microwave signals.

Radioisotope thermoelectric generators for the Voyager program

ently produce 470 W × 2−(34/87.74) ≈ 359 W, about 76% of its initial power. Additionally, the thermocouples that convert heat into electricity also degrade, reducing available power below this calculated level. By 7 October 2011 the power generated by Voyager 1 and Voyager 2 had dropped to 267.9 W and 269.2 W respectively, about 57% of the power at launch. The level of power output was better than pre-launch predictions based on a conservative thermocouple degradation model. As the electrical power decreases, spacecraft loads must be turned off, eliminating some capabilities.

Then between 1986 and 1989, new techniques were brought into play to combine the signals from multiple antennas on the ground into one, more powerful signal, in a kind of an antenna array. This was done at Goldstone, California, Canberra, and Madrid using the additional dish antennas available there. Also, in Australia, the Parkes Radio Telescope was brought into the array in time for the fly-by of Neptune in 1989. In the United States, the Very Large Array in New Mexico was brought into 2.3 Voyager Interstellar Mission temporary use along with the antennas of the Deep Space Network at Goldstone. Using this new technology of an- The Voyager primary mission was completed in 1989, tenna arrays helped to compensate for the immense radio with the close flyby of Neptune by Voyager 2. The Voydistance from Neptune to the Earth. ager Interstellar Mission (VIM) is a mission extension, which began when the two spacecraft had already been in flight for over 12 years.[29] The Heliophysics Division 2.2.4 Power of the NASA Science Mission Directorate conducted a Heliophysics Senior Review in 2008. The panel found Electrical power is supplied by three MHW-RTG that the VIM “is a mission that is absolutely imperative to radioisotope thermoelectric generators (RTGs). They continue” and that VIM “funding near the optimal level are powered by plutonium-238 (distinct from the Pu- and increased DSN (Deep Space Network) support is 239 isotope used in nuclear weapons) and provided ap- warranted.”[30] proximately 470 W at 30 volts DC when the spacecraft The main objective of the VIM is to extend the explowas launched. Plutonium-238 decays with a half-life of ration of the Solar System beyond the outer planets to the 87.74 years,[28] so RTGs using Pu-238 will lose a factor outer limit and if possible even beyond. The Voyagers of 1−0.5(1/87.74) = 0.79% of their power output per year. continue to search for the heliopause boundary which In 2011, 34 years after launch, such an RTG would inher- is the outer limit of the Sun’s magnetic field. Passing


2.3. VOYAGER INTERSTELLAR MISSION

11

through the heliopause boundary will allow the spacecraft turning scientific data from a full complement of Voyager to make measurements of the interstellar fields, particles Interstellar Mission (VIM) science instruments. and waves unaffected by the solar wind. Both spacecraft also have adequate electrical power and As of the present date, the Voyager 2 and Voyager 1 attitude control propellant to continue operating until scan platforms, including all of the platform instruments, around 2025, after which there may not be available elechave been powered down. The ultraviolet spectrometer trical power to support science instrument operation. At (UVS)[31] on Voyager 1 was active until 2003, when it that time, science data return and spacecraft operations too was deactivated. Gyro operations will end in 2016 will cease.[33] for Voyager 2 and 2017 for Voyager 1. Gyro operations are used to rotate the probe 360 degrees six times per year to measure the magnetic field of the spacecraft, which is then subtracted from the magnetometer science data. 2.3.1 Mission details

This diagram about the heliosphere was released on June 28, 2013 and incorporates results from the Voyager spacecraft.[32]

By the start of VIM, Voyager 1 was at a distance of 40 AU from the Earth while Voyager 2 was at 31 AU.[34] VIM is broken down into 3 distinct phases: termination shock, heliosheath exploration, interstellar exploration phase. The spacecraft began VIM in an environment controlled by the Sun’s magnetic field with the plasma particles being dominated by those contained in the expanding supersonic solar wind. This is the characteristic environment of the termination shock phase. At some distance from the Sun, the supersonic solar wind will be held back from further expansion by the interstellar wind. The first feature encountered by a spacecraft as a result of this interstellar wind/solar wind interaction was the termination shock where the solar wind slows from supersonic to subsonic speed and large changes in plasma flow direction and magnetic field orientation occur.

Voyager 1 completed the phase of termination shock in December 2004 at a distance of 94 AU while Voyager 2 completed it in August 2007 at a distance of 84 AU. After entering into the heliosheath the spacecraft are in an area that is dominated by the Sun’s magnetic field and solar wind particles. The thickness of the heliosheath is not known clearly so the time required to transverse this space is not quite clear. Scientists estimate this space to be tens of AU thick and that it could take several years to cross. After passing through the heliosheath the 2 Voyagers will begin the phase of interstellar exploration. The outer boundary of the heliosheath is called the heliopause which is where the spacecraft are headed now. This is the region where the Sun’s influence begins to decrease and the interstellar space can be detected. The heliopause has never been reached by any spacecraft so far and the Voyagers may be the first spacecraft to reach it. Currently, Voyager 1 is escaping the solar system at the speed of 3.6 AU per year, while Voyager 2’s speed is about 3.3 AU per year. The Voyager spacecraft will eventually go on to the stars. In about 40,000 years, Voyager 1 will be within 1.6 light years of AC+79 3888, which is a star in the constellation of Camelopardalis. In 40,000 years Voyager 2 will be within 1.7 light years from star Ross 248 and in 296,000 years will pass within 4.6 light years Humanity’s Farthest Journey of Sirius which is the brightest star in the sky.[1] The main The two spacecraft continue to operate, with some loss objective of the Voyager Interstellar Mission is interstelin subsystem redundancy, but retain the capability of re- lar exploration.


12

CHAPTER 2. VOYAGER PROGRAM

2.4 Telemetry The telemetry comes to the telemetry modulation unit (TMU) separately as a “low-rate” 40-bit-per-second (bit/s) channel and a “high-rate” channel. Low rate telemetry is routed through the TMU such that it can only be downlinked as uncoded bits (in other words there is no error correction). At high rate, one of a set of rates between 10 bit/s and 115.2 kbit/s is downlinked as coded symbols. The TMU encodes the high rate data stream with a convolutional code having constraint length of 7 with a symbol rate equal to twice the bit rate (k=7, r=1/2) Voyager telemetry operates at these transmission rates: • 7200, 1400 bit/s tape recorder playbacks • 600 bit/s real-time fields, particles, and waves; full The cover of the golden record UVS; engineering • 160 bit/s real-time fields, particles, and waves; UVS subset; engineering

2.5 Voyager Golden Record

• 40 bit/s real-time engineering data, no science data. Main article: Voyager Golden Record Note: At 160 and 600 bit/s different data types are interBoth craft carry with them a 12-inch golden phonograph leaved. record that contains pictures and sounds of Earth along The Voyager craft have three different telemetry formats: with symbolic directions on the cover for playing the record and data detailing the location of our planet.[14] High rate The record is intended as a combination of a time cap• CR-5T (ISA 35395) Science , note that this can con- sule and an interstellar message to any civilization, alien or far-future human, that may recover either of the Voytain some engineering data. agers. The contents of this record were selected by a com• FD-12 higher accuracy (and time resolution) Engi- mittee that included Timothy Ferris[14] and was chaired neering data, note that some science data may also by Carl Sagan. be encoded. Low rate

2.6 Pale blue dot

• EL-40 Engineering , note that this format can conMain article: Pale Blue Dot tain some science data, but not all systems represented. The Voyager program’s discoveries during the primary • This is an abbreviated format, with data truncation phase of its mission, including never-before-seen closefor some subsystems. up color photos of the major planets, were regularly documented by both print and electronic media outlets. It is understood that there is substantial overlap of EL- Among the best-known of these is an image of the Earth 40 and CR-5T (ISA 35395) telemetry, but the simpler as a pale blue dot, taken in 1990 by Voyager 1, and popEL-40 data does not have the resolution of the CR-5T ularized by Carl Sagan with the quote: telemetry. At least when it comes to representing available electricity to subsystems, EL-40 only transmits in in“Consider again that dot. That’s here. teger increments—so similar behaviors are expected elseThat’s home. That’s us. On it everyone you where. love, everyone you know, everyone you ever Memory dumps are available in both engineering formats. These routine diagnostic procedures have detected and corrected intermittent memory bit flip problems, as well as detecting the permanent bit flip problem that caused a two-week data loss event mid-2010.

heard of, every human being who ever was, lived out their lives. The aggregate of our joy and suffering, thousands of confident religions, ideologies, and economic doctrines, every hunter and forager, every hero and coward,


2.8. SEE ALSO

13 • The Space: 1999 episode Voyager’s Return featured two fictional 1985 space probes, called Voyager One and Voyager Two (not “1” and “2”). This episode was aired two years prior to the launch of the real Voyager craft. The plot hinges upon the dangerous radioactive engines of the probes, which bears a passing similarity to the radioisotope decay engines on the real Voyager vessels. • Star Trek: The Motion Picture featured a fictional Voyager probe, Voyager 6, making contact with a planet of living machines and returning to earth to fulfill the machine entity’s interpretation of its mission. In the film, the probe is referred to as V'Ger, due to the letters “O-Y-A” and the number 6 being obscured on its nameplate. • Starman features a scout from an alien race who comes to visit Earth after their race encounters Voyager 2 and listens to the golden record.

2.8 See also Seen from 6 billion kilometers (3.7 billion miles), Earth appears as a "pale blue dot" (the blueish-white speck approximately halfway down the brown band to the right).

• Interstellar probe • Timeline of Solar System exploration • Pioneer program

every creator and destroyer of civilization, every king and peasant, every young couple in love, every mother and father, hopeful child, inventor and explorer, every teacher of morals, every corrupt politician, every “superstar,” every “supreme leader,” every saint and sinner in the history of our species lived there – on a mote of dust suspended in a sunbeam”.

2.7 In popular culture

• Planetary Grand Tour • Family Portrait • Tom Krimigis, PI for the LECP

2.9 References [1] Jpl.Nasa.Gov. “Voyager Enters Interstellar Space - NASA Jet Propulsion Laboratory”. Jpl.nasa.gov. Retrieved 2013-09-14. [2] “Voyager Mission Operations Status Report # 2013-0531, Week Ending May 31, 2013”. JPL. Retrieved 19 August 2013. [3] “At last, Voyager 1 slips into interstellar space – Atom & Cosmos”. Science News. 2013-09-12. Retrieved 201309-17. [4] Chapter 11 “Voyager: The Grand Tour of Big Science” (sec. 268.), by Andrew,J. Butrica, found in From Engineering Science To Big Science ISBN 978-0-16-049640-0 edited by Pamela E. Mack, NASA, 1998 [5] “Planetary Voyage”. USA.gov. 2013-10-30. Archived from the original on 2013-12-09. Retrieved 2014-02-04.

Voyager One, from Space: 1999.

[6] David W. Swift (1 January 1997). Voyager Tales: Personal Views of the Grand Tour. AIAA. p. 69. ISBN 9781-56347-252-7.


14

[7] “Voyager FAQ”. Jet Propulsion Laboratory. Retrieved January 2015. Check date values in: |access-date= (help) [8] Jim Bell (24 February 2015). The Interstellar Age: Inside the Forty-Year Voyager Mission. Penguin Publishing Group. p. 94. ISBN 978-0-698-18615-6. [9] “What If Voyager Had Explored Pluto?". Retrieved 4 September 2015. [10] Voyager 2 Proves Solar System Is Squashed NASA.gov #2007-12-10 [11] Brown, Dwayne; Cook, Jia-Rui; Buckley, M. (December 14, 2010). “Nearing Interstellar Space, NASA Probe Sees Solar Wind Decline”. Applied Physics Lab, Johns Hopkins University. Retrieved 2011-01-28. [12] Smith, Catharine (2011-06-10). “WATCH: NASA Discovers 'Bubbles’ At Solar System’s Edge”. Huffington Post. [13] Amos, Jonathan (15 June 2012). “Particles point way for Nasa’s Voyager”. BBC News. Retrieved 15 June 2012. [14] Ferris, Timothy (May 2012). “Timothy Ferris on Voyagers’ Never-Ending Journey”. Smithsonian Magazine. Retrieved 15 June 2012. [15] Cook, Jia-Rui C.; Agle, D. C.; Brown, Dwayne (12 September 2013). “NASA Spacecraft Embarks on Historic Journey Into Interstellar Space”. NASA. Retrieved 12 September 2013. [16] “Voyager 1 has entered a new region of space, sudden changes in cosmic rays indicate”. Retrieved 20 March 2013. [17] “Report: NASA Voyager Status Update on Voyager 1 Location”. NASA. Retrieved 20 March 2013. [18] Haynes, Robert. “How We Get Pictures from Space, Revised Edition”. NASA facts. NTRS. [19] Voyager - Spacecraft Nasa website [20] NASA/JPL (2003-08-26). “Voyager 1 Narrow Angle Camera Description”. NASA / PDS. Retrieved 2011-0117.

CHAPTER 2. VOYAGER PROGRAM

[27] Ludwig, Roger; Taylor, Jim (March 2002). “Voyager Telecommunications” (PDF). NASA. Retrieved March 26, 2016. [28] The Actinide Research Quarterly: Summer 1997 [29] “Interstellar Mission”. NASA. [30] “Senior Review 2008 of the Mission Operations and Data Analysis Program for the Heliophysics Operating Missions” (PDF). NASA. p. 7. [31] “Ultraviolet Spectrometer”. Voyager: The Interstellar Mission. NASA JPL. Retrieved 2006-06-11. [32] NASA - Transitional Regions at the Heliosphere’s Outer Limits [33] “Voyager – Spacecraft Lifetime NASA website”. Retrieved 2011-09-13. [34] JPL.NASA.GOV. “Voyager - The Interstellar Mission”. voyager.jpl.nasa.gov. Retrieved 2016-05-27.

2.10 External links NASA sites • NASA Voyager website – Main source of information. • Voyager Mission state (more often than not at least 3 months out of date) • Voyager Spacecraft Lifetime • Space Exploration – Robotic Missions • NASA Facts – Voyager Mission to the Outer Planets (PDF format) • Voyager 1 and 2 atlas of six Saturnian satellites (PDF format) 1984 • JPL Voyager Telecom Manual NASA instrument information pages:

[21] NASA/JPL (2003-08-26). “Voyager 1 Wide Angle Camera Description”. NASA / PDS. Retrieved 2011-01-17.

• “Voyager instrument overview:".

[22] “Voyager Frequently Asked Questions”.

• “CRS – COSMIC RAY SUBSYSTEM”.

[23] “Voyager 1 Instrument Host Information”.

• “ISS NA – IMAGING SCIENCE SUBSYSTEM – NARROW ANGLE”.

[24] “Computers in Spaceflight: The NASA Experience - Ch 6 - Distributed Computing On Board Voyager and Galileo Voyager - The flying computer center”.

• “ISS WA – IMAGING SCIENCE SUBSYSTEM – WIDE ANGLE”.

[25] Tomayko, James (April 1987). “Computers in Spaceflight: The NASA Experience”. NASA. Retrieved February 6, 2010.

• “IRIS – INFRARED INTERFEROMETER SPECTROMETER AND RADIOMETER”.

[26] Johnson, Herb (November 2014). “COSMAC 1802 History in Space”. author. Retrieved July 27, 2015.

• “LECP – LOW ENERGY CHARGED PARTICLE”.


2.10. EXTERNAL LINKS • “MAG – TRIAXIAL FLUXGATE MAGNETOMETER”. • “PLS – PLASMA SCIENCE EXPERIMENT”. • “PPS – PHOTOPOLARIMETER SUBSYSTEM”. • “PRA – PLANETARY RADIO ASTRONOMY RECEIVER”. • “PWS – PLASMA WAVE RECEIVER”. • “RSS – RADIO SCIENCE SUBSYSTEM”. • “UVS – ULTRAVIOLET SPECTROMETER”. Non-NASA sites • Spacecraft Escaping the Solar System – current positions and diagrams • NPR: Science Friday 8/24/07 Interviews for 30th anniversary of Voyager spacecraft • Illustrated technical paper by RL Heacock, the project engineer • Gray, Meghan. “Voyager and Interstellar Space”. Deep Space Videos. Brady Haran.

15


Chapter 3

Pioneer program This article is about the U.S. space program. For the communist version of Scouting, see Pioneer movement. The Pioneer program is a series of United States

The Pioneer plaque attached to Pioneers 10 and 11

3.1 Naming Credit for naming the first probe has been attributed to Stephen A. Saliga, who had been assigned to the Air Force Orientation Group, Wright-Patterson AFB, as chief designer of Air Force exhibits. While he was at a briefing, the spacecraft was described to him as a “lunarorbiting vehicle with an infrared scanning device.” Saliga thought the title too long and lacked theme for an exhibit design. He suggested “Pioneer” as the name of the probe since “the Army had already launched and orbited the Explorer satellite and their Public Information Office was identifying the Army as 'Pioneers in Space,'" and by adopting the name the Air Force would “make a 'quantum jump' as to who really [were] the 'Pioneers in space.'"[1]

Pioneer 10, undergoing construction in 1971. Pioneer 10 and 11 are the most famous probes in the Pioneer program, the first probes to visit the outer planets, and the first to go beyond the orbit of Pluto.

unmanned space missions that were designed for planetary exploration. There were a number of such missions in the program, but the most notable were Pioneer 10 and Pioneer 11, which explored the outer planets and left the solar system. Pioneer 10 and Pioneer 11 carry a golden plaque, depicting a man and a woman and information about the origin and the creators of the probes, should any extraterrestrials find them someday.

3.2 Early Pioneer missions The earliest missions were attempts to achieve Earth’s escape velocity, simply to show it was feasible and study the Moon. This included the first launch by NASA which was formed from the old NACA. These missions were carried out by the US Air Force and Army.

16


3.2. EARLY PIONEER MISSIONS

3.2.1

17

Able space probes (1958–1960)

Pioneer 2

Artist’s conception of the Pioneer 6–9 spacecraft

Artist’s conception of the Pioneer 10–11 spacecraft

• Pioneer 1 (Thor-Able 2, Pioneer I) – Lunar orbiter, missed Moon (third stage partial failure) October 11, 1958 Pioneer 3

Most missions here are listed with their most recognised name, and alternate names after in parenthesis. • Pioneer 0 (Thor-Able 1, Pioneer) – Lunar orbiter, destroyed (Thor failure 77 seconds after launch) August 17, 1958

• Pioneer 2 (Thor-Able 3, Pioneer II) – Lunar orbiter, reentry (third stage failure) November 8, 1958 • Pioneer P-1 (Atlas-Able 4A, Pioneer W), probe lost September 24, 1959 • Pioneer P-3 (Atlas-Able 4, Atlas-Able 4B, Pioneer X) – Lunar probe, lost in launcher failure November 26, 1959


18

CHAPTER 3. PIONEER PROGRAM

• Pioneer 5 (Pioneer P-2, Thor-Able 4, Pioneer V) Since the probes’ orbital periods differ from that of the – interplanetary space between Earth and Venus, Earth, from time to time, they face a side of the Sun that launched March 11, 1960[2] cannot be seen from Earth. The probes can sense parts of the Sun several days before the Sun’s rotation reveals it to • Pioneer P-30 (Atlas-Able 5A, Pioneer Y) – Lunar ground-based Earth orbiting observatories. If a powerful probe, failed to achieve lunar orbit September 25, solar magnetic storm is formed, they can warn Earth in 1960 advance. • Pioneer P-31 (Atlas-Able 5B, Pioneer Z) – Lunar probe, lost in upper stage failure December 15, 1960

3.2.2

3.3.2 Outer Solar System missions

Juno II lunar probes (1958–1959)

• Pioneer 3 – Lunar flyby, missed Moon due to launcher failure December 6, 1958 • Pioneer 4 – Lunar flyby, achieved Earth escape velocity, launched March 3, 1959

3.3 Later Pioneer missions (1965– 1978)

Neptune

Pioneer-10

Voyager II

Uranus

Saturn

Pioneer-11

Pluto

Outer Solar System Probes Pioneer-10: 3 March 1972 Pioneer 11: 6 April, 1973 Voyager 2: 20 August 1977 Voyager I: 5 September 1977

Voyager I

Map showing location and trajectories of the Pioneer 10 (blue), Pioneer 11 (green), Voyager 1 (red) and Voyager 2 (purple) spacecraft, as of April 4, 2007

Five years after the early Able space probe missions ended, NASA Ames Research Center used the Pioneer name for a new series of missions, initially aimed at the inner Solar System, before the bold flyby missions to Jupiter and Saturn. While successful, the missions returned much poorer images than the Voyager program probes would five years later. In 1978, the end of the program saw a return to the inner Solar System, with the Pioneer Venus Orbiter and Multiprobe, this time using orbital insertion rather than flyby missions. The new missions were numbered from Pioneer 6 (alternate names in parentheses).

3.3.1

Pioneer 6, 7, 8, and 9

The spacecraft in Pioneer missions 6, 7, 8, and 9 comprised a new interplanetary space weather network: • Pioneer 6 (Pioneer A) – launched December 1965 • Pioneer 7 (Pioneer B) – launched August 1966 • Pioneer 8 (Pioneer C) – launched December 1967 • Pioneer 9 (Pioneer D) – launched November 1968 (inactive since 1983) • Pioneer E – lost in launcher failure August 1969 Pioneer 6 and Pioneer 9 are in solar orbits with 0.8 AU distance to the Sun. Their orbital periods are therefore slightly shorter than Earth’s. Pioneer 7 and Pioneer 8 are in solar orbits with 1.1 AU distance to the Sun. Their orbital periods are therefore slightly longer than Earth’s.

Artist’s conception of the Pioneer Venus spacecraft

• Pioneer 10 (Pioneer F) – Jupiter, interstellar medium, launched March 1972 • Pioneer 11 (Pioneer G) – Jupiter, Saturn, interstellar medium, launched April 1973 • Pioneer H – identical to Pioneers 10 and 11. Proposed out-of-the-ecliptic mission for 1974, but were not built.[3]

3.3.3 Pioneer Venus project • Pioneer Venus Orbiter (Pioneer Venus 1, Pioneer 12) – launched May 1978 • Pioneer Venus Multiprobe (Pioneer Venus 2, Pioneer 13) – launched August 1978


3.6. EXTERNAL LINKS • Pioneer Venus Probe Bus – transport vehicle and upper atmosphere probe • Pioneer Venus Large Probe – 300 kg parachuted probe • Pioneer Venus North Probe – 75 kg impactor probe • Pioneer Venus Night Probe – 75 kg impactor probe • Pioneer Venus Day Probe – 75 kg impactor probe

3.4 See also • Mariner program • Pioneer anomaly • Ranger program • Surveyor program • Timeline of Solar System exploration • Voyager program

3.5 References [1] “Origins of NASA Names”. NASA History. www.history. nasa.gov. Retrieved 2006-10-16. [2] “Aeronautics and Astronautics Chronology, 1960”. NASA. [3] “Pioneer H, Jupiter Swingby Out-of-the-Ecliptic Mission Study” (PDF). 20 August 1971. Retrieved 2 May 2012.

3.6 External links • Pioneer (Moon) Program Page by NASA’s Solar System Exploration • Mark Wolverton’s The Depths of Space online • Thor Able – Encyclopedia Astronautica • Space Technology Laboratories Documents Archive

19


Chapter 4

Copernican Revolution For the 1957 book by Thomas Kuhn, see The Copernican Revolution (book). For metaphorical uses of the term, see Copernican Revolution (metaphor). The Copernican Revolution was the paradigm shift

to only have uniform circular motion on solid spheres, which meant that it would be impossible for a comet to enter into the area.[1] Johannes Kepler followed Tycho and developed the three laws of planetary motion. Kepler would not have been able to produce his laws without the observations of Tycho, because they allowed Kepler to prove that planets traveled in ellipses, and that the Sun does not sit directly in the center of an orbit but at a focus. Galileo Galilei came after Kepler and developed his own telescope with enough magnification to allow him to study Venus and discover that it has phases like a moon. The discovery of the phases of Venus was one of the more influential reasons for the transition from geocentrism to heliocentrism.[2] Sir Isaac Newton’s Philosophiæ Naturalis Principia Mathematica concluded the Copernican Motion of Sun, Earth, and Mars according to heliocentrism Revolution. The development of his laws of planetary (left) and to geocentrism (right), before the Copernican-Galileanmotion and universal gravitation explained the presumed Newtonian revolution. Note the retrograde motion of Mars on the motion related to the heavens by asserting a gravitational right. Yellow dot, Sun; blue, Earth; red, Mars. [3] (In order to get a smooth animation, it is assumed that the period force of attraction between two objects. of revolution of Mars is exactly 2 years, instead of the actual value, 1.88 years). The orbits are assumed to be circular, in the heliocentric case.

from the Ptolemaic model of the heavens, which described the cosmos as having Earth stationary at the center of the universe, to the heliocentric model with the 4.1.1 Nicolaus Copernicus Sun at the center of the Solar System. Beginning with the publication of Nicolaus Copernicus’s De revolutionibus orbium coelestium, contributions to the “revolution” Main article: Nicolaus Copernicus continued until finally ending with Isaac Newton’s work Aware of the recent criticism of the Ptolemaic model, led by the arguments made by Arabic astronomer Averoes,[4] over a century later. Nicolaus Copernicus developed a detailed heliocentric model, which he summarized in his short work Commentariolus. He claimed it described the physical re4.1 Historical overview ality of the cosmos, something the Ptolemaic model was believed to lack. He removed Earth from the center of the The Copernican Revolution started with the publishing of universe, set the heavenly bodies in rotation around the the book De revolutionibus orbium coelestium by Nico- Sun, and introduced Earth’s daily rotation on its axis.[5] laus Copernicus, which was influenced by earlier theories of Aristarchus and of Mu’ayyad al-Din al-’Urdi and He continued to refine his system until publishing his (1543), Ibn al-Shatir. His book proposed a heliocentric system larger work, De revolutionibus orbium coelestium [5] which contained detailed diagrams and tables. contrary to the widely accepted geocentric system of that time. Tycho Brahe accepted Copernicus’s model but re- While Copernicus’s work sparked the Copernican revoasserted geocentricity. However, Tycho challenged the lution, it did not mark its end. In fact, Copernicus’s own Aristotelian model when he observed a comet that went system had multiple shortcomings that would have to be through the region of the planets. This region was said amended by later astronomers. 20


4.1. HISTORICAL OVERVIEW

21 was well known as an astronomer in his time. Further advancement in the understanding of the cosmos would require new, more accurate observations than those that Nicolaus Copernicus relied on and Tycho made great strides in this area. In 1572, Tycho Brahe observed a new star in the constellation Cassiopeia. For eighteen months, it shone brightly in the sky with no visible parallax, indicating it was part of the heavenly region of stars according to Aristotle’s model. However, according to that model, no change could take place in the heavens so Tycho’s observation was a major discredit to Aristotle’s theories. In 1577, Tycho observed a great comet in the sky. Based on his parallax observations, the comet passed through the region of the planets. According to Aristotelian theory, only uniform circular motion on solid spheres existed in this region, making it impossible for a comet to enter this region. Tycho concluded there were no such spheres, raising the question of what kept a planet in orbit.[1] With the patronage of the King of Denmark, Tycho Brahe established Uraniborg, an observatory in Hven.[6] For 20 years, Tycho and his team of astronomers compiled astronomical observations that were vastly more accurate than those made before. These observations would prove vital in future astronomical breakthroughs.

Nicolaus Copernicus’s heliocentric model

Tycho also formulated his own astronomical system, claiming it to be superior to those of Ptolemy and Copernicus. Although Tycho appreciated the advantages of 4.1.2 Tycho Brahe Copernicus’s system, he could not accept the movement of the Earth and settled on geoheliocentrism, meaning the Main article: Tycho Brahe Tycho Brahe (1546-1601) was a Danish nobleman who Sun moved around the Earth while the planets orbited the Sun.[1]

4.1.3 Johannes Kepler Main article: Johannes Kepler Johannes Kepler was a German scientist who is largely remembered for his work in astronomy. Kepler found employment as an assistant to Tycho Brahe and, upon Brahe’s unexpected death, replaced him as imperial mathematician of Emperor Rudolph II. He was then able to use Brahe’s extensive observations to make remarkable breakthroughs in astronomy. In 1596, Kepler published his first book, the Mysterium cosmographicum, which was the first to openly endorse Copernican cosmology by an astronomer since 1540.[1] The book described his model that used Pythagorean mathematics and the five Platonic solids to explain the number of planets, their proportions, and their order. The book garnered enough respect from Tycho Brahe to invite Kepler to Prague and serve as his assistant.

Tycho Brahe’s geoheliocentric model

In 1600, Kepler set to work on the orbit of Mars, the second most eccentric of the six planets known at that time. This work was the basis of his next book, the Astronomia


22

CHAPTER 4. COPERNICAN REVOLUTION

4.1.4 Galileo Galilei Main article: Galileo Galilei Galileo Galilei was an Italian scientist who is sometimes

EARTH

The phases of Venus, observed by Galileo in 1610 Kepler’s Platonic solid model of the Solar system from Mysterium Cosmographicum

referred to as the “father of modern observational astronomy”.[7] His improvements to the telescope, astronomical observations, and support for Copernicanism were all innova, which he published in 1609. The book argued he- tegral to the Copernican Revolution. liocentrism and ellipses for planetary orbits instead of circles modified by epicycles. This book contains the first Based on the designs of Hans Lippershey, Galileo defollowing year, two of his eponymous three laws of planetary motion. signed his own telescope which, in the [8] he had improved to 30x magnification. Using this new In 1619 Kepler published his third and final law which instrument, Galileo made a number of astronomical obshowed the relationship between two planets instead of servations which he published in the Sidereus Nuncius in single planet movement. 1610. In this book, he described the surface of the Moon Johannes Kepler’s work in astronomy was new in part. as rough, uneven, and imperfect. He also noted that “the Unlike those who came before him, he discarded the as- boundary dividing the bright from the dark part does not sumption that planets moved in uniform circular motion, form a uniformly oval line, as would happen in a perfectly replacing it with elliptical motion. Also, like Copernicus, spherical solid, but is marked by an uneven, rough, and he asserted the physical reality of a heliocentric model as very sinuous line, as the figure shows.”[9] These obseropposed to a geocentric one. Yet, despite all of his break- vations challenged Aristotle’s claim that the moon was a throughs, Kepler could not explain the physics that would perfect sphere and the larger idea that the heavens were keep a planet in its elliptical orbit. perfect and unchanging.

2. The Law of Equal Areas in Equal Time: A line that connects a planet to the Sun sweeps out equal areas in equal times.

Galileo’s next astronomical discovery would prove to be a surprising one. While observing Jupiter over the course of several days, he noticed four stars close to Jupiter whose positions were changing in a way that would be impossible if they were fixed stars. After much observation, he concluded these four stars were orbiting the planet Jupiter and were in fact moons, not stars.[10] This was a radical discovery because, according to Aristotelian cosmology, all heavenly bodies revolve around the Earth and a planet with moons obviously contradicted that popular belief.[11] While contradicting Aristotelian belief, it supported Copernican cosmology which stated that Earth is a planet like all others.[12]

3. The Law of Harmony:The time required for a planet to orbit the Sun, called its period, is proportional to long axis of the ellipse raised to the 3/2 power. The constant of proportionality is the same for all the planets.

In 1610, Galileo observed that Venus had a full set of phases, similar to the phases of the moon we can observe from Earth. This was explainable by the Copernican system which said that all phases of Venus would be visible due to the nature of its orbit around the Sun, unlike

Kepler’s laws of planetary motion Main article: Kepler’s laws of planetary motion

1. The Law of Ellipses: All planets move in elliptical orbits, with the Sun at one focus.


4.2. METAPHORICAL USE the Ptolemaic system which stated only some of Venus’s phases would be visible. Due to Galileo’s observations of Venus, Ptolemy’s system became highly suspect and the majority of leading astronomers subsequently converted to various heliocentric models, making his discovery one of the most influential in the transition from geocentrism to heliocentrism.[2]

4.1.5

Sphere of the fixed stars

23 the ending point of the Copernican Revolution. Without Newton’s laws we would not have an explanation for gravity, or how we observe motion related to the skies. Newton used Kepler’s laws of planetary motion to derive his law of universal gravitation. Newton’s law of universal gravitation was the first law he developed and proposed in his book Principia. The law states that any two objects exert a gravitational force of attraction on each other. The magnitude of the force is proportional to the product of the gravitational masses of the objects, and inversely proportional to the square of the distance between them.[3] Along with Newton’s law of universal gravitation, the Principia also presents his three laws of motion. These three laws explain inertia, acceleration, action and reaction when a net force is applied to an object.

In the sixteenth century, a number of writers inspired by Copernicus, such as Thomas Digges, Giordano Bruno and William Gilbert argued for an indefinitely extended or even infinite universe, with other stars as distant suns. This contrasts with the Aristotelian view of a sphere of the fixed stars. Although opposed by Copernicus and Kepler (with Galileo not expressing a view ), by the middle Newton’s laws of motion of the 17th century this became widely accepted, partly due to the support of René Descartes. Main article: Newton’s laws of motion

4.1.6

Isaac Newton

Main article: Isaac Newton Newton was a well known English physicist and

1. The law of Inertia: Every object will remain at rest or in a uniform motion unless acted on by an external force. 2. F=ma: The acceleration of a body is directly proportional to the net force acting on the body, and inversely proportional to its mass 3. Action & Reaction: For every action there is an equal and opposite reaction.

4.2 Metaphorical use Main article: Copernican Revolution (metaphor) The philosopher Immanuel Kant made an analogy to Copernicus when describing a problem from a different point of view, and some later philosophers have called it his “Copernican revolution”.[14] The conditions and qualities he ascribed to the subject of knowledge placed man at the centre of all conceptual and empirical experience, and overcame the rationalism-empiricism impasse, characteristic of the 17th and 18th centuries.

4.3 See also • History of science in the Renaissance Title page of Newton’s 'Philosophiæ Naturalis Principia Mathematica', first edition (1687)

mathematician who was known for his book Philosophiæ Naturalis Principia Mathematica.[13] He was a main figure in the Scientific Revolution for his laws of motion and universal gravitation. The laws of Newton are said to be

• Scientific revolution

4.4 References [1] Osler (2010), p.53


24

[2] Thoren (1989), p. 8 [3] Newton, Isaac (1999). The Principia: Mathematical Principles of Natural Philosophy. Translated by I. Bernard Cohen; Anne Whitman; Julia Budenz. Berkeley: University of California Press. ISBN 0-520-08817-4. [4] Osler (2010), p.42 [5] Osler (2010), p.44 [6] J J O'Connor and E F Robertson. Tycho Brahe biography. April 2003. Retrieved 2008-09-28 [7] Singer (1941), p.217 [8] Drake (1990), pp.133-134 [9] Galileo, Helden (1989), p.40 [10] Drake (1978), p.152 [11] Drake (1978), p. 157 [12] Osler (2010), p. 63 [13] See the Principia on line at Andrew Motte Translation [14] “Immanuel Kant”. Stanford Encyclopedia of Philosophy.

4.5 Works cited • Drake, Stillman (1978). Galileo At Work. Chicago: University of Chicago Press. ISBN 0-226-16226-5. • Drake, Stillman (1990). Galileo: Pioneer Scientist. Toronto: The University of Toronto Press. ISBN 0-8020-2725-3. • Galilei, Galileo (1989). Sidereus Nuncius. Albert Van Helden (trans.). Chicago, Illinois: University of Chicago Press. ISBN 9780226279039. • Kuhn, Thomas S. (1957). The Copernican Revolution: Planetary Astronomy in the Development of Western Thought. Cambridge, Massachusetts: Harvard University Press. ISBN 0-674-17103-9. • Osler, Margaret (2010). Reconfiguring the World. Baltimore, Maryland: The Johns Hopkins University Press. p. 184. ISBN 0-8018-9656-8. • Redd, Nola (May 2012). “Johannes Kepler Biography”. Tech Media Network. Retrieved October 23, 2013. • Singer, Charles (2007). A Short History of Science to the Nineteenth Century. Clarendon Press. • Thoren, Victor E. (1989). Tycho Brahe. In Taton and Wilson (1989, pp. 3–21). ISBN 0-521-351588.

CHAPTER 4. COPERNICAN REVOLUTION


Chapter 5

Celestial spheres Not to be confused with celestial sphere. For other uses, date them.[2] By combining this nested sphere model with see Celestial (disambiguation). astronomical observations, scholars calculated what became generally accepted values at the time for the distances to the Sun (about 4 million miles), to the other planets, and to the edge of the universe (about 73 million miles).[3] The nested sphere model’s distances to the Sun and planets differ significantly from modern measurements of the distances,[4] and the size of the universe is now known to be inconceivably large and possibly infinite.[5] Albert Van Helden has suggested that from about 1250 until the 17th century, virtually all educated Europeans were familiar with the Ptolemaic model of “nesting spheres and the cosmic dimensions derived from it”.[6] Even following the adoption of Copernicus’s heliocentric model of the universe, new versions of the celestial sphere model were introduced, with the planetary spheres following this sequence from the central Sun: Mercury, Venus, Earth-Moon, Mars, Jupiter and Saturn.

5.1 History Geocentric celestial spheres; Peter Apian’s Cosmographia (Antwerp, 1539)

The celestial spheres, or celestial orbs, were the fundamental entities of the cosmological models developed by Plato, Eudoxus, Aristotle, Ptolemy, Copernicus and others. In these celestial models the apparent motions of the fixed stars and the planets are accounted for by treating them as embedded in rotating spheres made of an aetherial, transparent fifth element (quintessence), like jewels set in orbs. Since it was believed that the fixed stars did not change their positions relative to one another, it was argued that they must be on the surface of a single starry sphere.[1] In modern thought, the orbits of the planets are viewed as the paths of those planets through mostly empty space. Ancient and medieval thinkers, however, considered the celestial orbs to be thick spheres of rarefied matter nested one within the other, each one in complete contact with the sphere above it and the sphere below.[2] When scholars applied Ptolemy’s epicycles, they presumed that each planetary sphere was exactly thick enough to accommo-

For more details on the causes of the motions of the celestial spheres, see Dynamics of the celestial spheres.

5.1.1 Early ideas of spheres and circles In Greek antiquity the ideas of celestial spheres and rings first appeared in the cosmology of Anaximander in the early 6th century BC.[7] In his cosmology both the Sun and Moon are circular open vents in tubular rings of fire enclosed in tubes of condensed air; these rings constitute the rims of rotating chariot-like wheels pivoting on the Earth at their centre. The fixed stars are also open vents in such wheel rims, but there are so many such wheels for the stars that their contiguous rims all together form a continuous spherical shell encompassing the Earth. All these wheel rims had originally been formed out of an original sphere of fire wholly encompassing the Earth, which had disintegrated into many individual rings.[8] Hence, in Anaximanders’s cosmogony, in the beginning was the

25


26

CHAPTER 5. CELESTIAL SPHERES

sphere, out of which celestial rings were formed, from some of which the stellar sphere was in turn composed. As viewed from the Earth, the ring of the Sun was highest, that of the Moon was lower, and the sphere of the stars was lowest. Following Anaximander, his pupil Anaximenes (c. 585– 528/4) held that the stars, Sun, Moon, and planets are all made of fire. But whilst the stars are fastened on a revolving crystal sphere like nails or studs, the Sun, Moon, and planets, and also the Earth, all just ride on air like leaves because of their breadth.[9] And whilst the fixed stars are carried around in a complete circle by the stellar sphere, the Sun, Moon and planets do not revolve under the Earth between setting and rising again like the stars do, but rather on setting they go laterally around the Earth like a cap turning halfway around the head until they rise again. And unlike Anaximander, he relegated the fixed stars to the region most distant from the Earth. The most enduring feature of Anaximenes’ cosmos was its conception of the stars being fixed on a crystal sphere as in a rigid frame, which became a fundamental principle of cosmology down to Copernicus and Kepler.

the spherical Earth is at the centre of the universe and the planets are moved by either 47 or 55 interconnected spheres that form a unified planetary system,[19] whereas in the models of Eudoxus and Callippus each planet’s individual set of spheres were not connected to those of the next planet. Aristotle says the exact number of spheres, and hence the number of movers, is to be determined by astronomical investigation, but he added additional spheres to those proposed by Eudoxus and Callippus, to counteract the motion of the outer spheres. Aristotle considers that these spheres are made of an unchanging fifth element, the aether. Each of these concentric spheres is moved by its own god — an unchanging divine unmoved mover, and who moves its sphere simply by virtue of being loved by it.[20]

After Anaximenes, Pythagoras, Xenophanes and Parmenides all held that the universe was spherical.[10] And much later in the fourth century BC Plato’s Timaeus proposed that the body of the cosmos was made in the most perfect and uniform shape, that of a sphere containing the fixed stars.[11] But it posited that the planets were spherical bodies set in rotating bands or rings rather than wheel rims as in Anaximander’s cosmology.

5.1.2

Emergence of the planetary spheres

Instead of bands, Plato’s student Eudoxus developed a planetary model using concentric spheres for all the planets, with three spheres each for his models of the Moon and the Sun and four each for the models of the other five planets, thus making 26 spheres in all.[12][13] Callippus modified this system, using five spheres for his models of the Sun, Moon, Mercury, Venus, and Mars and retaining four spheres for the models of Jupiter and Saturn, thus making 33 spheres in all.[13] Each planet is attached to the innermost of its own particular set of spheres. Although the models of Eudoxus and Callippus qualitatively describe the major features of the motion of the planets, they fail to account exactly for these motions and therefore cannot provide quantitative predictions.[14] Although historians of Greek science have traditionally considered these models to be merely geometrical representations,[15][16] recent studies have proposed that they were also intended to be physically real[17] or have withheld judgment, noting the limited evidence to resolve the question.[18]

Ptolemaic model of the spheres for Venus, Mars, Jupiter, and Saturn with epicycle, eccentric deferent and equant point. Georg von Peuerbach, Theoricae novae planetarum, 1474.

In his Almagest, the astronomer Ptolemy (fl. ca. 150 AD) developed geometrical predictive models of the motions of the stars and planets and extended them to a unified physical model of the cosmos in his Planetary hypotheses.[21][22][23][24] By using eccentrics and epicycles, his geometrical model achieved greater mathematical detail and predictive accuracy than had been exhibited by earlier concentric spherical models of the cosmos.[25] In Ptolemy’s physical model, each planet is contained in two or more spheres,[26] but in Book 2 of his Planetary Hypotheses Ptolemy depicted thick circular slices rather than In his Metaphysics, Aristotle developed a physical cos- spheres as in its Book 1. One sphere/slice is the deferent, mology of spheres, based on the mathematical models of with a centre offset somewhat from the Earth; the other Eudoxus. In Aristotle’s fully developed celestial model, sphere/slice is an epicycle embedded in the deferent, with


5.1. HISTORY the planet embedded in the epicyclical sphere/slice.[27] Ptolemy’s model of nesting spheres provided the general dimensions of the cosmos, the greatest distance of Saturn being 19,865 times the radius of the Earth and the distance of the fixed stars being at least 20,000 Earth radii.[26] The planetary spheres were arranged outwards from the spherical, stationary Earth at the centre of the universe in this order: the spheres of the Moon, Mercury, Venus, Sun, Mars, Jupiter, and Saturn. In more detailed models the seven planetary spheres contained other secondary spheres within them. The planetary spheres were followed by the stellar sphere containing the fixed stars; other scholars added a ninth sphere to account for the precession of the equinoxes, a tenth to account for the supposed trepidation of the equinoxes, and even an eleventh to account for the changing obliquity of the ecliptic.[28] In antiquity the order of the lower planets was not universally agreed. Plato and his followers ordered them Moon, Sun, Mercury, Venus, and then followed the standard model for the upper spheres.[29][30] Others disagreed about the relative place of the spheres of Mercury and Venus: Ptolemy placed both of them beneath the Sun with Venus above Mercury, but noted others placed them both above the Sun; some medieval thinkers, such as alBitruji, placed the sphere of Venus above the Sun and that of Mercury below it.[31]

5.1.3

Middle Ages

Astronomical discussions

27 etary spheres. Al-Farghānī's distance to the stars was 20,110 Earth radii which, on the assumption that the radius of the Earth was 3,250 miles, came to 65,357,500 miles.[32] An introduction to Ptolemy’s Almagest, the Tashil al-Majisti, believed to be written by Thābit ibn Qurra, presented minor variations of Ptolemy’s distances to the celestial spheres.[33] In his Zij, Al-Battānī presented independent calculations of the distances to the planets on the model of nesting spheres, which he thought was due to scholars writing after Ptolemy. His calculations yielded a distance of 19,000 Earth radii to the stars.[34] Around the turn of the millennium, the Arabic astronomer and polymath Ibn al-Haytham (Alhacen) presented a development of Ptolemy’s geocentric epicyclic models in terms of nested spheres. Despite the similarity of this concept to that of Ptolemy’s Planetary Hypotheses, al-Haytham’s presentation differs in sufficient detail that it has been argued that it reflects an independent development of the concept.[35] In chapters 15–16 of his Book of Optics, Ibn al-Haytham also said that the celestial spheres do not consist of solid matter.[36] Near the end of the twelfth century, the Spanish Muslim astronomer al-Bitrūjī (Alpetragius) sought to explain the complex motions of the planets without Ptolemy’s epicycles and eccentrics, using an Aristotelian framework of purely concentric spheres that moved with differing speeds from east to west. This model was much less accurate as a predictive astronomical model,[37] but it was discussed by later European astronomers and philosophers.[38][39] In the thirteenth century the astronomer, al-'Urḍi, proposed a radical change to Ptolemy’s system of nesting spheres. In his Kitāb al-Hayáh, he recalculated the distance of the planets using parameters which he redetermined. Taking the distance of the Sun as 1,266 Earth radii, he was forced to place the sphere of Venus above the sphere of the Sun; as a further refinement, he added the planet’s diameters to the thickness of their spheres. As a consequence, his version of the nesting spheres model had the sphere of the stars at a distance of 140,177 Earth radii.[34]

About the same time, scholars in European universities began to address the implications of the rediscovered philosophy of Aristotle and astronomy of Ptolemy. Both astronomical scholars and popular writers considered the implications of the nested sphere model for the dimensions of the universe.[40] Campanus of Novara's introductory astronomical text, the Theorica planetarum, used the model of nesting spheres to compute the distances of the various planets from the Earth, which he gave as 22,612 Earth radii or 73,387,747 100/660 miles.[41][42] The Earth within seven celestial spheres, from Bede, De natura In his Opus Majus, Roger Bacon cited Al-Farghānī's disrerum, late 11th century tance to the stars of 20,110 Earth radii, or 65,357,700 miles, from which he computed the circumference of the A series of astronomers, beginning with the Muslim as- universe to be 410,818,517 3/7 miles.[43] Clear evidence tronomer al-Farghãnī, used the Ptolemaic model of nest- that this model was thought to represent physical realing spheres to compute distances to the stars and plan-


28 ity is the accounts found in Bacon’s Opus Majus of the time needed to walk to the Moon[44] and in the popular Middle English South English Legendary, that it would take 8,000 years to reach the highest starry heaven.[45][46] General understanding of the dimensions of the universe derived from the nested sphere model reached wider audiences through the presentations in Hebrew by Moses Maimonides, in French by Gossuin of Metz, and in Italian by Dante Alighieri.[47] Philosophical and theological discussions Philosophers were less concerned with such mathematical calculations than with the nature of the celestial spheres, their relation to revealed accounts of created nature, and the causes of their motion.

CHAPTER 5. CELESTIAL SPHERES which maintained that all physical effects were caused directly by God’s will rather than by natural causes.[53] He maintained that the celestial spheres were “imaginary things” and “more tenuous than a spider’s web”.[54] His views were challenged by al-Jurjani (1339–1413), who maintained that even if the celestial spheres “do not have an external reality, yet they are things that are correctly imagined and correspond to what [exists] in actuality”.[54] Medieval astronomers and philosophers developed diverse theories about the causes of the celestial spheres’ motions. They attempted to explain the spheres’ motions in terms of the materials of which they were thought to be made, external movers such as celestial intelligences, and internal movers such as motive souls or impressed forces. Most of these models were qualitative, although a few incorporated quantitative analyses that related speed, motive force and resistance.[55] By the end of the Middle Ages, the common opinion in Europe was that celestial bodies were moved by external intelligences, identified with the angels of revelation.[56] The outermost moving sphere, which moved with the daily motion affecting all subordinate spheres, was moved by an unmoved mover, the Prime Mover, who was identified with God. Each of the lower spheres was moved by a subordinate spiritual mover (a replacement for Aristotle’s multiple divine movers), called an intelligence.[57]

Adi Setia describes the debate among Islamic scholars in the twelfth century, based on the commentary of Fakhr al-Din al-Razi about whether the celestial spheres are real, concrete physical bodies or “merely the abstract circles in the heavens traced out… by the various stars and planets.” Setia points out that most of the learned, and the astronomers, said they were solid spheres “on which the stars turn… and this view is closer to the apparent sense of the Qur'anic verses regarding the celestial orbits.” However, al-Razi mentions that some, such as the Islamic scholar Dahhak, considered them to be abstract. Al-Razi himself, was undecided, he said: “In truth, there 5.1.4 is no way to ascertain the characteristics of the heavens except by authority [of divine revelation or prophetic traditions].” Setia concludes: “Thus it seems that for al-Razi (and for others before and after him), astronomical models, whatever their utility or lack thereof for ordering the heavens, are not founded on sound rational proofs, and so no intellectual commitment can be made to them insofar as description and explanation of celestial realities are concerned.”[48]

Renaissance

Christian and Muslim philosophers modified Ptolemy’s system to include an unmoved outermost region, the empyrean heaven, which came to be identified as the dwelling place of God and all the elect.[49] Medieval Christians identified the sphere of stars with the Biblical firmament and sometimes posited an invisible layer of water above the firmament, to accord with Genesis.[50] An outer sphere, inhabited by angels, appeared in some accounts.[51] Edward Grant, a historian of science, has provided evidence that medieval scholastic philosophers generally considered the celestial spheres to be solid in the sense of three-dimensional or continuous, but most did not consider them solid in the sense of hard. The consensus was that the celestial spheres were made of some kind of continuous fluid.[52]

Thomas Digges’ 1576 Copernican heliocentric model of the celestial orbs

Early in the sixteenth century Nicolaus Copernicus drastically reformed the model of astronomy by displacing the Earth from its central place in favour of the Sun, Later in the century, the mutakallim Adud al-Din al-Iji yet he called his great work De revolutionibus orbium (1281–1355) rejected the principle of uniform and cir- coelestium (On the Revolutions of the Celestial Spheres). cular motion, following the Ash'ari doctrine of atomism, Although Copernicus does not treat the physical nature of


5.2. LITERARY AND SYMBOLIC EXPRESSIONS the spheres in detail, his few allusions make it clear that, like many of his predecessors, he accepted non-solid celestial spheres.[58] Copernicus rejected the ninth and tenth spheres, placed the orb of the Moon around the Earth and moved the Sun from its orb to the center of the world. The planetary orbs circled the center of the world in the order Mercury, Venus, the great orb containing the Earth and the orb of the Moon, then the orbs of Mars, Jupiter, and Saturn. Finally he retained the eighth starry sphere, which he held to be unmoving.[59] The English almanac maker, Thomas Digges, delineated the spheres of the new cosmological system in his Perfit Description of the Caelestiall Orbes… (1576). Here he arranged the “orbes” in the new Copernican order, expanding one sphere to carry “the globe of mortalitye”, the Earth, the four elements, and the Moon; and expanding the starry sphere infinitely upward to encompass all the stars, and also to serve as “the court of the Great God, the habitacle of the elect, and of the coelestiall angelles.”[60]

29 of the comet of 1577, which passed through the planetary orbs, led Tycho to conclude[63] that “the structure of the heavens was very fluid and simple.” Tycho opposed his view to that of “very many modern philosophers” who divided the heavens into “various orbs made of hard and impervious matter.” Edward Grant found relatively few believers in hard celestial spheres before Copernicus, and concluded that the idea first became common sometime between the publication of Copernicus’s De revolutionibus in 1542 and Tycho Brahe’s publication of his cometary research in 1588.[64][65] In Johannes Kepler's early Mysterium cosmographicum, he considered the distances of the planets, and the consequent gaps required between the planetary spheres implied by the Copernican system, which had been noted by his former teacher, Michael Maestlin.[66] Kepler’s Platonic cosmology filled the large gaps with the five Platonic polyhedra, which accounted for the spheres’ measured astronomical distance.[67] In his mature celestial physics, the spheres were regarded as the purely geometrical spatial regions containing each planetary orbit rather than as the rotating physical orbs of the earlier Aristotelian celestial physics. The eccentricity of each planet’s orbit thereby defined the lengths of the radii of the inner and outer limits of its celestial sphere and thus its thickness. In Kepler’s celestial mechanics the cause of planetary motion became the rotating Sun, itself rotated by its own motive soul.[68] However, an immobile stellar sphere was a lasting remnant of physical celestial spheres in Kepler’s cosmology.

5.2 Literary and symbolic expressions

Johannes Kepler’s diagram of the celestial spheres, and of the spaces between them, following the opinion of Copernicus (Mysterium Cosmographicum, 2nd ed., 1621)

In the course of the sixteenth century, a number of philosophers, theologians, and astronomers, among them Francesco Patrizi, Andrea Cisalpino, Peter Ramus, Robert Bellarmine, Giordano Bruno, Jerónimo Muñoz, Michael Neander, Jean Pena, and Christoph Rothmann, abandoned the concept of celestial spheres.[61] Rothmann argued from the observations of the comet of 1585 that the lack of observed parallax indicated that the Comet was beyond Saturn, while the absence of observed refraction indicated the celestial region was of the same material as air, hence there were no planetary spheres.[62]

“Because the medieval universe is finite, it has a shape, the perfect spherical shape, containing within itself an ordered variety.... “The spheres ... present us with an object in which the mind can rest, overwhelming in its greatness but satisfying in its harmony.” C. S. Lewis, The Discarded Image, p. 99 In Cicero's Dream of Scipio, the elder Scipio Africanus describes an ascent through the celestial spheres, compared to which the Earth and the Roman Empire dwindle into insignificance. A commentary on the Dream of Scipio by the late Roman writer Macrobius, which included a discussion of the various schools of thought on the order of the spheres, did much to spread the idea of the celestial spheres through the Early Middle Ages.[69]

Some late medieval figures noted that the celestial spheres’ physical order was inverse to their order on the Tycho Brahe's investigations of a series of comets from spiritual plane, where God was at the center and the Earth 1577 to 1585, aided by Rothmann’s discussion of the at the periphery. Near the beginning of the fourteenth comet of 1585 and Michael Maestlin's tabulated distances century Dante, in the Paradiso of his Divine Comedy, de-


30

CHAPTER 5. CELESTIAL SPHERES The late-16th-century Portuguese epic The Lusiads vividly portrays the celestial spheres as a “great machine of the universe” constructed by God.[73] The explorer Vasco da Gama is shown the celestial spheres in the form of a mechanical model. Contrary to Cicero’s representation, da Gama’s tour of the spheres begins with the Empyrean, then descends inward toward Earth, culminating in a survey of the domains and divisions of earthly kingdoms, thus magnifying the importance of human deeds in the divine plan.

5.3 See also • Christian angelic hierarchy • Firmament • Geocentric model Dante and Beatrice gaze upon the highest Heaven; from Gustave Doré's illustrations to the Divine Comedy, Paradiso Canto 28, lines 16–39

• History of the Center of the Universe • Musica universalis • Primum Mobile • Sphere of fire

5.4 Notes [1] Grant, Planets, Stars, and Orbs, p. 440. [2] Lindberg, Beginnings of Western Science, p. 251. [3] Van Helden, Measuring the Universe, pp. 28-40. [4] Grant, Planets, Stars, and Orbs, pp. 437-8. [5] Van Helden, Measuring the Universe, p. 3 [6] Van Helden, Measuring the Universe, pp. 37, 40. Nicole Oresme, Le livre du Ciel et du Monde, Paris, BnF, Manuscrits, Fr. 565, f. 69, (1377)

[7] See chapter 4 of Heath’s Aristarchus of Samos 1913/97 Oxford University Press/Sandpiper Books Ltd; see p.11 of Popper’s The World of Parmenides Routledge 1998

scribed God as a light at the center of the cosmos.[70] Here the poet ascends beyond physical existence to the Empyrean Heaven, where he comes face to face with God himself and is granted understanding of both divine and human nature. Later in the century, the illuminator of Nicole Oresme's Le livre du Ciel et du Monde, a translation of and commentary on Aristotle’s De caelo produced for Oresme’s patron, King Charles V, employed the same motif. He drew the spheres in the conventional order, with the Moon closest to the Earth and the stars highest, but the spheres were concave upwards, centered on God, rather than concave downwards, centered on the Earth.[71] Below this figure Oresme quotes the Psalms that “The heavens declare the Glory of God and the firmament showeth his handiwork.”[72]

[8] Heath ibid pp26–8 [9] See chapter 5 of Heath’s 1913 Aristarchus of Samos [10] For Xenophanes’ and Parmenides’ spherist cosmologies see Heath ibid chapter 7 and chapter 9 respectively, and Popper ibid Essays 2 & 3. [11] F. M. Cornford, Plato’s Cosmology: The Timaeus of Plato, pp. 54–7 [12] Neugebauer, History of Ancient Mathematical Astronomy, vol. 2, pp. 677–85. [13] Lloyd, “Heavenly aberrations,” p. 173. [14] Neugebauer, History of Ancient Mathematical Astronomy, vol. 2, pp. 677–85.


5.4. NOTES

[15] Dreyer, History of the Planetary Systems, pp. 90–1, 121–2

31

[16] Lloyd, Aristotle, p. 150.

[36] Edward Rosen (1985), “The Dissolution of the Solid Celestial Spheres”, Journal of the History of Ideas 46 (1), p. 13–31 [19–20, 21].

[17] Larry Wright, “The Astronomy of Eudoxus: Geometry or Physics,” Studies in History and Philosophy of Science, 4 (1973): 165–72.

[37] Bernard R. Goldstein, Al-Bitrūjī: On the Principles of Astronomy, New Haven: Yale Univ. Pr., 1971, vol. 1, p. 6.

[18] G. E. R. Lloyd, “Saving the Phenomena,” Classical Quarterly, 28 (1978): 202–222, at p. 219.

[38] Bernard R. Goldstein, Al-Bitrūjī: On the Principles of Astronomy, New Haven: Yale Univ. Pr., 1971, vol. 1, pp. 40–5.

[19] Aristotle, Metaphysics 1073b1–1074a13, pp. 882–883 in The Basic Works of Aristotle Richard McKeon, ed., The Modern Library 2001

[39] Grant, Planets, Stars, and Orbs, pp. 563–6. [40] Grant, Planets, Stars, and Orbs, pp. 433-43.

[20] “The final cause, then, produces motion by being loved, but all other things move by being moved” Aristotle Metaphysics 1072b4.

[41] Grant, Planets, Stars, and Orbs, pp. 434-8.

[21] Neugebauer, History of Ancient Mathematical Astronomy, pp. 111–12, 148

[43] Van Helden, Measuring the Universe, p. 36.

[22] Pedersen, Early Physics and Astronomy p. 87

[42] Van Helden, Measuring the Universe, pp. 33-4.

[44] Van Helden, Measuring the Universe, p. 35. [45] Lewis, The Discarded Image, pp. 97-8.

[23] Crowe, Theories of the World, pp.45, 49–50, 72,

[46] Van Helden, Measuring the Universe, p. 38.

[24] Linton, From Eudoxus to Einstein, pp.63–64, 81.

[47] Van Helden, Measuring the Universe, pp. 37-9.

[25] Taliaferro, Translator’s Introduction to the Almagest, p,1; Dreyer, History of the Planetary Systems, pp.160, 167.

[48] Adi Setia (2004), “Fakhr Al-Din Al-Razi on Physics and the Nature of the Physical World: A Preliminary Survey”, Islam & Science, 2, retrieved 2010-03-02

[26] Neugebauer, History of Ancient Mathematical Astronomy, vol. 2, pp. 917–926. [27] Andrea Murschel, “The Structure and Function of Ptolemy’s Physical Hypotheses of Planetary Motion,” Journal for the History of Astronomy, 26(1995): 33–61. [28] Francis R. Johnson, “Marlowe’s “Imperiall Heaven,” ELH, 12 (1945): 35–44, p. 39 [29] Bruce S. Eastwood, Ordering the Heavens: Roman Astronomy and Cosmology in the Carolingian Renaissance, (Leiden: Brill) 2007, pp. 36–45 [30] In his De Revolutionibus Bk1.10 Copernicus claimed the empirical reason why Plato’s followers put the orbits of Mercury and Venus above the Sun’s was that if they were sub-solar, then by the Sun’s reflected light they would only ever appear as hemispheres at most and would also sometimes eclipse the Sun, but they do neither. (See p521 Great Books of the Western World 16 Ptolemy– Copernicus–Kepler) [31] al-Biţrūjī. (1971) On the Principles of Astronomy, 7.159– 65, trans. Bernard R. Goldstein, vol. 1, pp. 123–5. New Haven: Yale Univ. Pr. ISBN 0-300-01387-6 [32] Van Helden, Measuring the Universe, pp. 29-31. [33] Van Helden, Measuring the Universe, p. 31. [34] Van Helden, Measuring the Universe, pp. 31-2. [35] Y. Tzvi Langermann (1990), Ibn al Haytham’s On the Configuration of the World, p. 11–25, New York: Garland Publishing.

[49] Grant, Planets, Stars, and Orbs, pp. 382–3. [50] Lindberg, Beginnings of Western Science, pp. 249–50. [51] Lindberg, Beginnings of Western Science, p. 250. [52] Grant, Planets, Stars, and Orbs, pp. 328–30. [53] Huff, Toby (2003). The Rise of Early Modern Science: Islam, China, and the West. Cambridge University Press. p. 175. ISBN 0-521-52994-8. [54] pp. 55–57 of Ragep, F. Jamil; Al-Qushji, Ali (2001). “Freeing Astronomy from Philosophy: An Aspect of Islamic Influence on Science”. Osiris. 2nd Series. 16 (Science in Theistic Contexts: Cognitive Dimensions): 49– 71. Bibcode:2001Osir...16...49R. doi:10.1086/649338. ISSN 0369-7827. JSTOR 301979. [55] Grant, Planets, Stars, and Orbs, p. 541. [56] Grant, Planets, Stars, and Orbs, p. 527. [57] Grant, Planets, Stars, and Orbs, pp. 526–45. [58] Nicholas Jardine, “The Significance of the Copernican Orbs,” Journal for the History of Astronomy, 13(1982): 168–194, esp. pp. 177–8. [59] Hilderich von Varel (Edo Hildericus), Propositiones Cosmographicae de Globi Terreni Dimensione, (Frankfurt a. d. Oder, 1576), quoted in Peter Barker and Bernard R. Goldstein, “Realism and Instrumentalism in Sixteenth Century Astronomy: A Reappraisal, Perspectives on Science 6.3 (1998): 232–258, pp. 242–3. [60] Koyre, From the Closed World, pp. 28-30.


32

[61] Michael A. Granada, “Did Tycho Eliminate the Celestial Spheres before 1586?" Journal for the History of Astronomy, 37 (2006): 126–145, pp. 127–9. [62] Bernard R. Goldstein and Peter Barker, “The Role of Rothmann in the Dissolution of the Celestial Spheres,” The British Journal for the History of Science, 28 (1995): 385–403, pp. 390–1. [63] Michael A. Granada, “Did Tycho Eliminate the Celestial Spheres before 1586?" Journal for the History of Astronomy, 37 (2006): 126–145, pp. 132–8. [64] Grant, “Celestial Orbs,” 2000, pp. 185–6. [65] Grant, Planets, Stars, and Orbs, pp. 345–8. [66] Grasshoff, “Michael Maestlin’s Mystery”. [67] See Judith Field, Kepler’s geometric cosmology for details of Kepler’s cosmology [68] See p514–5 of Kepler’s 1630 Epitome of Copernican Astronomy Vol.1 Bk4.2.3 for his arguments that the Sun has a driving soul on p896 of the Encyclopædia Britannica edition [69] Macrobius, Commentary on the Dream of Scipio, transl. by William Harris Stahl, New York: Columbia Univ. Pr., 1952; on the order of the spheres see pp. 162–5. [70] C. S. Lewis, The Discarded Image: An Introduction to Medieval and Renaissance Literature, Cambridge: Cambridge Univ. Pr., 1964, p. 116. ISBN 0-521-09450-X [71] Nicole Oreseme, “Le livre du Ciel et du Monde”, 1377, retrieved 2 June 2007. [72] Ps. 18: 2; quoted in Nicole Oresme, Le livre du ciel et du monde, edited and translated by A, D. Menut and A. J. Denomy, Madison: Univ. of Wisconsin Pr., 1968, pp. 282–3. [73] Luiz vaz de Camões, The Lusiads, translated by Landeg White. Oxford University Press, 2010.

5.5 Bibliography • Aristotle Metaphysics, in 'The Basic Works of Aristotle' Richard McKeon (Ed) The Modern Library, 2001 • Clagett, Marshall Science of Mechanics in the Middle Ages University of Wisconsin Press 1959 • Cohen, I.B. & Whitman, A. Principia University of California Press 1999

CHAPTER 5. CELESTIAL SPHERES • Crowe, Michael J. (1990). Theories of the World from Antiquity to the Copernican Revolution. Mineola, NY: Dover Publications, Inc. ISBN 0-48626173-5. • Duhem, Pierre. “History of Physics.” The Catholic Encyclopedia. Vol. 12. New York: Robert Appleton Company, 1911. 18 Jun. 2008 <http://www. newadvent.org/cathen/12047a.htm>. • Duhem, Pierre. Le Système du Monde: Histoire des doctrines cosmologiques de Platon à Copernic, 10 vols., Paris: Hermann, 1959. • Duhem, Pierre. Medieval Cosmology: Theories of Infinity, Place, Time, Void, and the Plurality of Worlds, excerpts from Le Système du Monde, translated and edited by Roger Ariew, Chicago: University of Chicago Press, 1987 ISBN 0-226-16923-5 • Dreyer, John Louis Emil (2007) [1905]. History of the Planetary Systems from Thales to Kepler. New York, NY: Cosimo. ISBN 1-60206-441-5. • Eastwood, Bruce, “Astronomy in Christian Latin Europe c. 500 – c. 1150,” Journal for the History of Astronomy, 28(1997): 235–258. • Eastwood, Bruce, Ordering the Heavens: Roman Astronomy and Cosmology in the Carolingian Renaissance, Leiden: Brill, 2007. ISBN 978-90-0416186-3. • Eastwood, Bruce and Gerd Graßhoff, Planetary Diagrams for Roman Astronomy in Medieval Europe, ca. 800-1500, Transactions of the American Philosophical Society, vol. 94, pt. 3, Philadelphia, 2004. ISBN 0-87169-943-5 • Field, J. V., Kepler’s geometrical cosmology. Chicago: Chicago University Press, 1988 ISBN 0-226-24823-2 • Golino, Carlo (ed.)Galileo Reappraised University of California Press 1966 • Grant, Edward, “Celestial Orbs in the Latin Middle Ages,” Isis, 78(1987): 153–73; reprinted in Michael H. Shank, ed., The Scientific Enterprise in Antiquity and the Middle Ages, Chicago: Univ. of Chicago Pr., 2000. ISBN 0-226-74951-7 • Grant, Edward, Planets, Stars, and Orbs: The Medieval Cosmos, 1200–1687, Cambridge: Cambridge Univ. Pr., 1994. ISBN 0-521-56509-X

• Cohen & Smith (eds) The Cambridge Companion to Newton CUP 2002

• Grant, Edward The Foundations of Modern Science in the Middle Ages, Cambridge: Cambridge Univ. Pr., 1996. ISBN 0-521-56762-9

• Copernicus, Nicolaus On the Revolutions of the Heavenly Spheres, in Great Books of the Western World : 16 Ptolemy Copernicus Kepler Encyclopædia Britannica Inc 1952

• Grasshoff, Gerd (2012). “Michael Maestlin’s Mystery: Theory Building with Diagrams”. Journal for the History of Astronomy. 43: 57–73. Bibcode:2012JHA....43...57G.


5.6. EXTERNAL LINKS • Gingerich, Owen The Eye of Heaven, American Institute of Physics 1993 • Hutchins, Robert Maynard; Adler, Mortimer J., eds. (1952). Ptolemy, Copernicus, Kepler. Great Books of the Western World. 16. Chicago, Ill: William Benton. • Heath, Thomas Aristarchus of Samos Oxford University Press/Sandpiper Books Ltd. 1913/97 • Jarrell, R.A. The contemporaries of Tycho Brahe in Taton & Wilson (eds)1989 • Koyré, Alexandre: Galileo Studies (translator Mepham) Harvester Press 1977 ISBN 0-85527354-2 • Koyré, Alexandre (1957). From the Closed World to the Infinite Universe. Forgotten Books. ISBN 9781-60620-143-5. Retrieved 8 May 2012. • Kepler, Johannes, Epitome of Copernican Astronomy (Bks 4 & 5), published in Great Books of the Western World : 16 Ptolemy Copernicus Kepler, Encyclopædia Britannica Inc. 1952 • Lewis, C. S., The Discarded Image: An Introduction to Medieval and Renaissance Literature, Cambridge: Cambridge University Press 1964 ISBN 0521-09450-X • Lindberg, David C. (1992). The Beginnings of Western Science. Chicago: University of Chicago Press. ISBN 0-226-48231-6. • Lindberg, David C. (ed) Science in the Middle Ages Chicago: Univ. of Chicago Pr., 1978. ISBN 0-22648233-2 • Linton, Christopher M. (2004). From Eudoxus to Einstein—A History of Mathematical Astronomy. Cambridge: Cambridge University Press. ISBN 978-0-521-82750-8. • Lloyd, G. E. R., Aristotle: The Growth and Structure of his Thought, pp. 133–153, Cambridge: Cambridge Univ. Pr., 1968. ISBN 0-521-09456-9. • Lloyd, G. E. R., “Heavenly aberrations: Aristotle the amateur astronomer,” pp. 160–183 in his Aristotelian Explorations, Cambridge: Cambridge Univ. Pr., 1996. ISBN 0-521-55619-8. • Mach, Ernst The Science of Mechanics Open Court 1960. • Maier, Annaliese, At the Threshold of Exact Science: Selected Writings of Annaliese Maier on Late Medieval Natural Philosophy, edited by Steven Sargent, Philadelphia: University of Pennsylvania Press, 1982.

33 • McCluskey, Stephen C., Astronomies and Cultures in Early Medieval Europe, Cambridge: Cambridge Univ. Pr., 1998. ISBN 0-521-77852-2 • Neugebauer, Otto, A History of Ancient Mathematical Astronomy, 3 vols., New York: Springer, 1975. ISBN 0-387-06995-X • Pederson, Olaf (1993) [1974]. Early Physics and Astronomy: A Historical Introduction. Cambridge: Cambridge University Press. ISBN 0-521-40340-5. • Popper, Karl The World of Parmenides Routledge 1996 • Rosen, Edward Three Copernican Treatises Dover 1939/59. • Sambursky, S. The Physical World of Late Antiquity Routledge & Kegan Paul, 1962 • Schofield, C. The Tychonic and Semi-Tychonic World Systems in Taton & Wilson (eds) 1989 • Sorabji, Richard Matter, Space and Motion London: Duckworth, 1988 ISBN 0-7156-2205-6 • Sorabji, Richard (ed) Philoponus and the Rejection of Aristotelian Science London & Ithaca NY 1987 • Sorabji, Richard The Philosophy of the Commentators, 200–600 AD: Volume 2 Physics Duckworth 2004 • Taliaferro, R. Catesby (1946). Translator’s Introduction to the Almagest. In Hutchins (1952, pp.1–4). • R. Taton & C. Wilson (eds.)The General History of Astronomy: Volume 2 Planetary astronomy from the Renaissance to the rise of astrophysics Part A Tycho Brahe to Newton Cambridge: Cambridge Univ. Pr., 1989 • Thoren, Victor E., “The Comet of 1577 and Tycho Brahe’s System of the World,” Archives Internationales d'Histoire des Sciences, 29 (1979): 53–67. • Thoren, Victor E., Tycho Brahe in Taton & Wilson 1989 • Van Helden, Albert (1985). Measuring the Universe: Cosmic Dimensions from Aristarchus to Halley. Chicago and London: University of Chicago Press. ISBN 0-226-84882-5.

5.6 External links • Working model and complete explanation of the Eudoxus’s Spheres • Dennis Duke, Animated Ptolemaic model of the nested spheres


34 • Henry Mendell, Vignettes of Ancient Mathematics: Eudoxus of Cnidus Ptolemy, Almagest

CHAPTER 5. CELESTIAL SPHERES


Chapter 6

Firmament The firmament is described in Genesis 1:6–8 in the Genesis creation narrative: Then God said, “Let there be a firmament in the midst of the waters, and let it divide the waters from the waters.” Thus God made the firmament, and divided the waters which were under the firmament from the waters which were above the firmament; and it was so. And God called the firmament Heaven. So the evening and the morning were the second day.[3]

6.2 Etymology The word “firmament” is first recorded in a Middle English narrative based on scripture dated 1250.[4] It later appeared in the King James Bible. The word is anglicised from Latin firmamentum, used in the Vulgate (4th century).[5] This in turn is derived from the Latin root firmus, a cognate with “firm”.[5] The word is a Latinization of the Greek stereōma, which appears in the Septuagint (c. 200 BC).[1]

The sun, planets and angels and the firmament. Woodcut dated 1475.

6.3 History

Main article: Hebrew astronomy § Biblical cosmology The word “firmament” is used to translate raqia, or In Biblical cosmology, the firmament is the structure raqiya` (‫) רקיע‬, a word used in Biblical Hebrew. It is above the atmosphere, conceived as a vast solid dome.[1] derived from the root raqa (‫) רקע‬, meaning “to beat or According to the Genesis creation narrative, God created spread out”, e.g., the process of making a dish by hamthe firmament to separate the “waters above” the earth mering thin a lump of metal.[5][6] from the “waters below” the earth.[2] The word is anglicized from Latin firmamentum, which appears in the Like most ancient peoples, the Hebrews believed the sky Vulgate, a late fourth-century Latin translation of the was a solid dome with the Sun, Moon and stars embedded in it.[7] According to The Jewish Encyclopedia: Bible. The Hebrews regarded the earth as a plain or a hill figured like a hemisphere, swimming on water. Over this is arched the solid vault of heaven. To this vault are fastened the lights, the stars. So slight is this elevation that birds may rise to it and fly along its expanse.[8]

6.1 Biblical use Main article: Biblical cosmology

35


36

CHAPTER 6. FIRMAMENT stationary). Tycho Brahe's studies of the nova of 1572 and the comet of 1577 were the first major challenges to the idea that orbs existed as solid, incorruptible, material objects.[14] In 1584, Giordano Bruno proposed a cosmology without firmament: an infinite universe in which the stars are actually suns with their own planetary systems.[15] After Galileo began using a telescope to examine the sky, it became harder to argue that the heavens were perfect, as Aristotelian philosophy required. By 1630, the concept of solid orbs was no longer dominant.[16]

6.5 See also The Flammarion engraving (1888) depicts a traveler who arrives at the edge of a flat Earth and sticks his head through the firmament.

Augustine wrote that too much learning had been expended on the nature of the firmament.[9] “We may understand this name as given to indicate not it is motionless but that it is solid.” he wrote.[9] Saint Basil argued for a fluid firmament.[9] According to St. Thomas Aquinas, the firmament had a “solid nature” and stood above a “region of fire, wherein all vapor must be consumed.”[10] The Copernican Revolution of the 16th century led to reconsideration of these matters. In 1554, John Calvin proposed that “firmament” be interpreted as clouds.[11] “He who would learn astronomy and other recondite arts, let him go elsewhere,” wrote Calvin.[11] “As it became a theologian, [Moses] had to respect us rather than the stars,” Calvin wrote. Calvin’s "doctrine of accommodation" allowed Protestants to accept the findings of science without rejecting the authority of scripture.[11][12]

6.4 Scientific development

• Heaven in Judaism • Primum Mobile

6.6 References [1] Herbermann, Charles, ed. (1913). "Firmament". Catholic Encyclopedia. New York: Robert Appleton Company. [2] “And God said, Let there be a firmament in the midst of the waters, and let it divide the waters from the waters”“Genesis 1:6”. [3] Genesis 1:6–8 [4] “firmament”, Oxford English Dictionary (1989). "ðo god bad ben ðe firmament”. From The story of Genesis and Exodus (1250). [5] “Online Etymology Dictionary – Firmament”. [6] “Lexicon Results Strong’s H7549 – raqiya`". Blue Letter Bible. Blue Letter Bible. Retrieved 2009-12-04. [7] Seely, Paul H. (1991). “The Firmament and the Water Above” (PDF). Westminster Theological Journal. 53: 227–40. Retrieved 2010-02-02.

Main article: Celestial spheres

[8] “Cosmogony”. 2014-05-15.

The Greeks and Stoics adopted a model of celestial spheres after the discovery of the spherical Earth in the 4th to 3rd centuries BC. The Medieval Scholastics adopted a cosmology that fused the ideas of the Greek philosophers Aristotle and Ptolemy.[13] This cosmology involved celestial orbs, nested concentrically inside one another, with the earth at the center. The outermost orb contained the stars and the term firmament was then transferred to this orb. (There were seven inner orbs for the seven wanderers of the sky, and their ordering is preserved in the naming of the days of the week.)

[9] Grant, Edward, Planets, stars, and orbs: the medieval cosmos, 1200–1687. p. 335.

JewishEncyclopedia.com.

Retrieved

[10] Saint Thomas Aquinas, Summa Theologica, "Whether there are waters above the firmament?" [11] Luigi Piccardi, W. Bruce Masse, Myth and geology, p. 40 [12] Firmament, Catholic Encyclopedia. [13] Grant, p. 308. [14] Grant, p. 348. [15] Giordano Bruno, De l'infinito universo e mondi (On the

Even Copernicus' heliocentric model included an outer Infinite Universe and Worlds), 1584. sphere that held the stars (and by having the earth rotate daily on its axis it allowed the firmament to be completely [16] Grant, p. 349.


6.7. EXTERNAL LINKS

6.7 External links • The Vault of Heaven. • Denver Radio / YouTube Debate on the Firmament between well-known creationist and atheist opponents. • The Firmament described in The Blueprint

37


Chapter 7

Primum Mobile In classical, medieval and Renaissance astronomy, the Primum Mobile, or “first moved,” was the outermost moving sphere in the geocentric model of the universe.[1] The concept was introduced by Ptolemy to account for the apparent daily movement of the heavens around the Earth, producing the east-to-west rising and setting of the sun and stars, and reached Western Europe via Avicenna.[2]

7.1 Appearance and rotation The Ptolemaic system presented a view of the universe in which apparent motion was taken for real – a viewpoint still maintained in common speech through such everyday terms as moonrise or sunset.[3] Rotation of the Earth on its polar axis – as seen in a heliocentric solar system, which (while anticipated by Aristarchus) was not to be 7.3 Copernicus and after widely accepted until well after Copernicus[4] – leads to what earlier astronomers saw as the real movement of all Copernicus accepted existence of the sphere of the the heavenly bodies around the Earth every 24 hours.[5] fixed stars, and (more ambiguously) that of the PriAstronomers believed that the seven naked-eye planets mum Mobile,[7] as too (initially) did Galileo[8] - though (including the Moon and the Sun) were carried around the he would later challenge its necessity in a heliocentric spherical Earth on invisible orbs, while an eighth sphere system.[9] contained the fixed stars. Motion was provided to the Francis Bacon was as sceptical of the Primum Mobile as whole system by the Primum Mobile, itself set within the he was of the rotation of the earth.[10] Once Kepler had Empyrean, and the fastest moving of all the spheres.[6] made the sun, not the Primum Mobile, the cause of planetary motion, however,[11] the Primum Mobile gradually declined into the realm of metaphor or literary allusion.

7.2 Spherical variations

7.4 Literary references

The total number of celestial spheres was not fixed. In this 16th-century illustration, the firmament (sphere of fixed stars) is eighth, a “crystalline” sphere (posited to account for the reference to “waters . . . above the firmament” in Genesis 1:7) is ninth, and the Primum Mobile is tenth. Outside all is the Empyrean, the “habitation of God and all the elect.” 38

• Dante made the Primum Mobile the ninth of the ten heavens into which he divided his Paradiso.[12] • W. B. Yeats wrote: “The Primum Mobile that fashioned us / Has made the very owls in circles move.”[13]


7.7. FURTHER READING

7.5 See also • Unmoved mover • Firmament

7.6 References [1] T. H. Greer, A Brief History of the Western World (2004) p. 419 [2] G. Galle, Peter of Auvergne (2003) p. 233 [3] Dante, Hell (1975) p. 292-5 [4] Hell p. 292 [5] F. A. C. Mantillo, Medieval Latin (1996) p. 365 [6] Dante, Purgatory (1971) p. 333 and p. 338 [7] O. Pederson, Early Physics and Astronomy (1993) p. 271 [8] J. Reston, Galileo: A Life (2005) p. 46 [9] Galileo Galilei, Dialogue.... (California nd) p. 261 [10] R. L. Ellis, Collected Works of Francis Bacon Vol 1 Pt 1 (1996) p. 450 [11] N. R. Hanson, Constellations and Conjectures (1973) p. 256-7 [12] Paradise p. 22-3 and end-piece [13] W. B. Yeats, The Poems (1984) p. 203

7.7 Further reading • C. S. Lewis, The Discarded Image (1964) • M. A. Orr, Dante and the Early Astronomers (1956)

39


Chapter 8

Geocentric model “Geocentric” redirects here. For orbits around the Earth, ancient Greeks believed that the motions of the planets see Geocentric orbit. were circular and not elliptical, a view that was not chalIn astronomy, the Geocentric model (also known as lenged in Western culture until the 17th century through the synthesis of theories by Copernicus and Kepler. The astronomical predictions of Ptolemy’s Geocentric model were used to prepare astrological and astronomical charts for over 1500 years. The Geocentric model held sway into the early modern age, but from the late 16th century onward, it was gradually superseded by the Heliocentric model of Copernicus, Galileo and Kepler. There was much resistance to the transition between these two theories. Christian theologians were reluctant to reject a theory that agreed with Bible passages (e.g. “Sun, stand you still upon Gibeon”, Joshua 10:12 – King James 2000 Bible). Others felt a new, unknown theory could not subvert an accepted consensus for Geocentrism. Figure of the heavenly bodies — An illustration of the Ptolemaic Geocentric system by Portuguese cosmographer and cartographer Bartolomeu Velho, 1568 (Bibliothèque Nationale, Paris)

8.1 Ancient Greece

Geocentrism, or the Ptolemaic system) is a superseded description of the universe with the Earth at the center. Under the geocentric model, the Sun, Moon, stars, and planets all circled Earth.[1] The geocentric model served as the predominant description of the cosmos in many ancient civilizations, such as those of Aristotle and Ptolemy. Two observations supported the idea that the Earth was the center of the Universe. First, the Sun appears to revolve around the Earth once per day. While the Moon and the planets have their own motions, they also appear to revolve around the Earth about once per day. The stars appeared to be on a celestial sphere, rotating once each day along an axis through the north and south geographic Illustration of Anaximander’s models of the universe. On the left, poles of the Earth.[2] Second, the Earth does not seem to daytime in summer; on the right, nighttime in winter. move from the perspective of an Earth-bound observer; it appears to be solid, stable, and unmoving. The Geocentric model entered Greek astronomy and phiAncient Greek, ancient Roman and medieval philoso- losophy at an early point; it can be found in Pre-Socratic phers usually combined the Geocentric model with a philosophy. In the 6th century BC, Anaximander prospherical Earth. It is not the same as the older flat Earth posed a cosmology with the Earth shaped like a section model implied in some mythology.[n 1][n 2][5] The ancient of a pillar (a cylinder), held aloft at the center of everyJewish Babylonian uranography pictured a flat Earth with thing. The Sun, Moon, and planets were holes in invisia dome-shaped rigid canopy named firmament placed ble wheels surrounding the Earth; through the holes, huover it. (‫רקיע‬- rāqîa').[n 3][n 4][n 5][n 6][n 7][n 8] However, the mans could see concealed fire. About the same time, the 40


8.2. PTOLEMAIC MODEL Pythagoreans thought that the Earth was a sphere (in accordance with observations of eclipses), but not at the center; they believed that it was in motion around an unseen fire. Later these views were combined, so most educated Greeks from the 4th century BC on thought that the Earth was a sphere at the center of the universe.[12] In the 4th century BC, two influential Greek philosophers, Plato and his student Aristotle, wrote works based on the Geocentric model. According to Plato, the Earth was a sphere, stationary at the center of the universe. The stars and planets were carried around the Earth on spheres or circles, arranged in the order (outwards from the center): Moon, Sun, Venus, Mercury, Mars, Jupiter, Saturn, fixed stars, with the fixed stars located on the celestial sphere. In his "Myth of Er", a section of the Republic, Plato describes the cosmos as the Spindle of Necessity, attended by the Sirens and turned by the three Fates. Eudoxus of Cnidus, who worked with Plato, developed a less mythical, more mathematical explanation of the planets’ motion based on Plato’s dictum stating that all phenomena in the heavens can be explained with uniform circular motion. Aristotle elaborated on Eudoxus’ system. In the fully developed Aristotelian system, the spherical Earth is at the center of the universe, and all other heavenly bodies are attached to 47–55 transparent, rotating spheres surrounding the Earth, all concentric with it. (The number is so high because several spheres are needed for each planet.) These spheres, known as crystalline spheres, all moved at different uniform speeds to create the revolution of bodies around the Earth. They were composed of an incorruptible substance called aether. Aristotle believed that the moon was in the innermost sphere and therefore touches the realm of Earth, causing the dark spots (macula) and the ability to go through lunar phases. He further described his system by explaining the natural tendencies of the terrestrial elements: Earth, water, fire, air, as well as celestial aether. His system held that Earth was the heaviest element, with the strongest movement towards the center, thus water formed a layer surrounding the sphere of Earth. The tendency of air and fire, on the other hand, was to move upwards, away from the center, with fire being lighter than air. Beyond the layer of fire, were the solid spheres of aether in which the celestial bodies were embedded. They, themselves, were also entirely composed of aether. Adherence to the Geocentric model stemmed largely from several important observations. First of all, if the Earth did move, then one ought to be able to observe the shifting of the fixed stars due to stellar parallax. In short, if the Earth was moving, the shapes of the constellations should change considerably over the course of a year. If they did not appear to move, the stars are either much farther away than the Sun and the planets than previously conceived, making their motion undetectable, or in reality they are not moving at all. Because the stars were actually much further away than Greek astronomers postulated (making movement extremely subtle), stellar par-

41 allax was not detected until the 19th century. Therefore, the Greeks chose the simpler of the two explanations. The lack of any observable parallax was considered a fatal flaw in any non-Geocentric theory. Another observation used in favor of the Geocentric model at the time was the apparent consistency of Venus’ luminosity, which implies that it is usually about the same distance from Earth, which in turn is more consistent with geocentrism than heliocentrism. In reality, that is because the loss of light caused by Venus’ phases compensates for the increase in apparent size caused by its varying distance from Earth. Objectors to heliocentrism noted that terrestrial bodies naturally tend to come to rest as near as possible to the center of the Earth. Further barring the opportunity to fall closer the center, terrestrial bodies tend not to move unless forced by an outside object, or transformed to a different element by heat or moisture. Atmospheric explanations for many phenomena were preferred because the Eudoxan–Aristotelian model based on perfectly concentric spheres was not intended to explain changes in the brightness of the planets due to a change in distance.[13] Eventually, perfectly concentric spheres were abandoned as it was impossible to develop a sufficiently accurate model under that ideal. However, while providing for similar explanations, the later deferent and epicycle model was flexible enough to accommodate observations for many centuries.

8.2 Ptolemaic model

The basic elements of Ptolemaic astronomy, showing a planet on an epicycle with an eccentric deferent and an equant point. The Green shaded area is the celestial sphere which the planet occupies.

Although the basic tenets of Greek Geocentrism were established by the time of Aristotle, the details of his system did not become standard. The Ptolemaic system, devel-


42

CHAPTER 8. GEOCENTRIC MODEL

oped by the Hellenistic astronomer Claudius Ptolemaeus in the 2nd century AD finally standardised Geocentrism. His main astronomical work, the Almagest, was the culmination of centuries of work by Hellenic, Hellenistic and Babylonian astronomers. For over a millennium European and Islamic astronomers assumed it was the correct cosmological model. Because of its influence, people sometimes wrongly think the Ptolemaic system is identical with the Geocentric model. Ptolemy argued that the Earth was a sphere in the center of the universe, from the simple observation that half the stars were above the horizon and half were below the horizon at any time (stars on rotating stellar sphere), and the assumption that the stars were all at some modest distance from the center of the universe. If the Earth was substantially displaced from the center, this division into visible and invisible stars would not be equal.[n 9]

8.2.1

Ptolemaic system

astronomers for centuries along with the idea of the eccentric (a deferent which is slightly off-center from the Earth), which was even older. In the illustration, the center of the deferent is not the Earth but the spot marked X, making it eccentric (from the Greek ἐκ ec- meaning “from,” and κέντρον kentron meaning “center”), from which the spot takes its name. Unfortunately, the system that was available in Ptolemy’s time did not quite match observations, even though it was considerably improved over Hipparchus’ system. Most noticeably the size of a planet’s retrograde loop (especially that of Mars) would be smaller, and sometimes larger, than expected, resulting in positional errors of as much as 30 degrees. To alleviate the problem, Ptolemy developed the equant. The equant was a point near the center of a planet’s orbit which, if you were to stand there and watch, the center of the planet’s epicycle would always appear to move at uniform speed; all other locations would see non-uniform speed, like on the Earth. By using an equant, Ptolemy claimed to keep motion which was uniform and circular, although it departed from the Platonic ideal of uniform circular motion. The resultant system, which eventually came to be widely accepted in the west, seems unwieldy to modern astronomers; each planet required an epicycle revolving on a deferent, offset by an equant which was different for each planet. It predicted various celestial motions, including the beginning and end of retrograde motion, to within a maximum error of 10 degrees, considerably better than without the equant.

The model with epicycles is in fact a very good model of an elliptical orbit with low eccentricity. The well known ellipse shape does not appear to a noticeable extent when the eccentricity is less than 5%, but the offset distance of the 'center' (in fact the focus occupied by the sun) is very noticeable even with low eccentricities as possessed Pages from 1550 Annotazione on Sacrobosco’s Tractatus de by the planets. Sphaera, showing the Ptolemaic system.

In the Ptolemaic system, each planet is moved by a system of two spheres: one called its deferent; the other, its epicycle. The deferent is a circle whose center point, called the eccentric and marked in the diagram with an X, is removed from the Earth. The original purpose of the eccentric was to account for the differences of the lengths of the seasons (autumn is the shortest by a week or so), by placing the Earth away from the center of rotation of the rest of the universe. Another sphere, the epicycle, is embedded inside the deferent sphere and is represented by the smaller dotted line to the right. A given planet then moves around the epicycle at the same time the epicycle moves along the path marked by the deferent. These combined movements cause the given planet to move closer to and further away from the Earth at different points in its orbit, and explained the observation that planets slowed down, stopped, and moved backward in retrograde motion, and then again reversed to resume normal, or prograde, motion. The deferent-and-epicycle model had been used by Greek

To summarize, Ptolemy devised a system that was compatible with Aristotelian philosophy and managed to track actual observations and predict future movement mostly to within the limits of the next 1000 years of observations. The observed motions and his mechanisms for explaining them include: The Geocentric model was eventually replaced by the heliocentric model. The earliest heliocentric model, Copernican heliocentrism, could remove Ptolemy’s epicycles because the retrograde motion could be seen to be the result of the combination of Earth and planet movement and speeds. Copernicus felt strongly that equants were a violation of Aristotelian purity, and proved that replacement of the equant with a pair of new epicycles was entirely equivalent. Astronomers often continued using the equants instead of the epicycles because the former was easier to calculate, and gave the same result. It has been determined, in fact, that the Copernican, Ptolemaic and even the Tychonic models provided iden-


8.2. PTOLEMAIC MODEL tical results to identical inputs. They are computationally equivalent. It wasn't until Kepler demonstrated a physical observation that could show that the physical sun is directly involved in determining an orbit that a new model was required. The Ptolemaic order of spheres from Earth outward is:[15] 1. Moon 2. Mercury 3. Venus 4. Sun 5. Mars 6. Jupiter

43 Early in the 11th century Alhazen wrote a scathing critique of Ptolemy's model in his Doubts on Ptolemy (c. 1028), which some have interpreted to imply he was criticizing Ptolemy’s geocentrism,[24] but most agree that he was actually criticizing the details of Ptolemy’s model rather than his geocentrism.[25] In the 12th century, Arzachel departed from the ancient Greek idea of uniform circular motions by hypothesizing that the planet Mercury moves in an elliptic orbit,[26][27] while Alpetragius proposed a planetary model that abandoned the equant, epicycle and eccentric mechanisms,[28] though this resulted in a system that was mathematically less accurate.[29] Alpetragius also declared the Ptolemaic system as an imaginary model that was successful at predicting planetary positions but not real or physical. His alternative system spread through most of Europe during the 13th century.[30]

Fakhr al-Din al-Razi (1149–1209), in dealing with his conception of physics and the physical world in his 7. Saturn Matalib, rejects the Aristotelian and Avicennian notion of the Earth’s centrality within the universe, but instead ar8. Fixed Stars gues that there are “a thousand thousand worlds (alfa alfi 'awalim) beyond this world such that each one of those 9. Primum Mobile (First Moved). worlds be bigger and more massive than this world as well as having the like of what this world has.” To support his Ptolemy did not invent or work out this order, which theological argument, he cites the Qur'anic verse, “All aligns with the ancient Seven Heavens religious cosmol- praise belongs to God, Lord of the Worlds,” emphasizing ogy common to the major Eurasian religious traditions. the term “Worlds.”[20] It also follows the decreasing orbital periods of the moon, The “Maragha Revolution” refers to the Maragha school’s sun, planets and stars. revolution against Ptolemaic astronomy. The “Maragha school” was an astronomical tradition beginning in the 8.2.2 Islamic astronomy and geocentrism Maragha observatory and continuing with astronomers from the Damascus mosque and Samarkand observaMain articles: Maragheh observatory, Astronomy in tory. Like their Andalusian predecessors, the Maragha astronomers attempted to solve the equant problem (the medieval Islam, and Islamic cosmology circle around whose circumference a planet or the center of an epicycle was conceived to move uniformly) Muslim astronomers generally accepted the Ptolemaic and produce alternative configurations to the Ptolemaic system and the Geocentric model,[16] but by the 10th model without abandoning geocentrism. They were more century texts appeared regularly whose subject mat- successful than their Andalusian predecessors in proter was doubts concerning Ptolemy (shukūk).[17] Sev- ducing non-Ptolemaic configurations which eliminated eral Muslim scholars questioned the Earth’s apparent the equant and eccentrics, were more accurate than the immobility[18][19] and centrality within the universe.[20] Ptolemaic model in numerically predicting planetary poSome Muslim astronomers believed that the Earth ro- sitions, and were in better agreement with empirical tates around its axis, such as Abu Sa'id al-Sijzi (d. circa observations.[31] The most important of the Maragha 1020).[21][22] According to al-Biruni, Sijzi invented an astronomers included Mo'ayyeduddin Urdi (d. 1266), astrolabe called al-zūraqī based on a belief held by some Nasīr al-Dīn al-Tūsī (1201–1274), Qutb al-Din al-Shirazi of his contemporaries “that the motion we see is due to (1236–1311), Ibn al-Shatir (1304–1375), Ali Qushji (c. the Earth’s movement and not to that of the sky.”[22][23] 1474), Al-Birjandi (d. 1525), and Shams al-Din alThe prevalence of this view is further confirmed by a ref- Khafri (d. 1550).[32] Ibn al-Shatir, the Damascene aserence from the 13th century which states: tronomer (1304–1375 AD) working at the Umayyad Mosque, wrote a major book entitled Kitab Nihayat alSul fi Tashih al-Usul (A Final Inquiry Concerning the RecAccording to the geometers [or engineers] tification of Planetary Theory) on a theory which departs (muhandisīn), the Earth is in constant circular largely from the Ptolemaic system known at that time. In motion, and what appears to be the motion of his book, Ibn al-Shatir, an Arab astronomer of the fourthe heavens is actually due to the motion of the [22] teenth century, E. S. Kennedy wrote “what is of most inEarth and not the stars.


44 terest, however, is that Ibn al-Shatir’s lunar theory, except for trivial differences in parameters, is identical with that of Copernicus (1473–1543 AD).” The discovery that the models of Ibn al-Shatir are mathematically identical to those of Copernicus suggests the possible transmission of these models to Europe.[33] At the Maragha and Samarkand observatories, the Earth’s rotation was discussed by al-Tusi and Ali Qushji (b. 1403); the arguments and evidence they used resemble those used by Copernicus to support the Earth’s motion.[18][19] However, the Maragha school never made the paradigm shift to heliocentrism.[34] The influence of the Maragha school on Copernicus remains speculative, since there is no documentary evidence to prove it. The possibility that Copernicus independently developed the Tusi couple remains open, since no researcher has yet demonstrated that he knew about Tusi’s work or that of the Maragha school.[34][35]

8.3 Geocentrism and rival systems

This drawing from an Icelandic manuscript dated around 1750 illustrates the Geocentric model.

Not all Greeks agreed with the Geocentric model. The Pythagorean system has already been mentioned; some Pythagoreans believed the Earth to be one of several planets going around a central fire.[36] Hicetas and Ecphantus, two Pythagoreans of the 5th century BC, and Heraclides Ponticus in the 4th century BC, believed that the Earth rotated on its axis but remained at the center of the universe.[37] Such a system still qualifies as Geocentric. It was revived in the Middle Ages by Jean Buridan. Heraclides Ponticus was once thought to have proposed that both Venus and Mercury went around the Sun rather than

CHAPTER 8. GEOCENTRIC MODEL the Earth, but this is no longer accepted.[38] Martianus Capella definitely put Mercury and Venus in orbit around the Sun.[39] Aristarchus of Samos was the most radical. He wrote a work, which has not survived, on heliocentrism, saying that the Sun was at the center of the universe, while the Earth and other planets revolved around it.[40] His theory was not popular, and he had one named follower, Seleucus of Seleucia.[41]

8.3.1 Copernican system Main article: Copernican heliocentrism In 1543, the Geocentric system met its first serious challenge with the publication of Copernicus' De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres), which posited that the Earth and the other planets instead revolved around the Sun. The Geocentric system was still held for many years afterwards, as at the time the Copernican system did not offer better predictions than the Geocentric system, and it posed problems for both natural philosophy and scripture. The Copernican system was no more accurate than Ptolemy’s system, because it still used circular orbits. This was not altered until Johannes Kepler postulated that they were elliptical (Kepler’s first law of planetary motion). With the invention of the telescope in 1609, observations made by Galileo Galilei (such as that Jupiter has moons) called into question some of the tenets of geocentrism but did not seriously threaten it. Because he observed dark “spots” on the moon, craters, he remarked that the moon was not a perfect celestial body as had been previously conceived. This was the first time someone could see imperfections on a celestial body that was supposed to be composed of perfect aether. As such, because the moon’s imperfections could now be related to those seen on Earth, one could argue that neither was unique: rather, they were both just celestial bodies made from Earth-like material. Galileo could also see the moons of Jupiter, which he dedicated to Cosimo II de' Medici, and stated that they orbited around Jupiter, not Earth.[42] This was a significant claim as it would mean not only that not everything revolved around Earth as stated in the Ptolemaic model, but also showed a secondary celestial body could orbit a moving celestial body, strengthening the heliocentric argument that a moving Earth could retain the Moon.[43] Galileo’s observations were verified by other astronomers of the time period who quickly adopted use of the telescope, including Christoph Scheiner, Johannes Kepler, and Giovan Paulo Lembo.[44] In December 1610, Galileo Galilei used his telescope to observe that Venus showed all phases, just like the Moon. He thought that while this observation was incompatible with the Ptolemaic system, it was a natural consequence of the heliocentric system. However, Ptolemy placed Venus’ deferent and epicycle


8.4. GRAVITATION

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EARTH

Phases of Venus

entirely inside the sphere of the Sun (between the Sun and Mercury), but this was arbitrary; he could just as easily have swapped Venus and Mercury and put them on the other side of the Sun, or made any other arrangement of Venus and Mercury, as long as they were always near a line running from the Earth through the Sun, such as placing the center of the Venus epicycle near the Sun. In this case, if the Sun is the source of all the light, under the Ptolemaic system: If Venus is between Earth and the Sun, the phase of Venus must always be crescent or all dark. If Venus is beyond the Sun, the phase of Venus must always be gibbous or full.

In this depiction of the Tychonic system, the objects on blue orbits (the moon and the sun) revolve around the Earth. The objects on orange orbits (Mercury, Venus, Mars, Jupiter, and Saturn) revolve around the sun. Around all is a sphere of stars, which rotates.

improved the accuracy of celestial observations and predictions. Because the heliocentric model by Copernicus was no more accurate than Ptolemy’s system, new observations were needed to persuade those who still held on to the Geocentric model. However, Kepler’s laws based on Brahe’s data became a problem which geocentrists could not easily overcome.

8.4 Gravitation

In 1687, Isaac Newton stated the law of universal gravitation, described earlier as a hypothesis by Robert Hooke and others. His main achievement was to mathematically derive Kepler’s laws of planetary motion from the law of gravitation, thus helping to prove the latter. This introduced gravitation as the force that both kept the Earth and planets moving through the heavens and also kept the air from flying away. The theory of gravity allowed scientists to construct a plausible heliocentric model for the solar system quickly. In his Principia, Newton explained his system of how gravity, (previously thought of as an occult force) directed the movements of celestial bodies, and kept our solar system in its working order. His descriptions of centripetal force[45] were a breakthrough in scientific thought which used the newly developed differential calculus, and finally replaced the previous schools of scientific thought, i.e. those of Aristotle and Ptolemy. However, the process was gradual.

Johannes Kepler analysed Tycho Brahe's famously accurate observations and afterwards constructed his three laws in 1609 and 1619, based on a heliocentric view where the planets move in elliptical paths. Using these laws, he was the first astronomer to successfully predict a transit of Venus (for the year 1631). The change from circular orbits to elliptical planetary paths dramatically

Several empirical tests of Newton’s theory, explaining the longer period of oscillation of a pendulum at the equator and the differing size of a degree of latitude, gradually became available over the period 1673–1738. In addition, stellar aberration was observed by Robert Hooke in 1674 and tested in a series of observations by Jean Picard over ten years finishing in 1680. However, it was not explained until 1729 when James Bradley provided an approximate

But Galileo saw Venus at first small and full, and later large and crescent. This showed that with a Ptolemaic cosmology, the Venus epicycle can be neither completely inside nor completely outside of the orbit of the Sun. As a result, Ptolemaics abandoned the idea that the epicycle of Venus was completely inside the Sun, and later 17th century competition between astronomical cosmologies focused on variations of Tycho Brahe's Tychonic system (in which the Earth was still at the center of the universe, and around it revolved the Sun, but all other planets revolved around the Sun in one massive set of epicycles), or variations on the Copernican system.


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explanation in terms of the Earth’s revolution about the sun. In 1838, astronomer Friedrich Wilhelm Bessel measured the parallax of the star 61 Cygni successfully, and disproved Ptolemy’s claim that parallax motion did not exist. This finally confirmed the assumptions made by Copernicus, provided accurate, dependable scientific observations, and displayed truly how far away stars were from Earth. A Geocentric frame is useful for many everyday activities and most laboratory experiments, but is a less appropriate choice for solar-system mechanics and space travel. While a heliocentric frame is most useful in those cases, galactic and extra-galactic astronomy is easier if the sun is treated as neither stationary nor the center of the universe, but rotating around the center of our galaxy, and in turn our galaxy is also not at rest in the cosmic background.

8.5 Relativity Albert Einstein and Leopold Infeld wrote in The Evolution of Physics (1938): “Can we formulate physical laws so that they are valid for all CS (=coordinate systems), not only those moving uniformly, but also those moving quite arbitrarily, relative to each other? If this can be done, our difficulties will be over. We shall then be able to apply the laws of nature to any CS. The struggle, so violent in the early days of science, between the views of Ptolemy and Copernicus would then be quite meaningless. Either CS could be used with equal justification. The two sentences, “the sun is at rest and the Earth moves”, or “the sun moves and the Earth is at rest”, would simply mean two different conventions concerning two different CS. Could we build a real relativistic physics valid in all CS; a physics in which there would be no place for absolute, but only for relative, motion? This is indeed possible!"[46]

8.6 Religious and contemporary adherence to geocentrism The Ptolemaic model of the solar system held sway into the early modern age; from the late 16th century onward it was gradually replaced as the consensus description by the heliocentric model. Geocentrism as a separate religious belief, however, never completely died out. In the United States between 1870 and 1920, for example, various members of the Lutheran Church – Missouri Synod published articles disparaging Copernican astronomy, and geocentrism was widely taught within the synod during that period.[47] However, in the 1902 Theological Quarterly, A. L. Graebner claimed that the synod had no doctrinal position on geocentrism, heliocentrism, or any scientific model, unless it were to contradict Scripture.

Map of the Square and Stationary Earth, by Orlando Ferguson (1893)

He stated that any possible declarations of geocentrists within the synod did not set the position of the church body as a whole.[48] Articles arguing that geocentrism was the biblical perspective appeared in some early creation science newsletters associated with the Creation Research Society pointing to some passages in the Bible, which, when taken literally, indicate that the daily apparent motions of the Sun and the Moon are due to their actual motions around the Earth rather than due to the rotation of the Earth about its axis. For example, in Joshua 10:12, the Sun and Moon are said to stop in the sky, and in Psalms 93:1 the world is described as immobile.[49] (Psalms 9:1 says in part “the world is established, firm and secure”.) Contemporary advocates for such religious beliefs include Robert Sungenis (president of Bellarmine Theological Forum and author of the 2006 book Galileo Was Wrong).[50] These people subscribe to the view that a plain reading of the Bible contains an accurate account of the manner in which the universe was created and requires a Geocentric worldview. Most contemporary creationist organizations reject such perspectives.[n 10] After all, Copernicanism was the first major victory of science over religion, so it’s inevitable that some folks would think that everything that’s wrong with the world began there. (Steven Dutch of the University of Wisconsin– Madison)[52] Morris Berman quotes a 2006 survey that show currently some 20% of the U.S. population believe that the sun goes around the Earth (Geocentricism) rather than the Earth goes around the sun (heliocentricism), while a further 9% claimed not to know.[53] Polls conducted by Gallup in the 1990s found that 16% of Germans, 18% of Americans and 19% of Britons hold that the Sun revolves around the Earth.[54] A study conducted in 2005 by Jon D. Miller of Northwestern University, an expert in the public understanding of science and technology,[55] found that about 20%, or one in five, of American adults believe that the


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Sun orbits the Earth.[56] According to 2011 VTSIOM Maurice Finocchiaro, author of a book on the Galileo poll, 32% of Russians believe that the Sun orbits the affair, notes that this is “a view of the relationship beEarth.[57] tween biblical interpretation and scientific investigation that corresponds to the one advanced by Galileo in the "Letter to the Grand Duchess Christina".[58] Pope Pius 8.6.1 Historical positions of the Roman XII (1939–1958) repeated his predecessor’s teaching:

Catholic hierarchy The famous Galileo affair pitted the Geocentric model against the claims of Galileo. In regards to the theological basis for such an argument, two Popes addressed the question of whether the use of phenomenological language would compel one to admit an error in Scripture. Both taught that it would not. Pope Leo XIII (1878– 1903) wrote: we have to contend against those who, making an evil use of physical science, minutely scrutinize the Sacred Book in order to detect the writers in a mistake, and to take occasion to vilify its contents. . . . There can never, indeed, be any real discrepancy between the theologian and the physicist, as long as each confines himself within his own lines, and both are careful, as St. Augustine warns us, “not to make rash assertions, or to assert what is not known as known.” If dissension should arise between them, here is the rule also laid down by St. Augustine, for the theologian: “Whatever they can really demonstrate to be true of physical nature, we must show to be capable of reconciliation with our Scriptures; and whatever they assert in their treatises which is contrary to these Scriptures of ours, that is to Catholic faith, we must either prove it as well as we can to be entirely false, or at all events we must, without the smallest hesitation, believe it to be so.” To understand how just is the rule here formulated we must remember, first, that the sacred writers, or to speak more accurately, the Holy Ghost “Who spoke by them, did not intend to teach men these things (that is to say, the essential nature of the things of the visible universe), things in no way profitable unto salvation.” Hence they did not seek to penetrate the secrets of nature, but rather described and dealt with things in more or less figurative language, or in terms which were commonly used at the time, and which in many instances are in daily use at this day, even by the most eminent men of science. Ordinary speech primarily and properly describes what comes under the senses; and somewhat in the same way the sacred writers-as the Angelic Doctor also reminds us – `went by what sensibly appeared,” or put down what God, speaking to men, signified, in the way men could understand and were accustomed to. (Providentissimus Deus 18).

The first and greatest care of Leo XIII was to set forth the teaching on the truth of the Sacred Books and to defend it from attack. Hence with grave words did he proclaim that there is no error whatsoever if the sacred writer, speaking of things of the physical order “went by what sensibly appeared” as the Angelic Doctor says,[5] speaking either “in figurative language, or in terms which were commonly used at the time, and which in many instances are in daily use at this day, even among the most eminent men of science.” For “the sacred writers, or to speak more accurately – the words are St. Augustine’s – [6] the Holy Spirit, Who spoke by them, did not intend to teach men these things – that is the essential nature of the things of the universe – things in no way profitable to salvation"; which principle “will apply to cognate sciences, and especially to history,"[7] that is, by refuting, “in a somewhat similar way the fallacies of the adversaries and defending the historical truth of Sacred Scripture from their attacks (Divino afflante Spiritu, 3). In 1664 Pope Alexander VII republished the Index Librorum Prohibitorum (List of Prohibited Books) and attached the various decrees connected with those books, including those concerned with heliocentrism. He stated in a Papal Bull that his purpose in doing so was that “the succession of things done from the beginning might be made known [quo rei ab initio gestae series innotescat].”[59] The position of the curia evolved slowly over the centuries towards permitting the heliocentric view. In 1757, during the papacy of Benedict XIV, the Congregation of the Index withdrew the decree which prohibited all books teaching the Earth’s motion, although the Dialogue and a few other books continued to be explicitly included. In 1820, the Congregation of the Holy Office, with the pope’s approval, decreed that Catholic astronomer Giuseppe Settele was allowed to treat the Earth’s motion as an established fact and removed any obstacle for Catholics to hold to the motion of the Earth: The Assessor of the Holy Office has referred the request of Giuseppe Settele, Professor of Optics and Astronomy at La Sapienza University, regarding permission to publish his work Elements of Astronomy in which he espouses the common opinion of the astronomers of our time regarding the Earth’s daily and yearly motions, to His Holiness through Divine Provi-


48

CHAPTER 8. GEOCENTRIC MODEL dence, Pope Pius VII. Previously, His Holiness had referred this request to the Supreme Sacred Congregation and concurrently to the consideration of the Most Eminent and Most Reverend General Cardinal Inquisitor. His Holiness has decreed that no obstacles exist for those who sustain Copernicus’ affirmation regarding the Earth’s movement in the manner in which it is affirmed today, even by Catholic authors. He has, moreover, suggested the insertion of several notations into this work, aimed at demonstrating that the above mentioned affirmation [of Copernicus], as it is has come to be understood, does not present any difficulties; difficulties that existed in times past, prior to the subsequent astronomical observations that have now occurred. [Pope Pius VII] has also recommended that the implementation [of these decisions] be given to the Cardinal Secretary of the Supreme Sacred Congregation and Master of the Sacred Apostolic Palace. He is now appointed the task of bringing to an end any concerns and criticisms regarding the printing of this book, and, at the same time, ensuring that in the future, regarding the publication of such works, permission is sought from the Cardinal Vicar whose signature will not be given without the authorization of the Superior of his Order.[60]

In 1822, the Congregation of the Holy Office removed the prohibition on the publication of books treating of the Earth’s motion in accordance with modern astronomy and Pope Pius VII ratified the decision: The most excellent [cardinals] have decreed that there must be no denial, by the present or by future Masters of the Sacred Apostolic Palace, of permission to print and to publish works which treat of the mobility of the Earth and of the immobility of the sun, according to the common opinion of modern astronomers, as long as there are no other contrary indications, on the basis of the decrees of the Sacred Congregation of the Index of 1757 and of this Supreme [Holy Office] of 1820; and that those who would show themselves to be reluctant or would disobey, should be forced under punishments at the choice of [this] Sacred Congregation, with derogation of [their] claimed privileges, where necessary.[61]

as too of the Redemption of mankind through the Passion and Death of Jesus Christ.”[62] In 1965 the Second Vatican Council stated that, “Consequently, we cannot but deplore certain habits of mind, which are sometimes found too among Christians, which do not sufficiently attend to the rightful independence of science and which, from the arguments and controversies they spark, lead many minds to conclude that faith and science are mutually opposed.”[63] The footnote on this statement is to Msgr. Pio Paschini’s, Vita e opere di Galileo Galilei, 2 volumes, Vatican Press (1964). Pope John Paul II regretted the treatment which Galileo received, in a speech to the Pontifical Academy of Sciences in 1992. The Pope declared the incident to be based on a “tragic mutual miscomprehension”. He further stated: Cardinal Poupard has also reminded us that the sentence of 1633 was not irreformable, and that the debate which had not ceased to evolve thereafter, was closed in 1820 with the imprimatur given to the work of Canon Settele. . . . The error of the theologians of the time, when they maintained the centrality of the Earth, was to think that our understanding of the physical world’s structure was, in some way, imposed by the literal sense of Sacred Scripture. Let us recall the celebrated saying attributed to Baronius “Spiritui Sancto mentem fuisse nos docere quomodo ad coelum eatur, non quomodo coelum gradiatur”. In fact, the Bible does not concern itself with the details of the physical world, the understanding of which is the competence of human experience and reasoning. There exist two realms of knowledge, one which has its source in Revelation and one which reason can discover by its own power. To the latter belong especially the experimental sciences and philosophy. The distinction between the two realms of knowledge ought not to be understood as opposition.[64]

8.6.2 Orthodox Judaism Some Orthodox Jewish leaders, particularly the Lubavitcher Rebbe, maintain a Geocentric model of the universe based on the aforementioned Biblical verses and an interpretation of Maimonides to the effect that he ruled that the Earth is orbited by the sun.[65][66] The Lubavitcher Rebbe also explained that geocentrism is defensible based on the theory of Relativity, which establishes that “when two bodies in space are in motion relative to one another, ... science declares with absolute certainty that from the scientific point of view both possibilities are equally valid, namely that the Earth revolves around the sun, or the sun revolves around the Earth.”[67]

The 1835 edition of the Catholic Index of Prohibited Books for the first time omits the Dialogue from the list.[58] In his 1921 papal encyclical, In praeclara summorum, Pope Benedict XV stated that, “though this Earth on which we live may not be the center of the universe as at one time was thought, it was the scene of the original happiness of our first ancestors, witness of their unhappy fall, While geocentrism is important in Maimonides’ calen-


8.9. SEE ALSO dar calculations,[68] the great majority of Jewish religious scholars, who accept the divinity of the Bible and accept many of his rulings as legally binding, do not believe that the Bible or Maimonides command a belief in geocentrism.[66][69]

49 (flat) world in his Geocentric alternate universe in 1492, instead of discovering North America and South America.

Sir Terry Pratchett’s Discworld, a flat disc balanced on the backs of four elephants which in turn stand on the back of However, there is some evidence that geocentrist be- a giant turtle, is Geocentric (or, perhaps, turtle-centric!) liefs are becoming increasingly common among Ortho- with a small sun and moon in orbit around the main mass. dox Jews.[65][66] Richard Garfinkle's Celestial Matters (1996) is set in a The Zohar implies: “The entire world and those upon it, spin round in a circle like a ball,' both those at the bottom of the ball and those at the top. All God’s creatures, wherever they live on the different parts of the ball, look different (in color, in their features) because the air is different in each place, but they stand erect as all other human beings.

more elaborated Geocentric cosmos, where Earth is divided by two contending factions, the Classical Greecedominated Delian League and the Chinese Middle Kingdom, both of which are capable of flight within an alternate universe based on Ptolemaic astronomy, Aristotle's physics and Taoist thought. Unfortunately, both superpowers have been fighting a thousand-year war since the Therefore there are places in the world where, when some time of Alexander the Great. have light, others have darkness; when some have day, In the C.S. Lewis novel, The Voyage of the Dawn Treader, others have night. one of the Chronicles of Narnia series, the characters involved set out on a naval voyage to discover the edge of the world. The events of the book follow their journey 8.6.3 Islam across a flat, Geocentric “world” and beyond its fringes. Prominent cases of modern geocentrism in Islam are very isolated. Very few individuals promoted a Geocentric view of the universe. One of them was Ahmed Raza Khan Barelvi, a Sunni scholar of Indian subcontinent. He rejected the heliocentric model and wrote a book[70] that explains the movement of sun, moon and other planets around the Earth. The Grand Mufti of Saudi Arabia from 1993 to 1999, Ibn Baz also promoted the Geocentric view between 1966 and 1985.

8.9 See also • Celestial spheres • Firmament • Flat Earth • Religious cosmology • Sphere of fire

8.7 Planetariums The Geocentric (Ptolemaic) model of the solar system is still of interest to planetarium makers, as, for technical reasons, a Ptolemaic-type motion for the planet light apparatus has some advantages over a Copernican-type motion.[71] The celestial sphere, still used for teaching purposes and sometimes for navigation, is also based on a Geocentric system[72] which in effect ignores parallax. However this effect is negligible at the scale of accuracy that applies to a planetarium.

8.8 Geocentric models in fiction Alternate history science fiction has produced some literature of interest on the proposition that some alternate universes and Earths might indeed have laws of physics and cosmologies that are Ptolemaic and Aristotelian in design. This subcategory began with Philip Jose Farmer's short story, "Sail On! Sail On!" (1952), where Columbus has access to radio technology, and where his Spanishfinanced exploratory and trade fleet sail off the edge of the

8.10 Notes [1] The Egyptian universe was substantially similar to the Babylonian universe; it was pictured as a rectangular box with a north-south orientation and with a slightly concave surface, with Egypt in the center. A good idea of the similarly primitive state of Hebrew astronomy can be gained from Biblical writings, such as the Genesis creation story and the various Psalms that extol the firmament, the stars, the sun, and the earth. The Hebrews saw the earth as an almost flat surface consisting of a solid and a liquid part, and the sky as the realm of light in which heavenly bodies move. The earth rested on cornerstones and could not be moved except by Jehovah (as in an earthquake). According to the Hebrews, the sun and the moon were only a short distance from one another[3] [2] The picture of the universe in Talmudic texts has the Earth in the center of creation with heaven as a hemisphere spread over it. The Earth is usually described as a disk encircled by water. Interestingly, cosmological and metaphysical speculations were not to be cultivated in public nor were they to be committed to writing. Rather, they were considered as “secrets of the Torah not to be


50

CHAPTER 8. GEOCENTRIC MODEL

passed on to all and sundry” (Ketubot 112a). While study of God’s creation was not prohibited, speculations about “what is above, what is beneath, what is before, and what is after” (Mishnah Hagigah: 2) were restricted to the intellectual elite.[4] [3] “firmament – The division made by God, according to the P account of creation, to restrain the cosmic water and form the sky (Gen. 1: 6–8). Hebrew cosmology pictured a flat earth, over which was a dome-shaped firmament, supported above the earth by mountains, and surrounded by waters. Holes or sluices (windows, Gen. 7: 11) allowed the water to fall as rain. The firmament was the heavens in which God set the sun (Ps. 19: 4) and the stars (Gen. 1: 14) on the fourth day of the creation. There was more water under the earth (Gen. 1: 7) and during the Flood the two great oceans joined up and covered the earth; sheol was at the bottom of the earth (Isa. 14: 9; Num. 16: 30).”[6] [4] The cosmographical structure assumed by this text is the ancient, traditional flat earth model that was common throughout the Near East and that persisted in Jewish tradition because of its place in the religiously authoritative biblical materials.[7] [5] “The term “firmament” (‫רקיע‬- rāqîa') denotes the atmosphere between the heavenly realm and the earth (Gen. 1:6–7, 20) where the celestial bodies move (Gen. 1:14– 17). It can also be used as a synonym for “heaven” (Gen. 1:8; Ps. 19:2). This “firmament is part of the heavenly structure whether it is the equivalent of “heaven/sky” or is what separates it from the earth. […] The ancient Israelites also used more descriptive terms for how God created the celestial realm, and based on the collection of these more specific and illustrative terms, I would propose that they had two basic ideas of the composition of the heavenly realm. First is the idea that the heavenly realm was imagined as a vast cosmic canopy. The verb used to describe metaphorically how God stretched out this canopy over earth is ‫( הטנ‬nātāh) “stretch out,” or “spread.” “I made the earth, and created humankind upon it; it was my hands that stretched out the heavens, and I commanded all their host (Isa. 45:12).” In the Bible this verb is used to describe the stretching out (pitching) of a tent. Since the texts that mention the stretching out of the sky are typically drawing on creation imagery, it seems that the figure intends to suggest that the heavens are Yahweh’s cosmic tent. One can imagine ancient Israelites gazing up to the stars and comparing the canopy of the sky to the roofs of the tents under which they lived. In fact, if one were to look up at the ceiling of a dark tent with small holes in the roof during the daytime, the roof, with the sunlight shining through the holes, would look very much like the night sky with all its stars. The second image of the material composition of the heavenly realm involves a firm substance. The term ‫( רקיע‬răqîa'), typically translated “firmament,” indicates the expanse above the earth. The root ‫ רקע‬means “stamp out” or “forge.” The idea of a solid, forged surface fits well with Ezekiel 1 where God’s throne rests upon the ‫( רקיע‬răqîa'). According to Genesis 1, the ‫(רקיע‬rāqîa') is the sphere of the celestial bodies (Gen. 1:6–8, 14–17; cf. ben Sira 43:8). It may be that some imagined the ‫ עיקר‬to be a firm substance on which

the celestial bodies rode during their daily journeys across the sky.”[8] [6] In the course of the Second Temple Period Jews, and eventually Christians, began to describe the universe in new terms. The model of the universe inherited form the Hebrew Bible and the Ancient Near East of a flat earth completely surrounded by water with a heavenly realm of the gods arching above from horizon to horizon became obsolete. In the past the heavenly realm was for gods only. It was the place where all events on earth were determined by the gods, and their decisions were irrevocable. The gulf between the gods and humans could not have been greater. The evolution of Jewish cosmography in the course of the Second Temple Period followed developments in Hellenistic astronomy.[9] [7] What is described in Genesis 1:1 to 2:3 was the commonly accepted structure of the universe from at least late in the second millennium BCE to the fourth or third century BCE. It represents a coherent model for the experiences of the people of Mesopotamia through that period. It reflects a world-view that made sense of water coming from the sky and the ground as well as the regular apparent movements of the stars, sun, moon, and planets. There is a clear understanding of the restrictions on breeding between different species of animals and of the way in which human beings had gained control over what were, by then, domestic animals. There is also recognition of the ability of humans to change the environment in which they lived. This same understanding occurred also in the great creation stories of Mesopotamia; these stories formed the basis for the Jewish theological reflections of the Hebrew Scriptures concerning the creation of the world. The Jewish priests and theologians who constructed the narrative took accepted ideas about the structure of the world and reflected theologically on them in the light of their experience and faith. There was never any clash between Jewish and Babylonian people about the structure of the world, but only about who was responsible for it and its ultimate theological meaning. The envisaged structure is simple: Earth was seen as being situated in the middle of a great volume of water, with water both above and below Earth. A great dome was thought to be set above Earth (like an inverted glass bowl), maintaining the water above Earth in its place. Earth was pictured as resting on foundations that go down into the deep. These foundations secured the stability of the land as something that is not floating on the water and so could not be tossed about by wind and wave. The waters surrounding Earth were thought to have been gathered together in their place. The stars, sun, moon, and planets moved in their allotted paths across the great dome above Earth, with their movements defining the months, seasons, and year.[10] [8] From Myth to Cosmos: The earliest speculations about the origin and nature of the world took the form of religious myths. Almost all ancient cultures developed cosmological stories to explain the basic features of the cosmos: Earth and its inhabitants, sky, sea, sun, moon, and stars. For example, for the Babylonians, the creation of the universe was seen as born from a primeval pair of human-like gods. In early Egyptian cosmology, eclipses were explained as the moon being swallowed temporarily


8.11. REFERENCES

51

by a sow or as the sun being attacked by a serpent. For the early Hebrews, whose account is preserved in the biblical book of Genesis, a single God created the universe in stages within the relatively recent past. Such pre-scientific cosmologies tended to assume a flat Earth, a finite past, ongoing active interference by deities or spirits in the cosmic order, and stars and planets (visible to the naked eye only as points of light) that were different in nature from Earth.[11] [9] This argument is given in Book I, Chapter 5, of the Almagest.[14] [10] Donald B. DeYoung, for example, states that “Similar terminology is often used today when we speak of the sun’s rising and setting, even though the earth, not the sun, is doing the moving. Bible writers used the 'language of appearance,' just as people always have. Without it, the intended message would be awkward at best and probably not understood clearly. When the Bible touches on scientific subjects, it is entirely accurate.”[51]

8.11 References [1] Lawson, Russell M. (2004). Science in the Ancient World: An Encyclopedia. ABC-CLIO. pp. 29–30. ISBN 1851095349. [2] Kuhn 1957, pp. 5–20. [3] Abetti, Giorgio (2012). “Cosmology”. Americana (Online ed.). Grolier.

Encyclopedia

[4] Tirosh-Samuelson, Hava (2003). “Topic Overview: Judaism”. In van Huyssteen, J. Wentzel Vrede. Encyclopedia of Science and Religion. 2. New York: Macmillan Reference USA. pp. 477–83. [5] Gandz, Solomon (1953). “The distribution of land and sea on the Earth’s surface according to Hebrew sources”. Proceedings of the American Academy for Jewish Research. 22: 23–53. Like the Midrash and the Talmud, the Targum does not think of a globe of the spherical earth, around which the sun revolves in 24 hours, but of a flat disk of the earth, above which the sun completes its semicircle in an average of 12 hours.

[11] Applebaum, Wilbur (2009). “Astronomy and Cosmology: Cosmology”. In Lerner, K. Lee; Lerner, Brenda Wilmoth. Scientific Thought: In Context. 1. Detroit: Gale. pp. 20– 31 – via Gale Virtual Reference Library. [12] Fraser, Craig G. (2006). The Cosmos: A Historical Perspective. p. 14. [13] Hetherington, Norriss S. (2006). Planetary Motions: A Historical Perspective. p. 28. [14] Crowe 1990, pp. 60–2 [15] Goldstein, Bernard R. (1967). “The Arabic version of Ptolemy’s planetary hypothesis”. Transactions of the American Philosophical Society. 57 (pt. 4): 6. JSTOR 1006040. [16] A. I. Sabra, “Configuring the Universe: Aporetic, Problem Solving, and Kinematic Modeling as Themes of Arabic Astronomy,” Perspectives on Science 6.3 (1998): 288– 330, at pp. 317–18: All Islamic astronomers from Thabit ibn Qurra in the ninth century to Ibn al-Shatir in the fourteenth, and all natural philosophers from al-Kindi to Averroes and later, are known to have accepted ... the Greek picture of the world as consisting of two spheres of which one, the celestial sphere ... concentrically envelops the other. [17] Hoskin, Michael (1999-03-18). The Cambridge Concise History of Astronomy. Cambridge University Press. p. 60. ISBN 9780521576000. [18] Ragep, F. Jamil (2001). “Tusi and Copernicus: The Earth’s motion in context”. Science in Context. Cambridge University Press. 14 (1-2): 145–163. doi:10.1017/s0269889701000060. [19] Ragep, F. Jamil (2001). “Freeing astronomy from philosophy: An aspect of Islamic influence on science”. Osiris. 2nd Series. 16 (Science in Theistic Contexts: Cognitive Dimensions): 49–64, 66–71. doi:10.1086/649338. [20] Setia, Adi (2004). “Fakhr Al-Din Al-Razi on physics and the nature of the physical world: A preliminary survey”. Islam & Science. 2. [21] Alessandro Bausani (1973). “Cosmology and Religion in Islam”. Scientia/Rivista di Scienza. 108 (67): 762.

[6] Browning, W. R. F. (1997). “firmament”. Dictionary of the Bible (Oxford Reference Online ed.). Oxford University Press.

[22] Young, M. J. L., ed. (2006-11-02). Religion, Learning and Science in the 'Abbasid Period. Cambridge University Press. p. 413. ISBN 9780521028875.

[7] Wright, J. Edward (2000). The Early History Of Heaven. Oxford University Press. p. 155.

[23] Nasr, Seyyed Hossein (1993-01-01). An Introduction to Islamic Cosmological Doctrines. SUNY Press. p. 135. ISBN 9781438414195.

[8] Wright 2000, pp. 55–6 [9] Wright 2000, p. 201 [10] Selley, Richard C.; Cocks, L. Robin M.; Plimer, Ian R., eds. (2005). “Biblical Geology”. Encyclopedia of Geology. 1. Amsterdam: Elsevier. p. 253 – via Gale Virtual Reference Library.

[24] Qadir (1989), p. 5–10. [25] Nicolaus Copernicus, Stanford Encyclopedia of Philosophy (2004). [26] Rufus, W. C. (May 1939). “The influence of Islamic astronomy in Europe and the far east”. Popular Astronomy. 47 (5): 233–8. Bibcode:1939PA.....47..233R.


52

CHAPTER 8. GEOCENTRIC MODEL

[27] Hartner, Willy (1955). “The Mercury horoscope of Marcantonio Michiel of Venice”. Vistas in Astronomy. 1: 118–22. Bibcode:1955VA......1...84H. doi:10.1016/0083-6656(55)90016-7. [28] Goldstein, Bernard R. (1972). vation in medieval astronomy”. doi:10.1086/350839.

“Theory and obserIsis. 63 (1): 41.

[29] “Ptolemaic Astronomy, Islamic Planetary Theory, and Copernicus’s Debt to the Maragha School”. Science and Its Times. Thomson Gale. 2006. [30] Samsó, Julio (1970–80). “Al-Bitruji Al-Ishbili, Abu Ishaq”. Dictionary of Scientific Biography. New York: Charles Scribner’s Sons. ISBN 0-684-10114-9. [31] Saliba, George (1994). A History of Arabic Astronomy: Planetary Theories During the Golden Age of Islam. New York University Press. pp. 233–234, 240. ISBN 0814780237. [32] Dallal, Ahmad (1999). “Science, Medicine and Technology”. In Esposito, John. The Oxford History of Islam. New York: Oxford University Press. p. 171. [33] Guessoum, N. (June 2008). “Copernicus and Ibn Al-Shatir: Does the Copernican revolution have Islamic roots?". The Observatory. 128: 231–9. Bibcode:2008Obs...128..231G. [34] Huff, Toby E. (2003). The Rise of Early Modern Science: Islam, China and the West. Cambridge University Press. p. 58. ISBN 9780521529945.

[44] Lattis, James L. (1995). Between Copernicus and Galileo: Christoph Clavius and the Collapse of Ptolemaic Cosmology, University of Chicago Press, pgs 186-190 [45] Densmore, Dana, ed. (2004). Selections from Newton’s Principia. Green Lion Press. p. 12. [46] Einstein, Albert (1938). The Evolution of Physics (1966 ed.). New York: Simon & Schuster. p. 212. ISBN 0671-20156-5. [47] Babinski, E. T., ed. (1995). “Excerpts from Frank Zindler’s 'Report from the center of the universe' and 'Turtles all the way down'". TalkOrigins Archive. Retrieved 2013-12-01. [48] Graebner, A. L. (1902). “Science and the church”. Theological Quarterly. St. Louis, MO: Lutheran Synod of Missouri, Ohio and other states, Concordia Publishing. 6: 37–45. [49] Numbers, Ronald L. (1993). The Creationists: The Evolution of Scientific Creationism. University of California Press. p. 237. ISBN 0520083938. [50] Sefton, Dru (2006-03-30). “In this world view, the sun revolves around the earth”. Times-News. Hendersonville, NC. p. 5A. [51] DeYoung, Donald B. (1997-11-05). “Astronomy and the Bible: Selected questions and answers excerpted from the book”. Answers in Genesis. Retrieved 2013-12-01. [52] Geocentrism lives

[35] Kirmani, M. Zaki; Singh, Nagendra Kr (2005). Encyclopaedia of Islamic Science and Scientists: A-H. Global Vision. ISBN 9788182200586.

[53] Berman, Morris (2006). Dark Ages America: The Final Phase of Empire. W.W. Norton & Company. ISBN 9780393058666.

[36] Johansen, K. F.; Rosenmeier, H. (1998). A History of Ancient Philosophy: From the Beginnings to Augustine. p. 43.

[54] Crabtree, Steve (1999-07-06). “New Poll Gauges Americans’ General Knowledge Levels”. Gallup.

[37] Sarton, George (1953). Ancient Science Through the Golden Age of Greece. p. 290. [38] Eastwood, B. S. (1992-11-01). “Heraclides and heliocentrism – Texts diagrams and interpretations”. Journal for the History of Astronomy. 23: 233. Bibcode:1992JHA....23..233E. [39] Lindberg, David C. (2010). The Beginnings of Western Science: The European Scientific Tradition in Philosophical, Religious, and Institutional Context, Prehistory to A.D. 1450 (2nd ed.). University of Chicago Press. p. 197. ISBN 9780226482040. [40] Lawson 2004, p. 19 [41] Russell, Bertrand (2013) [1945]. A History of Western Philosophy. Routledge. p. 215. ISBN 9781134343676. [42] Finocchiaro, Maurice A. (2008). The Essential Galileo. Indianapolis, IL: Hackett. p. 49. [43] “Galileo and the Telescope”. Commonwealth Scientific and Industrial Research Organisation. Retrieved 17 October 2014.

[55] “Jon D. Miller”. Northwestern University website. Retrieved 2007-07-19. [56] Dean, Cornelia (2005-08-30). “Scientific savvy? In U.S., not much”. New York Times. Retrieved 2007-07-19. [57] 'СОЛНЦЕ – СПУТНИК ЗЕМЛИ', ИЛИ РЕЙТИНГ НАУЧНЫХ ЗАБЛУЖДЕНИЙ РОССИЯН['Sunearth', or rating scientific fallacies of Russians] (in Russian) (Пресс-выпуск №1684 [Press release no. 1684]), ВЦИОМ [All-Russian Center for the Study of Public Opinion], 2011-02-08. [58] Finocchiaro, Maurice A. (1989). The Galileo Affair: A Documentary History. Berkeley: University of California Press. p. 307. ISBN 9780520066625. [59] Index librorum prohibitorum Alexandri VII (in Latin). Rome: Ex typographia Reurendae Camerae Apostolicae. 1664. p. v. [60] “Interdisciplinary Encyclopedia of Religion and Science”. [61] Fantoli, Annibale (1996). Galileo: For Copernicanism and For the Church. University of Notre Dame. p. 475. ISBN 0268010323.


8.13. EXTERNAL LINKS

[62] “In Praeclara Summorum: Encyclical of Pope Benedict XV on Dante to Professors and Students of Literature and Learning in the Catholic World”. Rome. 1921-04-30. § 4. [63] “Pastoral Constitution on the Church in the Modern World 'Gaudium Et Spes’ Promulgated by His Holiness, Pope Paul IV on December 7, 1965”. § 36. Archived from the original on April 11, 2011. [64] Pope John Paul II (1992-11-04). “Faith can never conflict with reason”. L'Osservatore Romano. 44 (1264). (Published English translation). [65] Nussbaum, Alexander (2007-12-19). “Orthodox Jews & science: An empirical study of their attitudes toward evolution, the fossil record, and modern geology”. Skeptic Magazine. Retrieved 2008-12-18. [66] Nussbaum, Alexander (January–April 2002). “Creationism and geocentrism among Orthodox Jewish scientists”. Reports of the National Center for Science Education: 38– 43. [67] Schneersohn, Menachem Mendel; Gotfryd, Arnie (2003). Mind over Matter: The Lubavitcher Rebbe on Science, Technology and Medicine. Shamir. pp. 76ff.; cf. xvi-xvii, 69, 100–1, 171–2, 408ff. ISBN 9789652930804. [68] “Sefer Zemanim: Kiddush HaChodesh: Chapter 11”. Mishneh Torah. Translated by Touger, Eliyahu. ChabadLubavitch Media Center. Halacha 13–14. [69] Rabinowitz, Avi (1987). “EgoCentrism and GeoCentrism; Human Significance and Existential Despair; Bible and Science; Fundamentalism and Skepticalism”. Science & Religion. Retrieved 2013-12-01. Published in Branover, Herman; Attia, Ilana Coven, eds. (1994). Science in the Light of Torah: A B'Or Ha'Torah Reader. Jason Aronson. ISBN 9781568210346. [70] “Fauz e Mubeen Dar Radd e Harkat e Zamin”. [71] Hort, William Jillard (1822). A General View of the Sciences and Arts. p. 182. [72] Kaler, James B. (2002). The Ever-changing Sky: A Guide to the Celestial Sphere. p. 25.

8.12 Bibliography • Crowe, Michael J. (1990). Theories of the World from Antiquity to the Copernican Revolution. Mineola, NY: Dover Publications. ISBN 0486261735. • Dreyer, J.L.E. (1953). A History of Astronomy from Thales to Kepler. New York: Dover Publications. • Evans, James (1998). The History and Practice of Ancient Astronomy. New York: Oxford University Press.

53 • Grant, Edward (1984-01-01). “In Defense of the Earth’s Centrality and Immobility: Scholastic Reaction to Copernicanism in the Seventeenth Century”. Transactions of the American Philosophical Society. New Series. 74 (4): 1–69. doi:10.2307/1006444. ISSN 0065-9746. JSTOR 1006444. Retrieved 2014-10-07. • Heath, Thomas (1913). Aristarchus of Samos. Oxford: Clarendon Press. • Hoyle, Fred (1973). Nicolaus Copernicus. • Koestler, Arthur (1986) [1959]. The Sleepwalkers: A History of Man’s Changing Vision of the Universe. Penguin Books. ISBN 014055212X. 1990 reprint: ISBN 0140192468. • Kuhn, Thomas S. (1957). The Copernican Revolution. Cambridge: Harvard University Press. ISBN 0674171039. • Linton, Christopher M. (2004). From Eudoxus to Einstein—A History of Mathematical Astronomy. Cambridge: Cambridge University Press. ISBN 9780521827508. • Walker, Christopher, ed. (1996). Astronomy Before the Telescope. London: British Museum Press. ISBN 0714117463.

8.13 External links • Another demonstration of the complexity of observed orbits when assuming a Geocentric model of the solar system • Geocentric Perspective animation of the Solar System in 150AD • Ptolemy’s system of astronomy • The Galileo Project – Ptolemaic System


Chapter 9

Geocentric orbit For the motion of the Earth around the Sun, see Earth’s orbit. For the shuttle simulator, see Earth Orbiter 1.

away indefinitely from the Earth. An object at this velocity will enter a parabolic trajectory; above this velocity it will enter a hyperbolic trajectory.

A geocentric orbit or Earth orbit involves any object orbiting the Earth, such as the Moon or artificial satellites. Impulse the integral of a force over the time during In 1997 NASA estimated there were approximately 2,465 which it acts. Measured in (N·sec or lb * sec). artificial satellite payloads orbiting the Earth and 6,216 pieces of space debris as tracked by the Goddard Space Flight Center.[1] Over 16,291 previously launched objects Inclination the angle between a reference plane and another plane or axis. In the sense discussed here the have decayed into the Earth’s atmosphere.[1] reference plane is the Earth’s equatorial plane.

9.1 List of terms and concepts

Orbital characteristics the six parameters of the Keplerian elements needed to specify that orbit uniquely. The following words may have more than one definition or other non-Earth specific definition(s). In the spirit of brevity some of the definitions have been Orbital period as defined here, time it takes a satellite altered or truncated to reflect only their usage on this to make one full orbit around the Earth. page.

Altitude as used here, the height of an object above the average surface of the Earth’s oceans.

Perigee is the nearest approach point of a satellite or celestial body from Earth, at which the orbital velocity will be at its maximum.

Analemma a term in astronomy used to describe the Sidereal day the time it takes for a celestial object to roplot of the positions of the Sun on the celestial tate 360°. For the Earth this is: 23 hours, 56 minsphere throughout one year. Closely resembles a utes, 4.091 seconds. figure-eight. Apogee is the farthest point that a satellite or celestial Solar time as used here, the local time as measured by a sundial. body can go from Earth, at which the orbital velocity will be at its minimum. Eccentricity a measure of how much an orbit deviates from a perfect circle. Eccentricity is strictly defined for all circular and elliptical orbits, and parabolic and hyperbolic trajectories. Equatorial plane as used here, an imaginary plane extending from the equator on the Earth to the celestial sphere.

Velocity an object’s speed in a particular direction. Since velocity is defined as a vector, both speed and direction are required to define it.:

9.2 Geocentric orbit types

Escape velocity as used here, the minimum velocity an The following is a list of different geocentric orbit classiobject without propulsion needs to have to move fications. 54


9.2. GEOCENTRIC ORBIT TYPES

55 Polar orbit - A satellite that passes above or nearly above both poles of the planet on each revolution. Therefore it has an inclination of (or very close to) 90 degrees. Polar sun synchronous orbit - A nearly polar orbit that passes the equator at the same local time on every pass. Useful for image-taking satellites because shadows will be the same on every pass.

Low (cyan) and Medium (yellow) Earth orbit regions to scale. The black dashed line is the geosynchronous orbit. The green dashed line is the 20,230 km orbit used for GPS satellites.

9.2.1

Altitude classifications

Low Earth orbit (LEO) - Geocentric orbits ranging in altitude from 160 kilometers (100 statute miles) to 2,000 kilometres (1,200 mi) above mean sea level. At 160 km, one revolution takes approximately 90 minutes, and the circular orbital speed is 8,000 metres per second (26,000 ft/s). Medium Earth orbit (MEO) - Geocentric orbits with altitudes at apogee ranging between 2,000 kilometres (1,200 mi) and that of the geosynchronous orbit at 35,786 kilometres (22,236 mi). Geosynchronous orbit (GEO) - Geocentric circular orbit with an altitude of 35,786 kilometres (22,236 mi). The period of the orbit equals one sidereal day, coinciding with the rotation period of the Earth. The speed is approximately 3,000 metres per second (9,800 ft/s). High Earth orbit (HEO) - Geocentric orbits with altitudes at apogee higher than that of the geosynchronous orbit. A special case of high Earth orbit is the highly elliptical orbit, where altitude at perigee is less than 2,000 kilometres (1,200 mi).[2]

9.2.2

Inclination classifications

Inclined orbit - An orbit whose inclination in reference to the equatorial plane is not 0.

9.2.3 Eccentricity classifications Circular orbit - An orbit that has an eccentricity of 0 and whose path traces a circle. Elliptic orbit - An orbit with an eccentricity greater than 0 and less than 1 whose orbit traces the path of an ellipse. Hohmann transfer orbit - An orbital maneuver that moves a spacecraft from one circular orbit to another using two engine impulses. This maneuver was named after Walter Hohmann. Geosynchronous transfer orbit A geocentric-elliptic orbit where the perigee is at the altitude of a Low Earth Orbit (LEO) and the apogee at the altitude of a geosynchronous orbit. Highly elliptical orbit (HEO) Geocentric orbit with apogee above 35,786 km and low perigee (about 1,000 km) that result in long dwell times near apogee. Molniya orbit - A highly elliptical orbit with inclination of 63.4° and orbital period of ½ of a sidereal day (roughly 12 hours). Such a satellite spends most of its time over a designated area of the Earth.


56

CHAPTER 9. GEOCENTRIC ORBIT Tundra orbit - A highly elliptical orbit with inclination of 63.4° and orbital period of one sidereal day (roughly 24 hours). Such a satellite spends most of its time over a designated area of the Earth. Hyperbolic trajectory - An “orbit” with eccentricity greater than 1. The object’s velocity reaches some value in excess of the escape velocity, therefore it will escape the gravitational pull of the Earth and continue to travel infinitely with a velocity (relative to Earth) decelerating to some finite value, known as the hyperbolic excess velocity. Escape Trajectory - This trajectory must be used to launch an interplanetary probe away from Earth, because the excess over escape velocity is what changes its heliocentric orbit from that of Earth. Capture Trajectory - This is the mirror image of the escape trajectory; an object traveling with sufficient speed, not aimed directly at Earth, will move toward it and accelerate. In the absence of a decelerating engine impulse to put it into orbit, it will follow the escape trajectory after periapsis. Parabolic trajectory - An “orbit” with eccentricity exactly equal to 1. The object’s velocity equals the escape velocity, therefore it will escape the gravitational pull of the Earth and continue to travel with a velocity (relative to Earth) decelerating to 0. A spacecraft launched from Earth with this velocity would travel some distance away from it, but follow it around the Sun in the same heliocentric orbit. It is possible, but not likely that an object approaching Earth could follow a parabolic capture trajectory, but speed and direction would have to be precise.

9.2.4

Directional classifications

Prograde orbit - an orbit in which the projection of the object onto the equatorial plane revolves about the Earth in the same direction as the rotation of the Earth. Retrograde orbit - an orbit in which the projection of the object onto the equatorial plane

revolves about the Earth in the direction opposite that of the rotation of the Earth.

9.2.5 Geosynchronous classifications Semi-synchronous orbit (SSO) - An orbit with an altitude of approximately 20,200 km (12,600 mi) and an orbital period of approximately 12 hours Geosynchronous orbit (GEO) - Orbits with an altitude of approximately 35,786 km (22,236 mi). Such a satellite would trace an analemma (figure 8) in the sky. Geostationary orbit (GSO): A geosynchronous orbit with an inclination of zero. To an observer on the ground this satellite would appear as a fixed point in the sky. Clarke orbit - Another name for a geostationary orbit. Named after the writer Arthur C. Clarke. Earth orbital libration points: The libration points for objects orbiting Earth are at 105 degrees west and 75 degrees east. More than 160 satellites are gathered at these two points.[3] Supersynchronous orbit - A disposal / storage orbit above GSO/GEO. Satellites will drift west. Subsynchronous orbit A drift orbit close to but below GSO/GEO. Satellites will drift east. Graveyard orbit An orbit a few hundred kilometers above geosynchronous that


9.5. REFERENCES

57

satellites are moved into at the end of their operation. Disposal orbit A synonym for graveyard orbit. Junk orbit A synonym for graveyard orbit.

9.2.6

Special classifications

Sun-synchronous orbit - An orbit which combines altitude and inclination in such a way that the satellite passes over any given point of the planet's surface at the same local solar time. Such an orbit can place a satellite in constant sunlight and is useful for imaging, spy, and weather satellites.

• Areostationary satellite • Escape velocity • Satellite • Space station

9.5 References [1] “Satellite Situation Report, 1997”. NASA Goddard Space Flight Center. 2000-02-01. Archived from the original on 2006-08-23. Retrieved 2006-09-10. [2] Definitions of geocentric orbits from the Goddard Space Flight Center Archived May 27, 2010, at the Wayback Machine. [3] Out-of-Control Satellite Threatens Other Nearby Spacecraft, by Peter B. de Selding, SPACE.com, 5/3/10. Archived May 5, 2010, at the Wayback Machine.

9.6 External links Moon orbit - The orbital characteristics of Earth’s Moon. Average altitude of 384,403 kilometres (238,857 mi), elliptical–inclined orbit.

9.2.7

Non-geocentric classifications

Horseshoe orbit - An orbit that appears to a ground observer to be orbiting a planet but is actually in co-orbit with it. See asteroids 3753 (Cruithne) and 2002 AA29 . Exo-orbit - A maneuver where a spacecraft approaches the height of orbit but lacks the velocity to sustain it. Sub-orbital spaceflight - A synonym for Exo-orbit.

9.3 Tangential velocities at altitude 9.4 See also • Earth’s orbit • List of orbits • Astrodynamics • Celestial sphere • Heliocentric orbit • Areosynchronous satellite

• http://www.freemars.org/jeff/speed/index.htm • http://www.tech-faq.com/medium-earth-orbit. shtml • http://www.hq.nasa.gov/office/pao/History/ conghand/traject.htm • https://web.archive.org/web/20100221072300/ http://www.space.com/scienceastronomy/ solarsystem/second_moon_991029.html • http://www.astro.uwo.ca/~{}wiegert/3753/3753. html • http://www.astro.uwo.ca/~{}wiegert/AA29/AA29. html


Chapter 10

Goddard Space Flight Center “GSFC” redirects here. (disambiguation).

For other uses, see GSFC GSFC, while unmanned planetary missions are managed by the Jet Propulsion Laboratory (JPL) in Pasadena, California.

The Goddard Space Flight Center (GSFC) is a major NASA space research laboratory established on May 1, 1959 as NASA’s first space flight center.[1] GSFC employs approximately 10,000 civil servants and contractors, and is located approximately 6.5 miles (10.5 km) northeast of Washington, D.C. in Greenbelt, Maryland, United States. GSFC, one of ten major NASA field centers, is named in recognition of Dr. Robert H. Goddard (1882–1945), the pioneer of modern rocket propulsion in the United States. GSFC is the largest combined organization of scientists and engineers in the United States dedicated to increasing knowledge of the Earth, the Solar System, and the Universe via observations from space. GSFC is a major U.S. laboratory for developing and operating unmanned scientific spacecraft. GSFC conducts scientific investigation, development and operation of space systems, and development of related technologies. Goddard scientists can develop and support a mission, and Goddard engineers and technicians can design and build the spacecraft for that mission. Goddard scientist John C. Mather shared the 2006 Nobel Prize in Physics for his work on COBE.

10.1 History

Goddard 50th anniversary logo

Main article: History of Goddard Space Flight Center Goddard is NASA’s first, and oldest, space center. Its original charter was to perform five major functions on behalf of NASA: technology development and fabrication, planning, scientific research, technical operations, and project management. The center is organized into several directorates, each charged with one of these key functions.

Until May 1, 1959, NASA’s presence in Greenbelt, Maryland was known as the Beltsville Space Center. It was then renamed the Goddard Space Flight Center (GSFC), after Dr. Robert H. Goddard. Its first 157 employees transferred from the United States Navy's Project Vanguard missile program, but continued their work at the Naval Research Laboratory in Washington, D.C., while GSFC manages operations for many NASA and in- the center was under construction. ternational missions including the Hubble Space Telescope (HST), the Explorer program, the Discovery Pro- Goddard Space Flight Center contributed to Project Mergram, the Earth Observing System (EOS), INTEGRAL, cury, America’s first manned space flight program. The MAVEN, OSIRIS-REx, the Solar and Heliospheric Center assumed a lead role for the project in its early Observatory (SOHO), the Solar Dynamics Observa- days and managed the first 250 employees involved in tory (SDO), and Swift. Past missions managed by the effort, who were stationed at Langley Research CenGSFC include the Rossi X-ray Timing Explorer (RXTE), ter in Hampton, Virginia. However, the size and scope Compton Gamma Ray Observatory, SMM, COBE, IUE, of Project Mercury soon prompted NASA to build a new and ROSAT. Typically, unmanned earth observation mis- Manned Spacecraft Center, now the Johnson Space Censions and observatories in Earth orbit are managed by ter, in Houston, Texas. Project Mercury’s personnel and activities were transferred there in 1961. GSFC also operates two spaceflight tracking and data acquisition networks (the Space Network and the Near Earth Network), develops and maintains advanced space and Earth science data information systems, and develops satellite systems for the National Oceanic and Atmospheric Administration (NOAA).

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10.2. FACILITIES

59 line.

10.2.1 Testing chambers The High Bay Cleanroom located in building 29 is the world’s largest ISO 7 cleanroom with 1.3 million cubic feet of space.[3] Vacuum chambers in adjacent buildings 10 and 7 can be chilled or heated to +/- 200 °C (392 °F). Adjacent building 15 houses the High Capacity Centrifuge which is capable of generating 30 G on up to a 2.5 tons load.[4] The Goddard network (STDN) tracked many early manned and unmanned spacecraft.

10.2.2 High Energy Astrophysics Science Archive Research Center

Goddard Space Flight Center remained involved in the manned space flight program, providing computer support and radar tracking of flights through a worldwide network of ground stations called the Spacecraft Tracking and Data Acquisition Network (STDN). However, the Center focused primarily on designing unmanned satellites and spacecraft for scientific research missions. Goddard pioneered several fields of spacecraft development, including modular spacecraft design, which reduced costs and made it possible to repair satellites in orbit. Goddard’s Solar Max satellite, launched in 1980, was repaired by astronauts on the Space Shuttle Challenger in 1984. The Hubble Space Telescope, launched in 1990, remains in service and continues to grow in capability thanks to its modular design and multiple servicing missions by the Space Shuttle.

The High Energy Astrophysics Science Archive Research Center (HEASARC) is NASA's designated center for the archiving and dissemination of high energy astronomy data and information. Information on X-ray and gamma-ray astronomy and related NASA mission archives are maintained for public information and science access.[5]

10.2.3 Software Assurance Technology Center The Software Assurance Technology Center (SATC) is a NASA department founded in 1992 as part of their Systems Reliability and Safety Office at Goddard Space Flight Center. Its purpose was “to become a center of excellence in software assurance, dedicated to making measurable improvement in both the quality and reliability of software developed for NASA at GSFC”. The Center has been the source of research papers on software metrics, assurance, and risk management.[6]

Today, the center remains involved in each of NASA’s key programs. Goddard has developed more instruments for planetary exploration than any other organization, among them scientific instruments sent to every planet in the Solar System.[2] The Center’s contribution to the Earth Science Enterprise includes several spacecraft in the Earth Observing System fleet as well as EOSDIS, a 10.2.4 science data collection, processing, and distribution system. For the manned space flight program, Goddard develops tools for use by astronauts during extra-vehicular activity, and operates the Lunar Reconnaissance Orbiter, a spacecraft designed to study the Moon in preparation for future manned exploration.

Goddard Visitor Center

10.2 Facilities Goddard’s partly wooded campus is a few miles northeast of Washington, D.C. in Prince George’s County. The center is on Greenbelt Road, which is Maryland Route 193. Baltimore, Annapolis, and NASA Headquarters in Hubble model on display in visitor center. Washington are 30–45 minutes away by highway. Greenbelt also has a train station with access to the Washington The Goddard Visitor Center is open to the public TuesMetro system and the MARC commuter train’s Camden days through Sundays, free of charge, and features dis-


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10.2.5 External facilities GSFC operates three facilities that are not located at the Greenbelt site. These facilities are:

Promotional video for the visitor center.

• The Wallops Flight Facility located in Wallops Island, Virginia was established in 1945, and is one of the oldest launch sites in the world. Wallops manages NASA’s sounding rocket program, and supports approximately 35 missions each year. • The Goddard Institute for Space Studies (GISS) located at Columbia University in New York City, where much of the Center’s theoretical research is conducted. Operated in close association with Columbia and other area universities, the institute provides support research in geophysics, astrophysics, astronomy and meteorology. • The Independent Verification and Validation Facility (IV&V) in Fairmont, West Virginia was established in 1993 to improve the safety, reliability, and quality of software used in NASA missions. GSFC is also responsible for the White Sands Complex, a set of two sites in Las Cruces, NM, but the site is owned by Johnson Space Center as part of the White Sands Test Facility.

10.3 Employees See also: History of the Goddard Space Flight Center § People

plays of spacecraft and technologies developed there. The Hubble Space Telescope is represented by models and deep space imagery from recent missions. The center also features a Science On a Sphere projection system.

Goddard Space Flight Center has a workforce of over 3,000 civil servant employees, 60% of which are engineers and scientists.[7] There are approximately 7,000 supporting contractors on site every day. It is one of the largest concentrations of the world’s premier space scientists and engineers. The Center is organized into 8 directorates, which includes Applied Engineering and Technology, Flight Projects, Science and Exploration, and Safety & Mission Assurance.[8]

The center also features an Educator’s Resource Center available for use by teachers and education volunteers such as Boy and Girl Scout leaders; and hosts special events during the year. As an example, in September 2008 the Center opened its gates for Goddard LaunchFest (see Goddard LaunchFest Site). The event, free to the public, included; robot competitions, tours of Goddard facilities hosted by NASA employees, and live entertainment on the Goddard grounds.

Co-op students from universities in all 50 States can be found around the campus every season through the Cooperative Education Program.[9] During the summers, programs such as the Summer Institute in Engineering and Computer Applications (SIECA) and Excellence through Challenging Exploration and Leadership (EXCEL) provide internship opportunities to students from the US and territories such as Puerto Rico to learn and partake in challenging scientific and engineering work.

Delta rocket on display in the rocket garden


10.5. SCIENCE

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10.4 Missions

ing from the upcoming year to a decade down the road. These operations also vary in what scientists hope they A fact sheet highlighting many of Goddard’s previous will uncover. missions are recorded on a 40th anniversary webpage [10] Particularly noteworthy operations include: the James Webb Space Telescope which will try to study the history of the universe.[13]

10.4.1

Past

Goddard has been involved in designing, building, and 10.5 Science operating spacecraft since the days of Explorer 1, the nation’s first artificial satellite. The list of these missions reflects a diverse set of scientific objectives and goals. The Landsat series of spacecraft has been studying the Earth’s resources since the launch of the first mission in 1972. TIROS-1 launched in 1960 as the first success in a long series of weather satellites. The Spartan platform deployed from the space shuttle, allowing simple, low-cost 2-3 day missions. The second of NASA’s Great Observatories, the Compton Gamma Ray Observatory, operated for nine years before re-entering the Earth’s atmosphere in 2000. Another of Goddard’s space science observatories, the Cosmic Background Explorer, provided unique scientific data about the early universe.[11] In this video, two Goddard technologists explain what innovation means and why it is so important to NASA.

10.4.2

Present

Goddard currently supports the operation of dozens of spacecraft collecting scientific data. These missions include earth science projects like the Earth Observing System (EOS) that includes the Terra, Aqua, and Aura spacecraft flying alongside several projects from other Centers or other countries. Other major Earth science projects that are currently operating include the Tropical Rainfall Measuring Mission (TRMM) and the Global Precipitation Measurement mission (GPM), missions that provide data critical to hurricane predictions. Many Goddard projects support other organizations, such as the US Geological Survey on Landsat-7 and −8, and the National Oceanic and Atmospheric Administration (NOAA) on the Geostationary Operational Environmental Satellite (GOES) system that provide weather predictions.

Addressing Scientific Questions NASA’s missions (and therefore Goddard’s missions) address a broad range of scientific questions generally classified around four key areas: Earth sciences, astrophysics, heliophysics, and the solar system.[14] To simplify, Goddard studies Earth and Space.[15] Within the Earth sciences area, Goddard plays a major role in research to advance our understanding of the Earth as an environmental system, looking at questions related to how the components of that environmental system have developed, how they interact and how they evolve. This is all important to enable scientists to understand the practical impacts of natural and human activities during the coming decades and centuries. Within Space Sciences, Goddard has distinguished itself with the 2006 Nobel Physics Prize given to John Mather and the COBE mission. Beyond the COBE mission, Goddard studies how the universe formed, what it is made of, how its components interact, and how it evolves. The Center also contributes to research seeking to understand how stars and planetary systems form and evolve and studies the nature of the Sun’s interaction with its surroundings.

Other Goddard missions support a variety of space science disciplines. Goddard’s most famous project is the Hubble Space Telescope, a unique science platform that has been breaking new ground in astronomy for nearly 20 years. Other missions such as the Wilkinson Microwave Anisotropy Probe (WMAP) study the structure and evolution of the universe. Other missions such as the Solar and Heliospheric Observatory (SOHO) are curFrom Scientific Questions to Science Missions rently studying the Sun and how its behavior affects life [12] Based on existing knowledge accumulated through previon the Earth. ous missions, new science questions are articulated. Missions are developed in the same way an experiment would 10.4.3 Future be developed using the scientific method. In this context, Goddard does not work as an independent entity but The Goddard community continually works on numer- rather as one of the 10 NASA centers working together ous operations and projects that have launch dates rang- to find answers to these scientific questions.


62 Each mission starts with a set of scientific questions to be answered, a set of scientific requirements for the mission, which build on what has already been discovered by prior missions. Scientific requirements spell out the types data that will need to be collected. These scientific requirements are then transformed into mission concepts that start to specify the kind of spacecraft and scientific instruments need to be developed for these scientific questions to be answered. Within Goddard, the Sciences and Exploration Directorate (SED) leads the center’s scientific endeavors, including the development of technology related to scientific pursuits. Collecting Data in Space – Scientific Instruments Some of the most important technological advances developed by Goddard (and NASA in general) come from the need to innovate with new scientific instruments in order to be able to observe or measure phenomena in space that have never been measured or observed before. Instrument names tend to be known by their initials. In some cases, the mission’s name gives an indication of the type of instrument involved. For example, the James Webb Space Telescope is, as its name indicates, a telescope, but it includes a suite of four distinct scientific instruments: Mid-Infrared Instrument (MIRI); NearInfrared Camera (NIRCam); Near-Infrared Spectrograph (NIRSpec); Fine Guidance Sensor/Near-Infrared Imager and Slitless Spectrograph (FGS-NIRISS).[16] Scientists at Goddard work closely with the engineers to develop these instruments.

CHAPTER 10. GODDARD SPACE FLIGHT CENTER ments have been developed by a range of partners. One of the instruments, the Lunar Orbiter Laser Altimeter (LOLA), was developed by Goddard. LOLA measures landing site slopes and lunar surface roughness in order to generate a 3-D map of the moon.[18] Another mission to be managed by Goddard is MAVEN. MAVEN is the second mission within the Mars Scout Program that is exploring the atmosphere of Mars in support of NASA’s broader efforts to go to Mars. MAVEN carries eight instruments to measure characteristics of Mars’ atmospheric gases, upper atmosphere, solar wind, and ionosphere. Instrument development partners include the University of Colorado at Boulder, and the University of California, Berkeley. Goddard contributed overall project management as well as two of the instruments, two magnetometers. Managing Scientific Data Once a mission is launched and reaches its destination, its instruments start collecting data. The data is transmitted back to earth where it needs to be analyzed and stored for future reference. Goddard manages large collections of scientific data resulting from past and ongoing missions. The Earth Science Division hosts the Goddard Earth Science Data and Information Services Division (GES DISC).[19] It offers Earth science data, information, and services to research scientists, applications scientists, applications users, and students.

The National Space Science Data Center (NSSDC), created at Goddard in 1966, hosts a permanent archive of space science data, including a large collection of images Typically, a mission consists of a spacecraft with an in- from space. strument suite (multiple instruments) on board. In some cases, the scientific requirements dictate the need for multiple spacecraft. For example, the Magnetospheric Multiscale Mission (MMS) studies magnetic reconnec- 10.6 Spinoff technologies tion, a 3-D process. In order to capture data about this complex 3-D process, a set of four spacecraft fly in a Section 102(d) of the National Aeronautics and Space tetrahedral formation. Each of the four spacecraft car- Act of 1958 calls for “the establishment of long-range ries identical instrument suites. MMS is part of a larger studies of the potential benefits to be gained from, the program (Solar Terrestrial Probes) that studies the impact opportunities for, and the problems involved in the utiof the sun on the solar system. lization of aeronautical and space activities for peaceful and scientific purposes.” [20] Because of this mandate, the Goddard’s Scientific Collaborations Technology Utilization Program was established in 1962 In many cases, Goddard works with partners (US Gov- which required technologies to be brought down to Earth ernment agencies, aerospace industry, university-based and commercialized in order to help the US economy and research centers, other countries) that are responsible improve the quality of life.[21] for developing the scientific instruments. In other cases, were spun Goddard develops one or more of the instruments. The Documentation of these technologies that [22] off started in 1976 with “Spinoff 1976”. Since then, individual instruments are then integrated into an instruNASA has produced a yearly publication of these “spinoff ment suite which is then integrated with the spacecraft. In the case of MMS, for example, Southwest Research Insti- technologies” through the Innovative Partnerships Protute (SwRI) was responsible for developing the scientific gram Office. instruments and Goddard provides overall project man- Goddard Space Flight Center has made significant conagement, mission systems engineering, the spacecraft, tributions to the US economy and quality of life with and mission operations.[17] the technologies it has spun off. Here are some examOn the Lunar Reconnaissance Orbiter (LRO), six instru- ples: Weather balloon technology has helped firefighters with its short-range radios; aluminized Mylar in satellites


10.9. REFERENCES has made sports equipment more insulated; laser optics systems have transformed the camera industry and life detection missions on other planets help scientists find bacteria in contaminated food.[23]

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10.9 References [1] Langley Research Center, however, is NASA’s oldest field center [2] Planetary Magnetospheres Laboratory Overview: http:// ssed.gsfc.nasa.gov/code695/

10.7 Community The Goddard Space Flight Center maintains ties with local area communities through external volunteer and educational programs. Employees are encouraged to take part in mentoring programs and take on speaking roles at area schools. On Center, Goddard hosts regular colloquiums in engineering, leadership and science. These events are open to the general public, but attendees must sign up in advance to procure a visitors pass for access to the Center’s main grounds. Passes can be obtained at the security office main gate on Greenbelt Road. Goddard also hosts several different internship opportunities, including NASA DEVELOP at Goddard Space Flight Center.

10.8 Queen Elizabeth II’s visit

[3] “NASA Cleanroom: Hubbles Last Stop”. NASA. [4] “Goddard Testing Chambers”. NASA. [5] “HEASARC: NASA’s Archive of Data on Energetic Phenomena”. nasa.gov. [6] SATC at NASA [7] “NASA - Goddard Information”. Nasa.gov. 2009-02-03. Retrieved 2009-08-29. NASA’s Goddard Space Flight Center (GSFC) is located within the City of Greenbelt, Maryland, approximately 6.5 miles northeast of Washington, D. C. The suburban campus is situated approximately 1 mile northeast of the Capital Beltway/Interstate 495. [8] “NASA - Goddard’s Organizations and Projects”. Nasa.gov. 2009-05-19. Retrieved 2009-08-29. [9] “NASA - Goddard Education Resources”. 2009-02-25. Retrieved 2009-08-29.

Nasa.gov.

[10] “NASA’s Goddard Space Flight Center The First Forty Years” (PDF) (Press release). NASA. April 1999. Retrieved 2009-08-29.

Queen Elizabeth II of the United Kingdom and her husband Prince Philip, Duke of Edinburgh visited Goddard Space Flight Center on Tuesday, May 8, 2007. The [11] For more future missions, see http://www.nasa.gov/ tour of Goddard was near the end of the queen’s visit missions/past.html to commemorate the 400th anniversary of the founding of Jamestown in Virginia. The queen spoke with crew [12] The Lunar Reconnaissance Orbiter (LRO) is mapping out the composition and topography of the moon and the Solar aboard the International Space Station.[24] Dynamics Observatory (SDO) is tracking the sun’s energy and influence on the Earth. For more current missions, see http://www.nasa.gov/missions/index.html

[13] For more future missions, see http://www.nasa.gov/ missions/future/index.html [14] See the NASA Science website – http://nasascience.nasa. gov/ [15] NASA’s Science Strategy documents can be found on the NASA Science site – http://nasascience.nasa.gov/ about-us/science-strategy. [16] For more information about the JWST instrument suite, see the JWST website – http://www.jwst.nasa.gov/ instruments.html. [17] For more information about the Magnetospheric Multiscale Mission (MMS) see the MMS brochure http://www.swri.org/9what/releases/2007/MMS_ – brochure%5B1%5D%5B2%5D.pdf

view of the Visitor’s Center at Goddard Space Flight [18] See additional information about LOLA – http://lunar. Center, with the top of a Delta rocket visible behind the gsfc.nasa.gov/lola.html main building and the gift shop at right. [19] GES DISC website – http://daac.gsfc.nasa.gov/


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[20] “National Aeronautics and Space Act of 1958, As Amended” 25. August 2008 - http://history.nasa.gov/ spaceact-legishistory.pdf [21] National Aeronautics and Space Administration. “Spinoff 2002: Fortieth Anniversary of the Technology Utilization Program”. Introduction, Pg 5 - http://www.sti.nasa.gov/ tto/spinoff2002/spin02.pdf [22] National Aeronautics and Space Administration. Scientific and Technical Information “History of Spinoff” http://www.sti.nasa.gov/tto/spinhist.html [23] For a complete list of spinoffs from GSFC - http: //www.sti.nasa.gov/spinoff/spinsearch?BOOL=AND& ALLFIELDS=&CENTER=Goddard+Space+Flight+ Center&BOOLM=AND&MANUFACT=&STATE= &CATEGORY=&ISSUE=&Spinsort=ISSUED [24] NASA Press Release on Queen Elizabeth II Visit Goddard, May 8, 2007 - Note: The visit followed a signing on April 19 of a statement of intent between NASA and the British National Space Centre, London, that confirmed a mutual desire for discussions on specific areas of potential collaboration involving lunar science and exploration.

10.10 External links • Official website • Dateline Goddard newsletter • Goddard Employees Welfare Association (GEWA) • Goddard Fact Sheets • cleanroom webcam • The Goddard Homer E. Newell Memorial Library • Goddard Visitor Center • Goddard Scientific Visualization Studio • Independent Verification and Validation Facility • Dreams, Hopes, Realities: NASA’s Goddard Space Flight Center, The First Forty Years by Lane E. Wallace, 1999 (full on-line book) • Goddard Amateur Radio Club WA3NAN is known worldwide for their HF retransmissions of space flight missions. • NASA Goddard Space Flight Center Documentary produced by WETA-TV - aired in 2008 Coordinates: 38°59′49″N 76°50′54″W / 38.99694°N 76.84833°W


Chapter 11

Moon This article is about Earth’s natural satellite. For moons The Soviet Union's Luna programme was the first to reach in general, see Natural satellite. For other uses, see the Moon with unmanned spacecraft in 1959; the United Moon (disambiguation). States' NASA Apollo program achieved the only manned missions to date, beginning with the first manned lunar The Moon is Earth's only permanent natural satellite. It is orbiting mission by Apollo 8 in 1968, and six manned luthe fifth-largest natural satellite in the Solar System, and nar landings between 1969 and 1972, with the first being the largest among planetary satellites relative to the size Apollo 11. These missions returned over 380 kg (840 of the planet that it orbits (its primary). It is the second- lb) of lunar rocks, which have been used to develop a densest satellite among those whose densities are known geological understanding of the Moon’s origin, the formation of its internal structure, and its subsequent his(after Jupiter's satellite Io). tory. Since the Apollo 17 mission in 1972, the Moon has The average distance of the Moon from the Earth been visited only by unmanned spacecraft. is 238,855 miles (384,400 km),[10][11] or 1.28 lightseconds. The Moon is thought to have formed about 4.5 billion years ago, not long after Earth. There are several hypotheses for its origin; the most widely accepted explanation is that the Moon formed from the debris left over after a giant impact between Earth and a Mars-sized body called Theia.

11.1 Name and etymology

The Moon is in synchronous rotation with Earth, always showing the same face, with its near side marked by dark volcanic maria that fill the spaces between the bright ancient crustal highlands and the prominent impact craters. It is the second-brightest regularly visible celestial object in Earth’s sky, after the Sun, as measured by illuminance on Earth’s surface. Its surface is actually dark, although compared to the night sky it appears very bright, with a reflectance just slightly higher than that of worn asphalt. Its prominence in the sky and its regular cycle of phases have made the Moon an important cultural influence since ancient times on language, calendars, art, mythology, and apparently, the menstrual cycles of the female of the human species. The Moon’s gravitational influence produces the ocean tides, body tides, and the slight lengthening of the day. The Moon’s current orbital distance is about thirty times the diameter of Earth, with its apparent size in the sky almost the same as that of the Sun, resulting in the Moon covering the Sun nearly precisely in total solar eclipse. This matching of apparent visual size will not continue in the far future. The Moon’s linear distance from Earth is currently increasing at a rate of 3.82 ± 0.07 centimetres (1.504 ± 0.028 in) per year, but this rate is not constant.

The Moon, tinted reddish, during a lunar eclipse

See also: list of lunar deities The usual English proper name for Earth’s natural satellite is “the Moon”.[12][13] The noun moon is derived from moone (around 1380), which developed from mone (1135), which is derived from Old English mōna (dating from before 725), which ultimately stems from Proto-Germanic *mǣnōn, like all Germanic language

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cognates.[14] Occasionally, the name “Luna” is used. In literature, especially science fiction, “Luna” is used to dis- Several mechanisms have been proposed for the Moon’s tinguish it from other moons, while in poetry, the name formation 4.53 billion years ago,[lower-alpha 6] and some has been used to denote personification of our moon.[15] 30–50 million years after the origin of the Solar The principal modern English adjective pertaining to the System.[19] Recent research presented by Rick Carlson Moon is lunar, derived from the Latin Luna. A less indicates a slightly lower age of between 4.40 and 4.45 common adjective is selenic, derived from the Ancient billion years.[20] [21] These mechanisms included the fisGreek Selene (Σελήνη), from which is derived the pre- sion of the Moon from Earth’s crust through centrifugal fix “seleno-" (as in selenography).[16][17] Both the Greek force[22] (which would require too great an initial spin Selene and the Roman goddess Diana were alternatively of Earth),[23] the gravitational capture of a pre-formed called Cynthia.[18] The names Luna, Cynthia, and Selene Moon[24] (which would require an unfeasibly extended are reflected in terminology for lunar orbits in words such atmosphere of Earth to dissipate the energy of the passing as apolune, pericynthion, and selenocentric. The name Di- Moon),[23] and the co-formation of Earth and the Moon together in the primordial accretion disk (which does not ana is connected to dies meaning 'day'. explain the depletion of metals in the Moon).[23] These The Moon hypotheses also cannot account for the high angular momentum of the Earth–Moon system.[25]

Near side of the Moon

The evolution of the Moon and a tour of the Moon

Far side of the Moon

Lunar north pole

Lunar south pole

11.2 Formation

The prevailing hypothesis is that the Earth–Moon system formed as a result of the impact of a Mars-sized body (named Theia) with the proto-Earth Earth (giant impact), that blasted material into orbit about the Earth that then accreted to form the present Earth-Moon system.[26][27] This hypothesis, although not perfect, perhaps best explains the evidence. Eighteen months prior to an October 1984 conference on lunar origins, Bill Hartmann, Roger Phillips, and Jeff Taylor challenged fellow lunar scientists: “You have eighteen months. Go back to your Apollo data, go back to your computer, do whatever you have to, but make up your mind. Don't come to our conference unless you have something to say about the Moon’s birth.” At the 1984 conference at Kona, Hawaii, the giant impact hypothesis emerged as the most popular. Before the conference, there were partisans of the three “traditional” theories, plus a few people who were starting to take the giant impact seriously, and there was a huge apathetic middle who didn’t think the debate would ever be resolved. Afterward there were essentially only two groups: the giant impact camp and the agnostics.[28]

Main articles: Origin of the Moon and Giant impact Giant impacts are thought to have been common in the hypothesis early Solar System. Computer simulations of a giant im-


11.3. PHYSICAL CHARACTERISTICS pact have produced results that are consistent with the mass of the lunar core and the present angular momentum of the Earth–Moon system. These simulations also show that most of the Moon derived from the impactor, rather than the proto-Earth.[29] More recent simulations suggest a larger fraction of the Moon derived from the original Earth mass.[30][31][32][33] Studies of meteorites originating from inner Solar System bodies such as Mars and Vesta show that they have very different oxygen and tungsten isotopic compositions as compared to Earth, whereas Earth and the Moon have nearly identical isotopic compositions. The isotopic equalization of the Earth-Moon system might be explained by the post-impact mixing of the vaporized material that formed the two,[34] although this is debated.[35]

67 an isotopic signature that was identical with rocks from Earth, and were different from almost all other bodies in the Solar System. Because most of the material that went into orbit to form the Moon was thought to come from Theia, this observation was unexpected. In 2007, researchers from the California Institute of Technology announced that there was less than a 1% chance that Theia and Earth had identical isotopic signatures.[40] Published in 2012, an analysis of titanium isotopes in Apollo lunar samples showed that the Moon has the same composition as Earth,[41] which conflicts with what is expected if the Moon formed far from Earth’s orbit or from Theia. Variations on the giant impact hypothesis may explain this data.

The great amount of energy released in the impact event and the subsequent re-accretion of that material into the 11.3 Physical characteristics Earth-Moon system would have melted the outer shell of Earth, forming a magma ocean.[36][37] Similarly, the 11.3.1 Internal structure newly formed Moon would also have been affected and had its own lunar magma ocean; estimates for its depth Main article: Internal structure of the Moon range from about 500 km (300 miles) to its entire depth The Moon is a differentiated body: it has a geochemically (1,737 km (1,079 miles)).[36] While the giant impact hypothesis might explain many lines of evidence, there are still some unresolved questions, most of which involve the Moon’s composition.[38] Oceanus Procellarum (“Ocean of Storms”)

Ancient rift valleys – rectangular structure (visible – topography – GRAIL gravity gradients)

Structure of the Moon

Ancient rift valleys – context.

Ancient rift valleys – closeup (artist’s concept). In 2001, a team at the Carnegie Institute of Washington reported the most precise measurement of the isotopic signatures of lunar rocks.[39] To their surprise, the team found that the rocks from the Apollo program carried

distinct crust, mantle, and core. The Moon has a solid iron-rich inner core with a radius of 240 km (150 mi) and a fluid outer core primarily made of liquid iron with a radius of roughly 300 km (190 mi). Around the core is a partially molten boundary layer with a radius of about 500 km (310 mi).[43] This structure is thought to have developed through the fractional crystallization of a global magma ocean shortly after the Moon’s formation 4.5 billion years ago.[44] Crystallization of this magma ocean would have created a mafic mantle from the precipitation and sinking of the minerals olivine, clinopyroxene, and orthopyroxene; after about three-quarters of the magma ocean had crystallised, lower-density plagioclase minerals could form and float into a crust atop.[45] The final liquids to crystallise would have been initially sandwiched between the crust and mantle, with a high abundance


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CHAPTER 11. MOON

of incompatible and heat-producing elements.[1] Consis- Volcanic features tent with this perspective, geochemical mapping made from orbit suggests the crust of mostly anorthosite.[9] The Main article: Lunar mare Moon rock samples of the flood lavas that erupted onto The dark and relatively featureless lunar plains, clearly the surface from partial melting in the mantle confirm the MARE FRIGORIS MARE SERENITATIS mafic mantle composition, which is more iron rich than Sea of cold Sea of serenity NORTH [1] MARE TRANQUILLITATIS PLATO (crater) that of Earth. The crust is on average about 50 km (31 Sea of tranquility MARE IMBRIUM [1] MARE CRISIUM mi) thick. Sea of showers / rain Sea of crises The Moon is the second-densest satellite in the Solar System, after Io.[46] However, the inner core of the Moon is small, with a radius of about 350 km (220 mi) or less,[1] around 20% of the radius of the Moon. Its composition is not well defined, but is probably metallic iron alloyed with a small amount of sulfur and nickel; analyses of the Moon’s time-variable rotation suggest that it is at least partly molten.[47]

COPERNICUS (crater)

Surface geology

LANGRENUS (crater)

KEPLER (crater)

EAST (on the moon) WEST (in the sky)

WEST (on the moon) EAST (in the sky)

MARE NECTARIS Sea of nectar

OCEANUS PROCELLARUM Ocean of storms

STEVINUS (crater) MARE VAPORUM Sea of vapours

GRIMALDI (crater) BYRGIUS (crater) MARE COGNITUM Sea that has become known MARE HUMORUM Sea of moisture

11.3.2

MARE FECUNDITATIS Sea of fecundity/fertility

ARISTARCHUS (crater)

MARE INSULARUM Sea of islands SOUTH

MARE NUBIUM Sea of clouds TYCHO (crater)

Lunar nearside with major maria and craters labeled

Main articles: Geology of the Moon and Moon rocks be seen with the naked eye, are called maria (Latin for The topography of the Moon has been measured with “seas"; singular mare), as they were once believed to be filled with water;[54] they are now known to be vast solidified pools of ancient basaltic lava. Although similar to terrestrial basalts, lunar basalts have more iron and no minerals altered by water.[55][56] The majority of these lavas erupted or flowed into the depressions associated with impact basins. Several geologic provinces containing shield volcanoes and volcanic domes are found within the near side “maria”.[57]

Topography of the Moon

laser altimetry and stereo image analysis.[48] Its most visible topographic feature is the giant far-side South Pole– Aitken basin, some 2,240 km (1,390 mi) in diameter, the largest crater on the Moon and the second-largest confirmed impact crater in the Solar System.[49][50] At 13 km (8.1 mi) deep, its floor is the lowest point on the surface of the Moon.[49][51] The highest elevations of the Moon’s surface are located directly to the northeast, and it has been suggested might have been thickened by the oblique formation impact of the South Pole–Aitken basin.[52] Other large impact basins, such as Imbrium, Serenitatis, Crisium, Smythii, and Orientale, also possess Evidence of young lunar volcanism regionally low elevations and elevated rims.[49] The far side of the lunar surface is on average about 1.9 km (1.2 Almost all maria are on the near side of the Moon, and mi) higher than that of the near side.[1] cover 31% of the surface of the near side,[58] compared The discovery of fault scarp cliffs by the Lunar Re- with 2% of the far side.[59] This is thought to be due connaissance Orbiter suggest that the Moon has shrunk to a concentration of heat-producing elements under the within the past billion years, by about 90 metres (300 crust on the near side, seen on geochemical maps obft).[53] Similar shrinkage features exist on Mercury. tained by Lunar Prospector's gamma-ray spectrometer,


11.3. PHYSICAL CHARACTERISTICS which would have caused the underlying mantle to heat up, partially melt, rise to the surface and erupt.[45][60][61] Most of the Moon’s mare basalts erupted during the Imbrian period, 3.0–3.5 billion years ago, although some radiometrically dated samples are as old as 4.2 billion years.[62] Until recently, the youngest eruptions, dated by crater counting, appeared to have been only 1.2 billion years ago.[63] In 2006, a study of Ina, a tiny depression in Lacus Felicitatis, found jagged, relatively dust-free features that, due to the lack of erosion by infalling debris, appeared to be only 2 million years old.[64] Moonquakes and releases of gas also indicate some continued lunar activity.[64] In 2014 NASA announced “widespread evidence of young lunar volcanism” at 70 irregular mare patches identified by the Lunar Reconnaissance Orbiter, some less than 50 million years old. This raises the possibility of a much warmer lunar mantle than previously believed, at least on the near side where the deep crust is substantially warmer due to the greater concentration of radioactive elements.[65][66][67][68] Just prior to this, evidence has been presented for 2–10 million years younger basaltic volcanism inside Lowell crater,[69][70] Orientale basin, located in the transition zone between the near and far sides of the Moon. An initially hotter mantle and/or local enrichment of heat-producing elements in the mantle could be responsible for prolonged activities also on the far side in the Orientale basin.[71][72]

69

Lunar crater Daedalus on the Moon’s far side

of these craters are well-preserved. Although only a few multi-ring basins have been definitively dated, they are useful for assigning relative ages. Because impact craters accumulate at a nearly constant rate, counting the number of craters per unit area can be used to estimate the age of the surface.[78] The radiometric ages of impactmelted rocks collected during the Apollo missions cluster The lighter-coloured regions of the Moon are called ter- between 3.8 and 4.1 billion years old: this has been used rae, or more commonly highlands, because they are to propose a Late Heavy Bombardment of impacts.[79] higher than most maria. They have been radiometrically dated to having formed 4.4 billion years ago, and Blanketed on top of the Moon’s crust is a highly may represent plagioclase cumulates of the lunar magma comminuted (broken into ever smaller particles) and ocean.[62][63] In contrast to Earth, no major lunar moun- impact gardened surface layer called regolith, formed by tains are believed to have formed as a result of tectonic impact processes. The finer regolith, the lunar soil of silicon dioxide glass, has a texture resembling snow and events.[73] a scent resembling spent gunpowder.[80] The regolith of The concentration of maria on the Near Side likely re- older surfaces is generally thicker than for younger surflects the substantially thicker crust of the highlands of faces: it varies in thickness from 10–20 km (6.2–12.4 the Far Side, which may have formed in a slow-velocity mi) in the highlands and 3–5 km (1.9–3.1 mi) in the impact of a second moon of Earth a few tens of millions maria.[81] Beneath the finely comminuted regolith layer of years after their formation.[74][75] is the megaregolith, a layer of highly fractured bedrock many kilometres thick.[82] Impact craters Further information: List of craters on the Moon The other major geologic process that has affected the Moon’s surface is impact cratering,[76] with craters formed when asteroids and comets collide with the lunar surface. There are estimated to be roughly 300,000 craters wider than 1 km (0.6 mi) on the Moon’s near side alone.[77] The lunar geologic timescale is based on the most prominent impact events, including Nectaris, Imbrium, and Orientale, structures characterized by multiple rings of uplifted material, between hundreds and thousands of kilometres in diameter and associated with a broad apron of ejecta deposits that form a regional stratigraphic horizon.[78] The lack of an atmosphere, Lunar swirls at Reiner Gamma weather and recent geological processes mean that many


70 Lunar swirls Main article: Lunar swirls Lunar swirls are enigmatic features found across the Moon’s surface, which are characterized by a high albedo, appearing optically immature (i.e. the optical characteristics of a relatively young regolith), and often displaying a sinuous shape. Their curvilinear shape is often accentuated by low albedo regions that wind between the bright swirls. Presence of water Main article: Lunar water

CHAPTER 11. MOON to 155 ± 12 kg (342 ± 26 lb).[94] In May 2011, 615–1410 ppm water in melt inclusions in lunar sample 74220 was reported,[95] the famous hightitanium “orange glass soil” of volcanic origin collected during the Apollo 17 mission in 1972. The inclusions were formed during explosive eruptions on the Moon approximately 3.7 billion years ago. This concentration is comparable with that of magma in Earth’s upper mantle. Although of considerable selenological interest, Hauri’s announcement affords little comfort to would-be lunar colonists—the sample originated many kilometers below the surface, and the inclusions are so difficult to access that it took 39 years to find them with a state-of-the-art ion microprobe instrument.

11.3.3 Gravitational field

Liquid water cannot persist on the lunar surface. When Main article: Gravity of the Moon exposed to solar radiation, water quickly decomposes The gravitational field of the Moon has been measured through a process known as photodissociation and is lost to space. However, since the 1960s, scientists have hypothesized that water ice may be deposited by impacting comets or possibly produced by the reaction of oxygen-rich lunar rocks, and hydrogen from solar wind, leaving traces of water which could possibly survive in cold, permanently shadowed craters at either pole on the Moon.[83][84] Computer simulations suggest that up to 14,000 km2 (5,400 sq mi) of the surface may be in permanent shadow.[85] The presence of usable quantities of water on the Moon is an important factor in rendering lunar habitation as a cost-effective plan; the alternative of transporting water from Earth would be prohibitively expensive.[86] In years since, signatures of water have been found to exist on the lunar surface.[87] In 1994, the bistatic radar experiment located on the Clementine spacecraft, indicated the existence of small, frozen pockets of water close to the surface. However, later radar observations by Arecibo, suggest these findings may rather be rocks ejected from young impact craters.[88] In 1998, the neutron spectrometer on the Lunar Prospector spacecraft, showed that high concentrations of hydrogen are present in the first meter of depth in the regolith near the polar regions.[89] Volcanic lava beads, brought back to Earth aboard Apollo 15, showed small amounts of water in their interior.[90]

GRAIL's gravity map of the Moon

through tracking the Doppler shift of radio signals emitted by orbiting spacecraft. The main lunar gravity features are mascons, large positive gravitational anomalies associated with some of the giant impact basins, partly caused by the dense mare basaltic lava flows that fill those basins.[96][97] The anomalies greatly influence the orbit of spacecraft about the Moon. There are some puzzles: lava flows by themselves cannot explain all of the gravitational signature, and some mascons exist that are not linked to [98] The 2008 Chandrayaan-1 spacecraft has since confirmed mare volcanism. the existence of surface water ice, using the on-board Moon Mineralogy Mapper. The spectrometer observed absorption lines common to hydroxyl, in reflected sun- 11.3.4 Magnetic field light, providing evidence of large quantities of water ice, on the lunar surface. The spacecraft showed that con- Main article: Magnetic field of the Moon centrations may possibly be as high as 1,000 ppm.[91] In 2009, LCROSS sent a 2,300 kg (5,100 lb) impactor The Moon has an external magnetic field of about 1–100 into a permanently shadowed polar crater, and detected nanoteslas, less than one-hundredth that of Earth. It does at least 100 kg (220 lb) of water in a plume of ejected not currently have a global dipolar magnetic field and only material.[92][93] Another examination of the LCROSS has crustal magnetization, probably acquired early in ludata showed the amount of detected water to be closer nar history when a dynamo was still operating.[99][100] Al-


11.4. RELATIONSHIP TO EARTH ternatively, some of the remnant magnetization may be from transient magnetic fields generated during large impact events through the expansion of an impact-generated plasma cloud in the presence of an ambient magnetic field. This is supported by the apparent location of the largest crustal magnetizations near the antipodes of the giant impact basins.[101]

71 bly generated from the sublimation of water ice in the regolith.[109] These gases either return into the regolith due to the Moon’s gravity or be lost to space, either through solar radiation pressure or, if they are ionized, by being swept away by the solar wind’s magnetic field.[107]

Dust

11.3.5

Atmosphere

A permanent asymmetric moon dust cloud exists around the Moon, created by small particles from comets. EsMain article: Atmosphere of the Moon timates are 5 tons of comet particles strike the Moon’s The Moon has an atmosphere so tenuous as to be nearly surface each 24 hours. The particles strike the Moon’s surface ejecting moon dust above the Moon. The dust stays above the Moon approximately 10 minutes, taking 5 minutes to rise, and 5 minutes to fall. On average, 120 kilograms of dust are present above the Moon, rising to 100 kilometers above the surface. The dust measurements were made by LADEE's Lunar Dust EXperiment (LDEX), between 20 and 100 kilometers above the surface, during a six-month period. LDEX detected an average of one 0.3 micrometer moon dust particle each minute. Dust particle counts peaked during the Geminid, Quadrantid, Northern Taurid, and Omicron Centaurid meteor showers, when the Earth, and Moon, pass through comet debris. The cloud is asymmetric, more dense near the boundary between the Moon’s dayside and nightside.[110][111]

11.3.6 Seasons

Sketch by the Apollo 17 astronauts. The lunar atmosphere was later studied by LADEE.[102][103]

vacuum, with a total mass of less than 10 metric tons (9.8 long tons; 11 short tons).[104] The surface pressure of this small mass is around 3 × 10−15 atm (0.3 nPa); it varies with the lunar day. Its sources include outgassing and sputtering, a product of the bombardment of lunar soil by solar wind ions.[9][105] Elements that have been detected include sodium and potassium, produced by sputtering (also found in the atmospheres of Mercury and Io); helium-4 and neon[106] from the solar wind; and argon-40, radon-222, and polonium-210, outgassed after their creation by radioactive decay within the crust and mantle.[107][108] The absence of such neutral species (atoms or molecules) as oxygen, nitrogen, carbon, hydrogen and magnesium, which are present in the regolith, is not understood.[107] Water vapour has been detected by Chandrayaan-1 and found to vary with latitude, with a maximum at ~60–70 degrees; it is possi-

The Moon’s axial tilt with respect to the ecliptic is only 1.5424°,[112] much less than the 23.44° of Earth. Because of this, the Moon’s solar illumination varies much less with season, and topographical details play a crucial role in seasonal effects.[113] From images taken by Clementine in 1994, it appears that four mountainous regions on the rim of Peary Crater at the Moon’s north pole may remain illuminated for the entire lunar day, creating peaks of eternal light. No such regions exist at the south pole. Similarly, there are places that remain in permanent shadow at the bottoms of many polar craters,[85] and these dark craters are extremely cold: Lunar Reconnaissance Orbiter measured the lowest summer temperatures in craters at the southern pole at 35 K (−238 °C; −397 °F)[114] and just 26 K (−247 °C; −413 °F) close to the winter solstice in north polar Hermite Crater. This is the coldest temperature in the Solar System ever measured by a spacecraft, colder even than the surface of Pluto.[113] Average temperatures of the Moon’s surface are reported, but temperatures of different areas will vary greatly depending upon whether it is in sunlight or shadow.[115]

11.4 Relationship to Earth


72

11.4.1

CHAPTER 11. MOON

Orbit

Main articles: Orbit of the Moon and Lunar theory The Moon makes a complete orbit around Earth

located 1,700 km (1,100 mi) (about a quarter of Earth’s radius) beneath Earth’s surface.[118]

11.4.3 Appearance from Earth See also: Lunar phase, Earthshine, and Observing the Moon The Moon is in synchronous rotation: it rotates about its

Earth–Moon system (schematic)

Moon setting in western sky over the High Desert in California

DSCOVR satellite sees the Moon passing in front of Earth

axis in about the same time it takes to orbit Earth. This results in it nearly always keeping the same face turned towards Earth. The Moon used to rotate at a faster rate, but early in its history, its rotation slowed and became tidally locked in this orientation as a result of frictional effects associated with tidal deformations caused by Earth.[119] With time, the energy of rotation of the Moon on its axis was dissipated as heat, until there was no rotation of the Moon relative to the Earth. The side of the Moon that faces Earth is called the near side, and the opposite the far side. The far side is often inaccurately called the “dark side”, but it is in fact illuminated as often as the near side: once per lunar day, during the new moon phase we observe on Earth when the near side is dark.[120] In 2016, planetary scientists, using data collected on the much earlier Nasa Lunar Prospector mission, found two hydrogenrich areas on opposite sides of the Moon, probably in the form of water ice. It is speculated that these patches were the poles of the Moon billions of years ago, before it was tidally locked to Earth.[121]

with respect to the fixed stars about once every 27.3 days[lower-alpha 7] (its sidereal period). However, because Earth is moving in its orbit around the Sun at the same time, it takes slightly longer for the Moon to show the same phase to Earth, which is about 29.5 days[lower-alpha 8] (its synodic period).[58] Unlike most satellites of other planets, the Moon orbits closer to the ecliptic plane than to the planet’s equatorial plane. The Moon’s orbit is subtly perturbed by the Sun and Earth in many small, complex and interacting ways. For example, the plane of the Moon’s orbital motion gradually rotates, which affects The Moon has an exceptionally low albedo, giving it a reother aspects of lunar motion. These follow-on effects flectance that is slightly brighter than that of worn asphalt. Despite this, it is the brightest object in the sky after the are mathematically described by Cassini’s laws.[116] Sun.[58][lower-alpha 11] This is partly due to the brightness enhancement of the opposition effect; at quarter phase, the Moon is only one-tenth as bright, rather than half as 11.4.2 Relative size bright, as at full moon.[122] The Moon is exceptionally large relative to Earth: a quarter its diameter and 1/81 its mass.[58] It is the largest moon in the Solar System relative to the size of its planet,[lower-alpha 9] though Charon is larger relative to the dwarf planet Pluto, at 1/9 Pluto’s mass.[lower-alpha 10][117] Earth and the Moon are nevertheless still considered a planet–satellite system, rather than a double planet, because their barycentre, the common centre of mass, is

Additionally, colour constancy in the visual system recalibrates the relations between the colours of an object and its surroundings, and because the surrounding sky is comparatively dark, the sunlit Moon is perceived as a bright object. The edges of the full moon seem as bright as the centre, with no limb darkening, due to the reflective properties of lunar soil, which reflects more light back towards the Sun than in other directions. The Moon does appear


11.4. RELATIONSHIP TO EARTH

73

larger when close to the horizon, but this is a purely psychological effect, known as the Moon illusion, first described in the 7th century BC.[123] The full moon subtends an arc of about 0.52° (on average) in the sky, roughly the same apparent size as the Sun (see § Eclipses). The highest altitude of the Moon in the sky varies with the lunar phase and the season of the year. The full moon is highest during winter. The 18.6-year nodes cycle also has an influence: when the ascending node of the lunar orbit is in the vernal equinox, the lunar declination can go as far as 28° each month. This means the Moon can go overhead at latitudes up to 28° from the equator, instead of only 18°. The orientation of the Moon’s crescent also depends on the latitude of the observation site: close to monthly changes of angle between the direction of illuthe equator, an observer can see a smile-shaped crescent mination by the Sun and viewing from Earth, and the [124] moon. phases of the Moon that result The Moon is visible for two weeks every 27.3 days at the North and South Pole. The Moon’s light is used by The illuminated area of the visible sphere (degree of ilzooplankton in the Arctic when the sun is below the horilumination) is given by 12 (1 − cos e) , where e is the [125] zon for months on end. elongation (i.e. the angle between Moon, the observer The distance between the Moon and Earth varies from (on Earth) and the Sun). around 356,400 km (221,500 mi) to 406,700 km (252,700 mi) at perigees (closest) and apogees (farthest), respectively. On 19 March 2011, it was closer to Earth 11.4.4 Tidal effects when at full phase than it has been since 1993, 14% closer than its farthest position in apogee.[126] Reported as a Main articles: Tidal force, Tidal acceleration, Tide, and "super moon", this closest point coincides within an hour Theory of tides of a full moon, and it was 30% more luminous than when The gravitational attraction that masses have for one anat its greatest distance due to its angular diameter being [127][128][129] 14% greater, because 1.142 ≈1.30 . At lower levels, the human perception of reduced brightness as a percentage is provided by the following formula:[130][131] √ actual% reduction perceived% = 100 × reduction 100 When the actual reduction is 1.00 / 1.30, or about 0.770, the perceived reduction is about 0.877, or 1.00 / 1.14. This gives a maximum perceived increase of 14% between apogee and perigee moons of the same phase.[132] There has been historical controversy over whether features on the Moon’s surface change over time. Today, many of these claims are thought to be illusory, resulting from observation under different lighting conditions, poor astronomical seeing, or inadequate drawings. However, outgassing does occasionally occur, and could be responsible for a minor percentage of the reported lunar transient phenomena. Recently, it has been suggested that a roughly 3 km (1.9 mi) diameter region of the lunar surface was modified by a gas release event about a million years ago.[133][134] The Moon’s appearance, like that of the Sun, can be affected by Earth’s atmosphere: common effects are a 22° halo ring formed when the Moon’s light is refracted through the ice crystals of high cirrostratus cloud, and smaller coronal rings when the Moon is seen through thin clouds.[135]

The libration of the Moon over a single lunar month. Also visible is the slight variation in the Moon’s visual size from Earth.

other decreases inversely with the square of the distance of those masses from each other. As a result, the slightly greater attraction that the Moon has for the side of Earth closest to the Moon, as compared to the part of the Earth opposite the Moon, results in tidal forces. Tidal forces affect both the Earth’s crust and oceans.


74 The most obvious effect of tidal forces is to cause two bulges in the Earth’s oceans, one on the side facing the Moon and the other on the side opposite. This results in elevated sea levels called ocean tides.[136] As the Earth spins on its axis, one of the ocean bulges (high tide) is held in place “under” the Moon, while another such tide is opposite. As a result, there are two high tides, and two low tides in about 24 hours.[136] Since the Moon is orbiting the Earth in the same direction of the Earth’s rotation, the high tides occur about every 12 hours and 25 minutes; the 25 minutes is due to the Moon’s time to orbit the Earth. The Sun has the same tidal effect on the Earth, but its forces of attraction are only 40% that of the Moon’s; the Sun’s and Moon’s interplay is responsible for spring and neap tides.[136] If the Earth was a water world (one with no continents) it would produce a tide of only one meter, and that tide would be very predictable, but the ocean tides are greatly modified by other effects: the frictional coupling of water to Earth’s rotation through the ocean floors, the inertia of water’s movement, ocean basins that grow shallower near land, the sloshing of water between different ocean basins.[137] As a result, the timing of the tides at most points on the Earth is a product of observations that are explained, incidentally, by theory. While gravitation causes acceleration and movement of the of the Earth’s fluid oceans, gravitational coupling between the Moon and Earth’s solid body is mostly elastic and plastic. The result is a further tidal effect of the Moon on the Earth that causes a bulge of the solid portion of the Earth nearest the Moon that acts as a torque in opposition to the Earth’s rotation. This “drains” angular momentum and rotational kinetic energy from Earth’s spin, slowing the Earth’s rotation.[136][138] That angular momentum, lost from the Earth, is transfered to the Moon in a process (confusingly known as tidal acceleration), which lifts the Moon into a higher orbit and results in its lower orbital speed about the Earth. Thus the distance between Earth and Moon is increasing, and the Earth’s spin is slowing in reaction.[138] Measurements from laser reflectors left during the Apollo missions (lunar ranging experiments) have found that the Moon’s distance increases by 38 mm (1.5 in) per year[139] (roughly the rate at which human fingernails grow).[140] Atomic clocks also show that Earth’s day lengthens by about 15 microseconds every year,[141] slowly increasing the rate at which UTC is adjusted by leap seconds. Left to run its course, this tidal drag would continue until the spin of Earth and the orbital period of the Moon matched, creating mutual tidal locking between the two. As a result, the Moon would be suspended in the sky over one meridian, as is already currently the case with Pluto and its moon Charon. However, the Sun will become a red giant long before that, engulfing Earth and we need not worry about the consequences.[142][143] In a like manner, the lunar surface experiences tides of around 10 cm (4 in) amplitude over 27 days, with two components: a fixed one due to Earth, because they are in synchronous rotation, and a varying component from

CHAPTER 11. MOON the Sun.[138] The Earth-induced component arises from libration, a result of the Moon’s orbital eccentricity (if the Moon’s orbit were perfectly circular, there would only be solar tides).[138] Libration also changes the angle from which the Moon is seen, allowing a total of about 59% of its surface to be seen from Earth over time.[58] The cumulative effects of stress built up by these tidal forces produces moonquakes. Moonquakes are much less common and weaker than are earthquakes, although moon quakes can last for up to an hour—a significantly longer time than terrestrial quakes—because of the absence of water to damp out the seismic vibrations. The existence of moonquakes was an unexpected discovery from seismometers placed on the Moon by Apollo astronauts from 1969 through 1972.[144]

11.4.5 Eclipses Main articles: Solar eclipse, Lunar eclipse, and Eclipse cycle

From Earth, the Moon and the Sun appear the same size, as seen in the 1999 solar eclipse (left), whereas from the STEREO-B spacecraft in an Earth-trailing orbit, the Moon appears much smaller than the Sun (right).[145] Eclipses can only occur when the Sun, Earth, and Moon are all in a straight line (termed "syzygy"). Solar eclipses occur at new moon, when the Moon is between the Sun and Earth. In contrast, lunar eclipses occur at full moon, when Earth is between the Sun and Moon. The apparent size of the Moon is roughly the same as that of the Sun, with both being viewed at close to one-half a degree wide. The Sun is much larger than the Moon but it is the precise vastly greater distance that gives it the same apparent size as the much closer and much smaller Moon from the perspective of Earth. The variations in apparent size, due to the non-circular orbits, are nearly the same as well, though occurring in different cycles. This makes possible both total (with the Moon appearing larger than the Sun) and annular (with the Moon appearing smaller than the Sun) solar eclipses.[146] In a total eclipse, the Moon completely covers the disc of the Sun and the solar corona becomes visible to the naked eye. Because the distance between the Moon and Earth is very slowly increasing over time,[136] the angular diameter of the Moon is decreasing. Also, as it evolves toward becoming a red giant, the size of the Sun, and its apparent diameter in the


11.5. OBSERVATION AND EXPLORATION

75

sky, are slowly increasing.[lower-alpha 12] The combination of these two changes means that hundreds of millions of years ago, the Moon would always completely cover the Sun on solar eclipses, and no annular eclipses were possible. Likewise, hundreds of millions of years in the future, the Moon will no longer cover the Sun completely, and total solar eclipses will not occur.[147] Because the Moon’s orbit around Earth is inclined by about 5° to the orbit of Earth around the Sun, eclipses do not occur at every full and new moon. For an eclipse to occur, the Moon must be near the intersection of the two orbital planes.[148] The periodicity and recurrence of eclipses of the Sun by the Moon, and of the Moon by Earth, is described by the saros, which has a period of approximately 18 years.[149] Because the Moon is continuously blocking our view of a half-degree-wide circular area of the sky,[lower-alpha 13][150] the related phenomenon of occultation occurs when a bright star or planet passes behind the Moon and is occulted: hidden from view. In this way, a solar eclipse is an occultation of the Sun. Because the Moon is comparatively close to Earth, occultations of individual stars are not visible everywhere on the planet, nor at the same time. Because of the precession of the lunar orbit, each year different stars are occulted.[151] A study of the Moon in Robert Hooke’s Micrographia, 1665

11.5 Observation and exploration

lunar eclipses,[152] and Indian astronomers had described the Moon’s monthly elongation.[153] The Chinese as11.5.1 Ancient and medieval studies tronomer Shi Shen (fl. 4th century BC) gave instructions for predicting solar and lunar eclipses.[154] Later, the Main articles: Exploration of the Moon: Early history, physical form of the Moon and the cause of moonlight Selenography, and Lunar theory became understood. The ancient Greek philosopher Understanding of the Moon’s cycles was an early devel- Anaxagoras (d. 428 BC) reasoned that the Sun and Moon were both giant spherical rocks, and that the latter reflected the light of the former.[155][156] Although the Chinese of the Han Dynasty believed the Moon to be energy equated to qi, their 'radiating influence' theory also recognized that the light of the Moon was merely a reflection of the Sun, and Jing Fang (78–37 BC) noted the sphericity of the Moon.[157] In the 2nd century AD Lucian wrote a novel where the heroes travel to the Moon, which is inhabited. In 499 AD, the Indian astronomer Aryabhata mentioned in his Aryabhatiya that reflected sunlight is the cause of the shining of the Moon.[158] The astronomer and physicist Alhazen (965–1039) found that sunlight was not reflected from the Moon like a mirror, but that light was emitted from every part of the Moon’s sunlit surface in all directions.[159] Shen Kuo (1031–1095) of the Song dynasty created an allegory equating the waxing and waning of the Moon to a round ball of reflective silver that, when doused with white powder and viewed from the Map of the Moon by Johannes Hevelius from his Selenographia side, would appear to be a crescent.[160] (1647), the first map to include the libration zones In Aristotle's (384–322 BC) description of the universe, opment of astronomy: by the 5th century BC, Babylonian the Moon marked the boundary between the spheres of astronomers had recorded the 18-year Saros cycle of the mutable elements (earth, water, air and fire), and the


76

CHAPTER 11. MOON sand mountains, and introduced the study of the Moon at accuracies possible in earthly geography.[166] Lunar craters, first noted by Galileo, were thought to be volcanic until the 1870s proposal of Richard Proctor that they were formed by collisions.[58] This view gained support in 1892 from the experimentation of geologist Grove Karl Gilbert, and from comparative studies from 1920 to the 1940s,[167] leading to the development of lunar stratigraphy, which by the 1950s was becoming a new and growing branch of astrogeology.[58]

11.5.2 By spacecraft See also: Robotic exploration of the Moon, List of proposed missions to the Moon, Colonization of the Moon, and List of artificial objects on the Moon

20th century Soviet missions Main articles: Luna program and Lunokhod programme Galileo's sketches of the Moon from Sidereus Nuncius

imperishable stars of aether, an influential philosophy that would dominate for centuries.[161] However, in the 2nd century BC, Seleucus of Seleucia correctly theorized that tides were due to the attraction of the Moon, and that their height depends on the Moon’s position relative to the Sun.[162] In the same century, Aristarchus computed the size and distance of the Moon from Earth, obtaining a value of about twenty times the radius of Earth for the distance. These figures were greatly improved by Ptolemy (90–168 AD): his values of a mean distance of 59 times Earth’s radius and a diameter of 0.292 Earth diameters were close to the correct values of about 60 and 0.273 respectively.[163] Archimedes (287–212 BC) designed a planetarium that could calculate the motions of the Moon and other objects in the Solar System.[164] During the Middle Ages, before the invention of the telescope, the Moon was increasingly recognised as a sphere, though many believed that it was “perfectly smooth”.[165] In 1609, Galileo Galilei drew one of the first telescopic drawings of the Moon in his book Sidereus Nuncius and noted that it was not smooth but had mountains and craters. Telescopic mapping of the Moon followed: later in the 17th century, the efforts of Giovanni Battista Riccioli and Francesco Maria Grimaldi led to the system of naming of lunar features in use today. The more exact 1834–36 Mappa Selenographica of Wilhelm Beer and Johann Heinrich Mädler, and their associated 1837 book Der Mond, the first trigonometrically accurate study of lunar features, included the heights of more than a thou-

Luna 2, the first human-made object to reach the surface of the Moon (left) and Soviet Moon rover Lunokhod 1 The Cold War-inspired Space Race between the Soviet Union and the U.S. led to an acceleration of interest in exploration of the Moon. Once launchers had the necessary capabilities, these nations sent unmanned probes on both flyby and impact/lander missions. Spacecraft from the Soviet Union’s Luna program were the first to accomplish a number of goals: following three unnamed, failed missions in 1958,[168] the first human-made object to escape Earth’s gravity and pass near the Moon was Luna 1; the first human-made object to impact the lunar surface was Luna 2, and the first photographs of the normally occluded far side of the Moon were made by Luna 3, all in 1959. The first spacecraft to perform a successful lunar soft landing was Luna 9 and the first unmanned vehicle to orbit the Moon was Luna 10, both in 1966.[58] Rock and soil samples were brought back to Earth by three Luna sample return missions (Luna 16 in 1970, Luna 20 in 1972, and Luna 24 in 1976), which returned 0.3 kg total.[169] Two pioneering robotic rovers landed on the Moon in 1970 and 1973 as a part of Soviet Lunokhod programme.


11.5. OBSERVATION AND EXPLORATION United States missions gram and Moon landing

77

Main articles: Apollo pro-

Earthrise (Apollo 8, 1968)

Neil Armstrong working at the lunar module

Moon rock (Apollo lived instrument stations, including heat flow probes, seismometers, and magnetometers, were installed at the Apollo 12, 14, 15, 16, and 17 landing sites. Direct transmission of data to Earth concluded in late 1977 due The United States launched unmanned probes to develop to budgetary considerations,[177][178] but as the stations’ an understanding of the lunar surface for an eventual lunar laser ranging corner-cube retroreflector arrays are manned landing: the Jet Propulsion Laboratory's Ranger passive instruments, they are still being used. Ranging program produced the first close-up pictures; the Lunar to the stations is routinely performed from Earth-based Orbiter program produced maps of the entire Moon; the stations with an accuracy of a few centimetres, and data Surveyor program landed its first spacecraft four months from this experiment are being used to place constraints after Luna 9. NASA's manned Apollo program was on the size of the lunar core.[179] developed in parallel; after a series of unmanned and manned tests of the Apollo spacecraft in Earth orbit, and spurred on by a potential Soviet lunar flight, in 1968 1980s–2000 After the first Moon race there were Apollo 8 made the first crewed mission to lunar orbit. The years of near quietude but starting in the 1990s, many subsequent landing of the first humans on the Moon in more countries have become involved in direct explo1969 is seen by many as the culmination of the Space ration of the Moon. In 1990, Japan became the third Race.[170] country to place a spacecraft into lunar orbit with its 17, 1972)

Neil Armstrong became the first person to walk on the Moon as the commander of the American mission Apollo 11 by first setting foot on the Moon at 02:56 UTC on 21 July 1969.[171] An estimated 500 million people worldwide watched the transmission by the Apollo TV camera, the largest television audience for a live broadcast at that time.[172][173] The Apollo missions 11 to 17 (except Apollo 13, which aborted its planned lunar landing) returned 380.05 kilograms (837.87 lb) of lunar rock and soil in 2,196 separate samples.[174] The American Moon landing and return was enabled by considerable technological advances in the early 1960s, in domains such as ablation chemistry, software engineering and atmospheric re-entry technology, and by highly competent management of the enormous technical undertaking.[175][176]

Hiten spacecraft. The spacecraft released a smaller probe, Hagoromo, in lunar orbit, but the transmitter failed, preventing further scientific use of the mission.[180] In 1994, the U.S. sent the joint Defense Department/NASA spacecraft Clementine to lunar orbit. This mission obtained the first near-global topographic map of the Moon, and the first global multispectral images of the lunar surface.[181] This was followed in 1998 by the Lunar Prospector mission, whose instruments indicated the presence of excess hydrogen at the lunar poles, which is likely to have been caused by the presence of water ice in the upper few meters of the regolith within permanently shadowed craters.[182]

India, Japan, China, the United States, and the European Space Agency each sent lunar orbiters, especially ISRO's Chandrayaan-1 has contributed to confirming the discovScientific instrument packages were installed on the lu- ery of lunar water ice in permanently shadowed craters at nar surface during all the Apollo landings. Long- the poles and bound into the lunar regolith. The postApollo era has also seen two rover missions: the final


78

CHAPTER 11. MOON rover mission since Lunokhod 2 in 1973. China intends to launch another rover mission (Chang'e 4) before 2020, followed by a sample return mission (Chang'e 5) soon after.[185] Between 4 October 2007 and 10 June 2009, the Japan Aerospace Exploration Agency's Kaguya (Selene) mission, a lunar orbiter fitted with a high-definition video camera, and two small radio-transmitter satellites, obtained lunar geophysics data and took the first highdefinition movies from beyond Earth orbit.[186][187] India’s first lunar mission, Chandrayaan I, orbited from 8 November 2008 until loss of contact on 27 August 2009, creating a high resolution chemical, mineralogical and photo-geological map of the lunar surface, and confirming the presence of water molecules in lunar soil.[188] The Indian Space Research Organisation planned to launch Chandrayaan II in 2013, which would have included a Russian robotic lunar rover.[189][190] However, the failure of Russia’s Fobos-Grunt mission has delayed this project.

An artificially coloured mosaic constructed from a series of 53 images taken through three spectral filters by Galileo' s imaging system as the spacecraft flew over the northern regions of the Moon on December 7, 1992.

Soviet Lunokhod mission in 1973, and China’s ongoing Chang'e 3 mission, which deployed its Yutu rover on 14 December 2013. The Moon remains, under the Outer Space Treaty, free to all nations to explore for peaceful purposes.

Copernicus's central peaks as observed by the LRO, 2012

21st century The European spacecraft SMART-1, the second ionpropelled spacecraft, was in lunar orbit from 15 November 2004 until its lunar impact on 3 September 2006, and made the first detailed survey of chemical elements on the lunar surface.[183] China has pursued an ambitious program of lunar exploration, beginning with Chang'e 1, which successfully orbited the Moon from 5 November 2007 until its controlled lunar impact on 1 March 2009.[184] In its sixteenmonth mission, it obtained a full image map of the Moon. China followed up this success with Chang'e 2 beginning in October 2010, which reached the Moon over twice as fast as Chang'e 1, mapped the Moon at a higher resolution over an eight-month period, then left lunar orbit in favor of an extended stay at the Earth–Sun L2 Lagrangian point, before finally performing a flyby of asteroid 4179 Toutatis on 13 December 2012, and then heading off into deep space. On 14 December 2013, Chang'e 3 improved upon its orbital mission predecessors by landing a lunar lander onto the Moon’s surface, which in turn deployed a lunar rover, named Yutu (Chinese: ; literally “Jade Rabbit”). In so doing, Chang'e 3 made the first lunar soft landing since Luna 24 in 1976, and the first lunar

The Ina formation, 2009 The U.S. co-launched the Lunar Reconnaissance Orbiter (LRO) and the LCROSS impactor and follow-up observation orbiter on 18 June 2009; LCROSS completed its mission by making a planned and widely observed impact in the crater Cabeus on 9 October 2009,[191] whereas LRO is currently in operation, obtaining precise lunar altimetry and high-resolution imagery. In November 2011, the LRO passed over the Aristarchus crater, which spans 40 km (25 mi) and sinks more than 3.5 km (2.2 mi) deep. The crater is one of the most visible ones from Earth.


11.7. LEGAL STATUS

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“The Aristarchus plateau is one of the most geologically 11.7 Legal status diverse places on the Moon: a mysterious raised flat plateau, a giant rille carved by enormous outpourings of lava, fields of explosive volcanic ash, and all surrounded Main article: Space law by massive flood basalts”, said Mark Robinson, principal During the Cold War, the United States Army coninvestigator of the Lunar Reconnaissance Orbiter Camera at Arizona State University. NASA released photos of the crater on 25 December 2011.[192] Two NASA GRAIL spacecraft began orbiting the Moon around 1 January 2012,[193] on a mission to learn more about the Moon’s internal structure. NASA’s LADEE probe, designed to study the lunar exosphere, achieved orbit on 6 October 2013. Upcoming lunar missions include Russia’s Luna-Glob: an unmanned lander with a set of seismometers, and an orbiter based on its failed Martian Fobos-Grunt mission.[194][195] Privately funded lunar exploration has been promoted by the Google Lunar X Prize, announced 13 September 2007, which offers US$20 million to anyone who can land a robotic rover on the Moon and meet other specified criteria.[196] Shackleton Energy Company is building a program to establish operations on the south pole of the Moon to harvest water and supply their Propellant Depots.[197] NASA began to plan to resume manned missions following the call by U.S. President George W. Bush on 14 January 2004 for a manned mission to the Moon by 2019 and the construction of a lunar base by 2024.[198] The Constellation program was funded and construction and testing begun on a manned spacecraft and launch vehicle,[199] and design studies for a lunar base.[200] However, that program has been cancelled in favor of a manned asteroid landing by 2025 and a manned Mars orbit by 2035.[201] India has also expressed its hope to send a manned mission to the Moon by 2020.[202]

11.6 Astronomy from the Moon For many years, the Moon has been recognized as an excellent site for telescopes.[203] It is relatively nearby; astronomical seeing is not a concern; certain craters near the poles are permanently dark and cold, and thus especially useful for infrared telescopes; and radio telescopes on the far side would be shielded from the radio chatter of Earth.[204] The lunar soil, although it poses a problem for any moving parts of telescopes, can be mixed with carbon nanotubes and epoxies in the construction of mirrors up to 50 meters in diameter.[205] A lunar zenith telescope can be made cheaply with ionic liquid.[206] In April 1972, the Apollo 16 mission recorded various astronomical photos and spectra in ultraviolet with the Far Ultraviolet Camera/Spectrograph.[207]

Marius crater

ducted a classified feasibility study in the late 1950s called Project Horizon, to construct a manned military outpost on the Moon, which would have been home to a bombing system targeted at rivals on Earth. The study included the possibility of conducting a lunar-based nuclear test.[208] The Air Force, which at the time was in competition with the Army for a leading role in the space program, developed its own, similar plan called Lunex.[209][210] However, both these proposals were ultimately passed over as the space program was largely transferred from the military to the civilian agency NASA.[210] Although Luna landers scattered pennants of the Soviet Union on the Moon, and U.S. flags were symbolically planted at their landing sites by the Apollo astronauts, no nation claims ownership of any part of the Moon’s surface.[211] Russia and the U.S. are party to the 1967 Outer Space Treaty,[212] which defines the Moon and all outer space as the "province of all mankind".[211] This treaty also restricts the use of the Moon to peaceful purposes, explicitly banning military installations and weapons of mass destruction.[213] The 1979 Moon Agreement was created to restrict the exploitation of the Moon’s resources by any single nation, but as of 2014, it has been signed and ratified by only 16 nations, none of which engages in self-launched human space exploration or has plans to do so.[214] Although several individuals have made claims to the Moon in whole or in part, none of these are considered credible.[215][216][217]


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CHAPTER 11. MOON (Helios/Sol and Selene/Luna). The crescent shape form an early time was used as a symbol representing the Moon. The Moon goddess Selene was represented as wearing a crescent on her headgear in an arrangement reminiscent of horns. The star and crescent arrangement also goes back to the Bronze Age, representing either the Sun and Moon, or the Moon and planet Venus, in combination. It came to represent the goddess Artemis or Hecate, and via the patronage of Hecate came to be used as a symbol of Byzantium. An iconographic tradition of representing Sun and Moon with faces developed in the late medieval period.

Luna, the Moon, from a 1550 edition of Guido Bonatti's Liber astronomiae

The splitting of the moon (Arabic: ‫ )انشقاق القمر‬is a miracle attributed to Muhammad.[219]

11.8 In culture

11.8.2 Calendar

11.8.1

Mythology

Further information: Lunar calendar, Lunisolar calendar, Metonic cycle, Blue moon, and Movable feast

Further information: Lunar deity, Selene, Luna (goddess), Man in the Moon, and Crescent The Moon’s regular phases make it a very convenient The Moon was often personified as a lunar deity in timepiece, and the periods of its waxing and waning form the basis of many of the oldest calendars. Tally sticks, notched bones dating as far back as 20–30,000 years ago, are believed by some to mark the phases of the Moon.[220][221][222] The ~30-day month is an approximation of the lunar cycle. The English noun month and its cognates in other Germanic languages stem from ProtoGermanic *mǣnṓth-, which is connected to the abovementioned Proto-Germanic *mǣnōn, indicating the usage of a lunar calendar among the Germanic peoples (Germanic calendar) prior to the adoption of a solar calendar.[223] The PIE root of moon, *méh1 nōt, derives from the PIE verbal root *meh1 -, “to measure”, “indicat[ing] a functional conception of the moon, i.e. marker of the month” (cf. the English words measure and menstrual),[224][225][226] and echoing the Moon’s importance to many ancient cultures in measuring time (see Latin mensis and Ancient Greek μείς (meis) or μήν (mēn), meaning “month”).[227][228][229][230] Most historical calendars are lunisolar. The 7th-century Islamic calenSun and Moon with faces (1493 woodcut) dar is an exceptional example of a purely lunar calendar. Months are traditionally determined by the visual mythology and religion. A 5,000-year-old rock carving at sighting of the hilal, or earliest crescent moon, over the Knowth, Ireland, may represent the Moon, which would horizon.[231] [218] The contrast bebe the earliest depiction discovered. tween the brighter highlands and the darker maria creates the patterns seen by different cultures as the Man in the Moon, the rabbit and the buffalo, among others. In many 11.8.3 Modern art and literature prehistoric and ancient cultures, the Moon was personified as a deity or other supernatural phenomenon, and Main article: Moon in fiction astrological views of the Moon continue to be propagated today. The Moon has been the subject of many works of art and In the Ancient Near East, the moon god (Sin/Nanna) literature and the inspiration for countless others. It is a was masculine. In Greco-Roman mythology, Sun and motif in the visual arts, the performing arts, poetry, prose Moon are represented as male and female, respectively and music.


11.10. REFERENCES

11.8.4

81

Lunacy

value (for a distant new moon) is based on a similar scaling using the maximum Earth–Moon distance of 407 000 km (given in the factsheet) and by calculating the brightness of the earthshine onto such a new moon. The brightness of the earthshine is [ Earth albedo × (Earth radius / Radius of Moon’s orbit)2 ] relative to the direct solar illumination that occurs for a full moon. (Earth albedo = 0.367; Earth radius = (polar radius × equatorial radius)½ = 6 367 km.)

Further information: Lunar effect The Moon has long been associated with insanity and irrationality; the words lunacy and lunatic (popular shortening loony) are derived from the Latin name for the Moon, Luna. Philosophers Aristotle and Pliny the Elder argued that the full moon induced insanity in susceptible individuals, believing that the brain, which is mostly water, must be affected by the Moon and its power over the tides, but the Moon’s gravity is too slight to affect any single person.[232] Even today, people who believe in a lunar effect claim that admissions to psychiatric hospitals, traffic accidents, homicides or suicides increase during a full moon, but dozens of studies invalidate these claims.[232][233][234][235][236]

11.9 See also • Former classification of planets • Other moons of Earth • 2006 RH120 • List of natural satellites • Tourism on the Moon • Timeline of the far future

11.10 References 11.10.1

Notes

[1] Between 18.29° and 28.58° to Earth’s equator.[1] </ref> [lower-alpha 3] [lower-alpha 4] [lower-alpha 5] [lower-alpha 2] [lower-alpha 10] [lower-alpha 6] [lower-alpha 7] [lower-alpha 8] [lower-alpha 11] [lower-alpha 13]

<ref name='size changes’ group='lower-alpha'> See graph in Sun#Life phases. At present, the diameter of the Sun is increasing at a rate of about five percent per billion years. This is very similar to the rate at which the apparent angular diameter of the Moon is decreasing as it recedes from Earth. [2] There are a number of near-Earth asteroids, including 3753 Cruithne, that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term (Morais et al, 2002). These are quasisatellites – they are not moons as they do not orbit Earth. For more information, see Other moons of Earth. [3] The maximum value is given based on scaling of the brightness from the value of −12.74 given for an equator to Moon-centre distance of 378 000 km in the NASA factsheet reference to the minimum Earth–Moon distance given there, after the latter is corrected for Earth’s equatorial radius of 6 378 km, giving 350 600 km. The minimum

[4] The range of angular size values given are based on simple scaling of the following values given in the fact sheet reference: at an Earth-equator to Moon-centre distance of 378 000 km, the angular size is 1896 arcseconds. The same fact sheet gives extreme Earth–Moon distances of 407 000 km and 357 000 km. For the maximum angular size, the minimum distance has to be corrected for Earth’s equatorial radius of 6 378 km, giving 350 600 km. [5] Lucey et al. (2006) give 107 particles cm−3 by day and 105 particles cm−3 by night. Along with equatorial surface temperatures of 390 K by day and 100 K by night, the ideal gas law yields the pressures given in the infobox (rounded to the nearest order of magnitude): 10−7 Pa by day and 10−10 Pa by night. [6] This age is calculated from isotope dating of lunar rocks. [7] More accurately, the Moon’s mean sidereal period (fixed star to fixed star) is 27.321661 days (27 d 07 h 43 min 11.5 s), and its mean tropical orbital period (from equinox to equinox) is 27.321582 days (27 d 07 h 43 min 04.7 s) (Explanatory Supplement to the Astronomical Ephemeris, 1961, at p.107). [8] More accurately, the Moon’s mean synodic period (between mean solar conjunctions) is 29.530589 days (29 d 12 h 44 min 02.9 s) (Explanatory Supplement to the Astronomical Ephemeris, 1961, at p.107). [9] There is no strong correlation between the sizes of planets and the sizes of their satellites. Larger planets tend to have more satellites, both large and small, than smaller planets. [10] With 27% the diameter and 60% the density of Earth, the Moon has 1.23% of the mass of Earth. The moon Charon is larger relative to its primary Pluto, but Pluto is now considered to be a dwarf planet. [11] The Sun’s apparent magnitude is −26.7, while the full moon’s apparent magnitude is −12.7. [12] [13] On average, the Moon covers an area of 0.21078 square degrees on the night sky.

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[3] Morais, M.H.M.; Morbidelli, A. (2002). “The Population of Near-Earth Asteroids in Coorbital Motion with the Earth”. Icarus. 160 (1): 1–9. Bibcode:2002Icar..160....1M. doi:10.1006/icar.2002.6937. [4] Williams, Dr. David R. (2 February 2006). “Moon Fact Sheet”. NASA (National Space Science Data Center). Retrieved 31 December 2008. [5] Smith, David E.; Zuber, Maria T.; Neumann, Gregory A.; Lemoine, Frank G. (1 January 1997). “Topography of the Moon from the Clementine lidar”. Journal of Geophysical Research. Bibcode:1997JGR...102.1591S. 102 (E1): 1601. doi:10.1029/96JE02940. [6] Williams, James G.; Newhall, XX; Dickey, Jean O. (1996). “Lunar moments, tides, orientation, and coordinate frames”. Planetary and Space Science. 44 (10): 1077–1080. Bibcode:1996P&SS...44.1077W. doi:10.1016/0032-0633(95)00154-9. [7] Matthews, Grant (2008). “Celestial body irradiance determination from an underfilled satellite radiometer: application to albedo and thermal emission measurements of the Moon using CERES”. Applied Optics. 47 (27): 4981–93. Bibcode:2008ApOpt..47.4981M. doi:10.1364/AO.47.004981. PMID 18806861.

CHAPTER 11. MOON

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circle moon to study gravity field”. The Sun News. [212] “How many States have signed and ratified the five interAssociated Press. Retrieved 27 December 2011. national treaties governing outer space?". United Nations Office for Outer Space Affairs. 1 January 2006. ReCovault, C. (4 June 2006). “Russia Plans Ambitious trieved 28 March 2010. Robotic Lunar Mission”. Aviation Week. Retrieved 12 April 2007. [213] “Do the five international treaties regulate military activities in outer space?". United Nations Office for Outer “Russia to send mission to Mars this year, Moon in three Space Affairs. Retrieved 28 March 2010. years”. “TV-Novosti”. 25 February 2009. Retrieved 13 April 2010. [214] “Agreement Governing the Activities of States on the Moon and Other Celestial Bodies”. United Nations Of“About the Google Lunar X Prize”. X-Prize Foundation. fice for Outer Space Affairs. Retrieved 28 March 2010. 2010. Archived from the original on 28 February 2010. [215] “The treaties control space-related activities of States. Retrieved 24 March 2010. What about non-governmental entities active in outer Wall, Mike (14 January 2011). “Mining the Moon’s Waspace, like companies and even individuals?". United Nater: Q&A with Shackleton Energy’s Bill Stone”. Space tions Office for Outer Space Affairs. Retrieved 28 March News. 2010.

[198] “President Bush Offers New Vision For NASA” (Press [216] “Statement by the Board of Directors of the IISL On Claims to Property Rights Regarding The Moon and release). NASA. 14 December 2004. Retrieved 12 April Other Celestial Bodies (2004)" (PDF). International In2007. stitute of Space Law. 2004. Retrieved 28 March 2010. [199] “Constellation”. NASA. Retrieved 13 April 2010. [217] “Further Statement by the Board of Directors of the IISL [200] “NASA Unveils Global Exploration Strategy and Lunar On Claims to Lunar Property Rights (2009)" (PDF). InArchitecture” (Press release). NASA. 4 December 2006. ternational Institute of Space Law. 22 March 2009. ReRetrieved 12 April 2007. trieved 28 March 2010.


11.11. FURTHER READING

89

[218] “Carved and Drawn Prehistoric Maps of the Cosmos”. [235] Kelly, Ivan; Rotton, James; Culver, Roger (1986), “The Space Today Online. 2006. Retrieved 12 April 2007. Moon Was Full and Nothing Happened: A Review of Studies on the Moon and Human Behavior”, Skeptical [219] “Muhammad.” Encyclopædia Britannica. 2007. EncyInquirer, 10 (2): 129–43. Reprinted in The Hundredth clopædia Britannica Online, p.13 Monkey - and other paradigms of the paranormal, edited by Kendrick Frazier, Prometheus Books. Revised and [220] Marshack, Alexander (1991), The Roots of Civilization, updated in The Outer Edge: Classic Investigations of the Colonial Hill, Mount Kisco, NY. Paranormal, edited by Joe Nickell, Barry Karr, and Tom Genoni, 1996, CSICOP. [221] Brooks, A. S. and Smith, C. C. (1987): “Ishango revisited: new age determinations and cultural interpretations”, The [236] Foster, Russell G.; Roenneberg, Till (2008). “Human Responses to the Geophysical Daily, Annual and LuAfrican Archaeological Review, 5 : 65–78. nar Cycles”. Current Biology. 18 (17): R784–R794. doi:10.1016/j.cub.2008.07.003. PMID 18786384. [222] Duncan, David Ewing (1998). The Calendar. Fourth Estate Ltd. pp. 10–11. ISBN 978-1-85702-721-1. [223] For etymology, see Barnhart, Robert K. (1995). The Barnhart Concise Dictionary of Etymology. Harper Collins. p. 487. ISBN 978-0-06-270084-1.. For the lunar calendar of the Germanic peoples, see Birley, A. R. (Trans.) (1999). Agricola and Germany. Oxford World’s Classics. USA: Oxford. p. 108. ISBN 978-0-19-2833006.. [224] Mallory, J. P.; Adams, D. Q. (2006). The Oxford Introduction to Proto-Indo-European and the Proto-IndoEuropean World. Oxford Linguistics. Oxford University Press. pp. 98, 128, 317. ISBN 978-0-19-928791-8.

11.10.3 Bibliography • Needham, Joseph (1986). Science and Civilization in China, Volume III: Mathematics and the Sciences of the Heavens and Earth. Taipei: Caves Books. ISBN 978-0-521-05801-8.

11.11 Further reading • “Revisiting the Moon”. New York Times. Retrieved 8 September 2014.

[225] Harper, Douglas. “measure”. Online Etymology Dictionary.

• The Moon. Discovery 2008. BBC World Service.

[226] Harper, Douglas. “menstrual”. Online Etymology Dictionary.

• Bussey, B.; Spudis, P.D. (2004). The Clementine Atlas of the Moon. Cambridge University Press. ISBN 0-521-81528-2.

[227] Smith, William George (1849). Dictionary of Greek and Roman Biography and Mythology: Oarses-Zygia. 3. J. Walton. p. 768. Retrieved 29 March 2010.

• Cain, Fraser. “Where does the Moon Come From?". Universe Today. Retrieved 1 April 2008. (podcast and transcript)

[228] Estienne, Henri (1846). Thesaurus graecae linguae. 5. Didot. p. 1001. Retrieved 29 March 2010.

• Jolliff, B. (2006). Wieczorek, M.; Shearer, C.; Neal, C., eds. New views of the Moon. Rev. Mineral. Geochem. 60. Chantilly, Virginia: Min. Soc. Amer. p. 721. doi:10.2138/rmg.2006.60.0. ISBN 0-939950-72-3. Retrieved 12 April 2007.

[229] mensis. Charlton T. Lewis and Charles Short. A Latin Dictionary on Perseus Project. [230] μείς in Liddell and Scott. [231] “Islamic Calendars based on the Calculated First Visibility of the Lunar Crescent”. University of Utrecht. Retrieved 11 January 2014.

• Jones, E.M. (2006). “Apollo Lunar Surface Journal”. NASA. Retrieved 12 April 2007. • “Exploring the Moon”. Lunar and Planetary Institute. Retrieved 12 April 2007.

[232] Lilienfeld, Scott O.; Arkowitz, Hal (2009). “Lunacy and the Full Moon”. Scientific American. Retrieved 13 April 2010.

• Mackenzie, Dana (2003). The Big Splat, or How Our Moon Came to Be. Hoboken, New Jersey: John Wiley & Sons, Inc. ISBN 0-471-15057-6.

[233] Rotton, James; Kelly, I. W. (1985). “Much ado about the full moon: A meta-analysis of lunar-lunacy research.”. Psychological Bulletin. 97 (2): 286–306. doi:10.1037/0033-2909.97.2.286.

• Moore, P. (2001). On the Moon. Tucson, Arizona: Sterling Publishing Co. ISBN 0-304-35469-4.

[234] Martens, R.; Kelly, I. W.; Saklofske, D. H. (1988). “Lunar Phase and Birthrate: A 50-year Critical Review”. Psychological Reports. 63 (3): 923–934. doi:10.2466/pr0.1988.63.3.923.

• “Moon Articles”. Planetary Science Research Discoveries. • Spudis, P. D. (1996). The Once and Future Moon. Smithsonian Institution Press. ISBN 1-56098-6344.


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• Taylor, S.R. (1992). Solar system evolution. Cambridge Univ. Press. p. 307. ISBN 0-521-37212-7. • Teague, K. (2006). “The Project Apollo Archive”. Retrieved 12 April 2007. • Wilhelms, D.E. (1987). “Geologic History of the Moon”. U.S. Geological Survey Professional paper. 1348. Retrieved 12 April 2007. • Wilhelms, D.E. (1993). To a Rocky Moon: A Geologist’s History of Lunar Exploration. Tucson, Arizona: University of Arizona Press. ISBN 0-81651065-2. Retrieved 10 March 2009.

11.12 External links • NASA Astronomy Picture of the Day: Video of lunar drive (29 January 2013) • The Moon on Google Maps, a 3-D rendition of the moon akin to Google Earth

11.12.1

Cartographic resources

• “Consolidated Lunar Atlas”. Lunar and Planetary Institute. Retrieved 26 February 2012. • Gazetteer of Planetary Nomenclature (USGS) List of feature names. • “Clementine Lunar Image Browser”. U.S. Navy. 15 October 2003. Retrieved 12 April 2007. • 3D zoomable globes: • “Google Moon”. Google. 2007. Retrieved 12 April 2007. • “Moon”. World Wind Central. NASA. 2007. Retrieved 12 April 2007. • Aeschliman, R. “Lunar Maps”. Planetary Cartography and Graphics. Retrieved 12 April 2007. Maps and panoramas at Apollo landing sites • Japan Aerospace Exploration Agency (JAXA) Kaguya (Selene) images • Large image of the Moon’s north pole area

11.12.2

Observation tools

• “NASA’s SKYCAL—Sky Events Calendar”. NASA Eclipse Home Page. Retrieved 27 August 2007. • “Find moonrise, moonset and moonphase for a location”. 2008. Retrieved 18 February 2008. • “HMNAO’s Moon Watch”. 2005. Retrieved 24 May 2009. See when the next new crescent moon is visible for any location.

11.12.3 General • Lunar shelter (building a lunar base with 3D printing)


Chapter 12

Space Network This article is about the NASA spacecraft communication system. For the Canadian specialty television channel, see Space (TV channel). Space Network (SN) is a NASA program that combines space and ground elements to support spacecraft communications in Earth vicinity. The SN Project Office at Goddard Space Flight Center (GSFC) manages the SN, which consists of:[1] • The geosynchronous Tracking and Data Relay Satellites (TDRS), • Supporting ground terminal systems, • The Bilateration Ranging and Transponder System Second Generation Tracking and Data Relay Satellite (F8-F10 also known as H, I, J) (BRTS), • Merritt Island Launch Annex (MILA) relay, • Network Control Center Data System (NCCDS).

12.1 Satellite generations

communications satellites are allocated longitudes for relaying forward and return service signals to and from customers, any entity with an Earth-orbiting satellite that has an agreement with SN to use its communications services, for data transfer and tracking. An additional TDRS, F1, provides dedicated support to the National Science Foundation (NSF) through the use of the WSC Alternate Relay Terminal (WART). Additional spare TDRSs may be in geosynchronous orbit. All first generation TDRSs (F1-F7, also known as TDRS A-G) carry functionally identical payloads and all second generation TDRSs (F8-F10, also known as TDRS H-J) carry functionally identical payloads. A third generation, TDRS K and L, are planned for launch 2012-2013. See TDRS launch history. Click on the figures to the right, which identify the pertinent communications components and associated parameters of the orbiting relay platforms.

First Generation Tracking and Data Relay Satellite (F1-F7)

Tracking and Data Relay Satellite (TDRS) currently con- 12.2 Coverage sists of first generation (F1-F7), and second generation (F8-F10) satellites. For spacecraft operating in a low earth orbit (LEO) 73 The space segment of the SN consists of up to six op- km to 3000 km altitude, the SN is capable of providerational relay satellites in geosynchronous orbit. These ing tracking and data acquisition services over 100% of 91


92 the spacecraft’s orbit.[2] Spacecraft sent to more distant or exotic destinations rely on either Deep Space Network or their own custom, dedicated networks.

12.3 See also • Deep Space Network • Near Earth Network • Indian Deep Space Network • Tracking and Data Relay Satellite • Eastern Range • SCaN Program

12.4 References [1] NASA, Exploration and Space Communications Projects Division; Goddard Space Flight Center (August 2007). Space Network User’s Guide (SNUG), 2.3.2.1, Dedicated Ground Elements (Rev 9 ed.). National Aeronautics and Space Administration. 450-SNUG. [2] NASA, Exploration and Space Communications Projects Division; Goddard Space Flight Center (August 2007). Space Network User’s Guide (SNUG), 1.1.2, Scope, and 2.3.1.2, TDRS Line-of-Sight Coverage (Rev 9 ed.). National Aeronautics and Space Administration. 450SNUG.

12.5 External links • NASA’s Goddard Space Flight Center Space Network Official Page

CHAPTER 12. SPACE NETWORK


Chapter 13

NASA 13.1 Creation

For other uses, see NASA (disambiguation).

Coordinates: 38°52′59″N 77°0′59″W / 38.88306°N Main article: Creation of NASA From 1946, the National Advisory Committee for Aero77.01639°W The National Aeronautics and Space Administration (NASA) is an independent agency of the executive branch of the United States federal government responsible for the civilian space program as well as aeronautics and aerospace research.[note 1] President Dwight D. Eisenhower established NASA in 1958[7] with a distinctly civilian (rather than military) orientation encouraging peaceful applications in space science. The National Aeronautics and Space Act was passed on July 29, 1958, disestablishing NASA’s predecessor, the National Advisory Committee for Aeronautics (NACA). The new agency became operational on October 1, 1958.[8][9] Since that time, most US space exploration efforts have been led by NASA, including the Apollo moon-landing missions, the Skylab space station, and later the Space Shuttle. Currently, NASA is supporting the International Space Station and is overseeing the development of the Orion Multi-Purpose Crew Vehicle, the Space Launch System and Commercial Crew vehicles. The agency is also responsible for the Launch Services Program (LSP) which provides oversight of launch operations and countdown management for unmanned NASA launches. NASA science is focused on better understanding Earth through the Earth Observing System,[10] advancing heliophysics through the efforts of the Science Mission Directorate’s Heliophysics Research Program,[11] exploring bodies throughout the Solar System with advanced robotic spacecraft missions such as New Horizons,[12] and researching astrophysics topics, such as the Big Bang, through the Great Observatories and associated programs.[13] NASA shares data with various national and international organizations such as from the Greenhouse Gases Observing Satellite.

William H. Pickering, (center) JPL Director, President John F. Kennedy, (right). NASA Administrator James E. Webb (background) discussing the Mariner program, with a model presented.

nautics (NACA) had been experimenting with rocket planes such as the supersonic Bell X-1.[14] In the early 1950s, there was challenge to launch an artificial satellite for the International Geophysical Year (1957–58). An effort for this was the American Project Vanguard. After the Soviet launch of the world’s first artificial satellite (Sputnik 1) on October 4, 1957, the attention of the United States turned toward its own fledgling space efforts. The US Congress, alarmed by the perceived threat to national security and technological leadership (known as the "Sputnik crisis"), urged immediate and swift action; President Dwight D. Eisenhower and his advisers counseled more deliberate measures. This led to an agreement that a new federal agency mainly based on NACA was needed to conduct all non-military activity in space. The Advanced Research Projects Agency (ARPA) was created in February 1958 to develop space technology for military application.[15] On July 29, 1958, Eisenhower signed the National Aeronautics and Space Act, establishing NASA. When it began operations on October 1, 1958, NASA absorbed the

93


94 43-year-old NACA intact; its 8,000 employees, an annual budget of US$100 million, three major research laboratories (Langley Aeronautical Laboratory, Ames Aeronautical Laboratory, and Lewis Flight Propulsion Laboratory) and two small test facilities.[16] A NASA seal was approved by President Eisenhower in 1959.[17] Elements of the Army Ballistic Missile Agency and the United States Naval Research Laboratory were incorporated into NASA. A significant contributor to NASA’s entry into the Space Race with the Soviet Union was the technology from the German rocket program led by Wernher von Braun, who was now working for the Army Ballistic Missile Agency (ABMA), which in turn incorporated the technology of American scientist Robert Goddard's earlier works.[18] Earlier research efforts within the US Air Force[16] and many of ARPA’s early space programs were also transferred to NASA.[19] In December 1958, NASA gained control of the Jet Propulsion Laboratory, a contractor facility operated by the California Institute of Technology.[16]

13.2 Space flight programs

CHAPTER 13. NASA nations including post-Soviet Russia. Some missions include both manned and unmanned aspects, such as the Galileo probe, which was deployed by astronauts in Earth orbit before being sent unmanned to Jupiter.

13.2.1 Manned programs The experimental rocket-powered aircraft programs started by NACA were extended by NASA as support for manned spaceflight. This was followed by a one-man space capsule program, and in turn by a two-man capsule program. Reacting to loss of national prestige and security fears caused by early leads in space exploration by the Soviet Union, in 1961 President John F. Kennedy proposed the ambitious goal “of landing a man on the Moon by the end of [the 1960s], and returning him safely to the Earth.” This goal was met in 1969 by the Apollo program, and NASA planned even more ambitious activities leading to a manned mission to Mars. However, reduction of the perceived threat and changing political priorities almost immediately caused the termination of most of these plans. NASA turned its attention to an Apollo-derived temporary space laboratory, and a semireusable Earth orbital shuttle. In the 1990s, funding was approved for NASA to develop a permanent Earth orbital space station in cooperation with the international community, which now included the former rival, postSoviet Russia. To date, NASA has launched a total of 166 manned space missions on rockets, and thirteen X15 rocket flights above the USAF definition of spaceflight altitude, 260,000 feet (80 km).[20] X-15 rocket plane (1959–68) Main article: North American X-15

At launch control for the May 28, 1964, Saturn I SA-6 launch. Wernher von Braun is at center.

Main article: List of NASA missions NASA has conducted many manned and unmanned spaceflight programs throughout its history. Unmanned programs launched the first American artificial satellites into Earth orbit for scientific and communications purposes, and sent scientific probes to explore the planets of the solar system, starting with Venus and Mars, and including "grand tours" of the outer planets. Manned programs sent the first Americans into low Earth orbit (LEO), won the Space Race with the Soviet Union by landing twelve men on the Moon from 1969 to 1972 in the Apollo program, developed a semi-reusable LEO Space Shuttle, and developed LEO space station capability by itself and with the cooperation of several other

The X-15 was an NACA experimental rocket-powered hypersonic research aircraft, developed in conjunction with the US Air Force and Navy. The design featured a slender fuselage with fairings along the side containing fuel and early computerized control systems.[21] Requests for proposal were issued on December 30, 1954 for the airframe, and February 4, 1955 for the rocket engine. The airframe contract was awarded to North American Aviation in November 1955, and the XLR30 engine contract was awarded to Reaction Motors in 1956, and three planes were built. The X-15 was drop-launched from the wing of one of two NASA Boeing B-52 Stratofortresses, NB52A tail number 52-003, and NB52B, tail number 52008 (known as the Balls 8). Release took place at an altitude of about 45,000 feet (14 km) and a speed of about 500 miles per hour (805 km/h). Twelve pilots were selected for the program from the Air Force, Navy, and NACA (later NASA). A total of 199 flights were made between 1959 and 1968, resulting in the official world record for the highest speed


13.2. SPACE FLIGHT PROGRAMS

95

ever reached by a manned powered aircraft (current as of 2014), and a maximum speed of Mach 6.72, 4,519 miles per hour (7,273 km/h).[22] The altitude record for X-15 was 354,200 feet (107.96 km).[23] Eight of the pilots were awarded Air Force astronaut wings for flying above 260,000 feet (80 km), and two flights by Joseph A. Walker exceeded 100 kilometers (330,000 ft), qualifying as spaceflight according to the International Aeronautical Federation. The X-15 program employed mechanical techniques used in the later manned spaceflight programs, including reaction control system jets for controlling the orientation of a spacecraft, space suits, and horizon definition for navigation.[23] The reentry and landing data collected were valuable to NASA for designing the Space Shuttle.[21]

became the first American in space aboard Freedom 7, launched by a Redstone booster on a 15-minute ballistic (suborbital) flight.[26] John Glenn became the first American to be launched into orbit by an Atlas launch vehicle on February 20, 1962 aboard Friendship 7.[27] Glenn completed three orbits, after which three more orbital flights were made, culminating in L. Gordon Cooper's 22-orbit flight Faith 7, May 15–16, 1963.[28] The Soviet Union (USSR) competed with its own singlepilot spacecraft, Vostok. They sent the first man in space, by launching cosmonaut Yuri Gagarin into a single Earth orbit aboard Vostok 1 in April 1961, one month before Shepard’s flight.[29] In August 1962, they achieved an almost four-day record flight with Andriyan Nikolayev aboard Vostok 3, and also conducted a concurrent Vostok 4 mission carrying Pavel Popovich.

Project Mercury (1959–63) Project Gemini (1961–66) Main article: Project Mercury Friendship 7, first US manned orbital spaceflight

Mercury-Atlas

6

launch

on

February 20, 1962

Ed White performs the first US spacewalk in 1965 during the Gemini 4.

Still frame of John Glenn in orbit from camera inside Friendship 7 Main article: Project Gemini Shortly after the Space Race began, an early objective was to get a person into Earth orbit as soon as possible, therefore the simplest spacecraft that could be launched by existing rockets was favored. The US Air Force’s Man in Space Soonest program considered many manned spacecraft designs, ranging from rocket planes like the X-15, to small ballistic space capsules.[24] By 1958, the space plane concepts were eliminated in favor of the ballistic capsule.[25]

Based on studies to grow the Mercury spacecraft capabilities to long-duration flights, developing space rendezvous techniques, and precision Earth landing, Project Gemini was started as a two-man program in 1962 to overcome the Soviets’ lead and to support the Apollo manned lunar landing program, adding extravehicular activity (EVA) and rendezvous and docking to its objectives. The first manned Gemini flight, Gemini 3, was flown by Gus Grissom and John Young on March 23, 1965.[30] Nine missions followed in 1965 and 1966, demonstrating an endurance mission of nearly fourteen days, rendezvous, docking, and practical EVA, and gathering medical data on the effects of weightlessness on humans.[31][32]

When NASA was created that same year, the Air Force program was transferred to it and renamed Project Mercury. The first seven astronauts were selected among candidates from the Navy, Air Force and Marine test pilot programs. On May 5, 1961, astronaut Alan Shepard Under

the

direction

of

Soviet

Premier

Nikita


96

CHAPTER 13. NASA

Khrushchev, the USSR competed with Gemini by converting their Vostok spacecraft into a two- or three-man Voskhod. They succeeded in launching two manned flights before Gemini’s first flight, achieving a three-cosmonaut flight in 1963 and the first EVA in 1964. After this, the program was canceled, and Gemini caught up while spacecraft designer Sergei Korolev developed the Soyuz spacecraft, their answer to Apollo.

Buzz Aldrin on the Moon, 1969

July 1969.[42] The first person to stand on the Moon was Neil Armstrong, who was followed by Buzz Aldrin, while Michael Collins orbited above. Five subsequent Apollo missions also landed astronauts on the Moon, the last in December 1972. Throughout these six Apollo spaceflights, twelve men walked on the Moon. These missions returned a Project Apollo (1961–72) wealth of scientific data and 381.7 kilograms (842 lb) of lunar samples. Topics covered by experiments performed Main article: Apollo program included soil mechanics, meteoroids, seismology, heat flow, lunar ranging, magnetic fields, and solar wind.[43] The U.S public’s perception of the Soviet lead in the space The Moon landing marked the end of the space race; race (by putting the first man in space) motivated Presi- and as a gesture, Armstrong mentioned mankind when dent John F. Kennedy to ask the Congress on May 25, he stepped down on the Moon.[44] 1961 to commit the federal government to a program to land a man on the Moon by the end of the 1960s, which effectively launched the Apollo program.[33] Spacecraft and launch vehicle comparison of Apollo, Gemini and Mercury. The Saturn IB and Mercury-Redstone launch vehicles are left out.

Apollo was one of the most expensive American scientific programs ever. It cost more than $20 billion in 1960s dollars[34] or an estimated $206 billion in present-day US dollars.[35] (In comparison, the Manhattan Project cost roughly $26.3 billion, accounting for inflation.)[35][36] It used the Saturn rockets as launch vehicles, which were far bigger than the rockets built for previous projects.[37] The spacecraft was also bigger; it had two main parts, the combined command and service module (CSM) and the lunar landing module (LM). The LM was to be left on the Moon and only the command module (CM) containing the three astronauts would eventually return to Earth. The second manned mission, Apollo 8, brought astronauts for the first time in a flight around the Moon in December 1968.[38] Shortly before, the Soviets had sent an unmanned spacecraft around the Moon.[39] On the next two missions docking maneuvers that were needed for Apollo 17’s lunar roving vehicle, 1972 the Moon landing were practiced[40][41] and then finally the Moon landing was made on the Apollo 11 mission in Apollo set major milestones in human spaceflight. It


13.2. SPACE FLIGHT PROGRAMS stands alone in sending manned missions beyond low Earth orbit, and landing humans on another celestial body.[45] Apollo 8 was the first manned spacecraft to orbit another celestial body, while Apollo 17 marked the last moonwalk and the last manned mission beyond low Earth orbit to date. The program spurred advances in many areas of technology peripheral to rocketry and manned spaceflight, including avionics, telecommunications, and computers. Apollo sparked interest in many fields of engineering and left many physical facilities and machines developed for the program as landmarks. Many objects and artifacts from the program are on display at various locations throughout the world, notably at the Smithsonian’s Air and Space Museums.

97 To save cost, NASA used one of the Saturn V rockets originally earmarked for a canceled Apollo mission to launch the Skylab. Apollo spacecraft were used for transporting astronauts to and from the station. Three threeman crews stayed aboard the station for periods of 28, 59, and 84 days. Skylab’s habitable volume was 11,290 cubic feet (320 m3 ), which was 30.7 times bigger than that of the Apollo Command Module.[47] Apollo-Soyuz Test Project (1972–75)

Skylab (1965–79) Main article: Skylab Skylab was the United States’ first and only independently

Apollo-Soyuz crews with models of spacecraft, 1975

Main article: Apollo-Soyuz Test Project

Skylab space station, 1974

built space station.[46] Conceived in 1965 as a workshop to be constructed in space from a spent Saturn IB upper stage, the 169,950 lb (77,088 kg) station was constructed on Earth and launched on May 14, 1973 atop the first two stages of a Saturn V, into a 235-nauticalmile (435 km) orbit inclined at 50° to the equator. Damaged during launch by the loss of its thermal protection and one electricity-generating solar panel, it was repaired to functionality by its first crew. It was occupied for a total of 171 days by 3 successive crews in 1973 and 1974.[46] It included a laboratory for studying the effects of microgravity, and a solar observatory.[46] NASA planned to have a Space Shuttle dock with it, and elevate Skylab to a higher safe altitude, but the Shuttle was not ready for flight before Skylab’s re-entry on July 11, 1979.[47]

On May 24, 1972, US President Richard M. Nixon and Soviet Premier Alexei Kosygin signed an agreement calling for a joint manned space mission, and declaring intent for all future international manned spacecraft to be capable of docking with each other.[48] This authorized the Apollo-Soyuz Test Project (ASTP), involving the rendezvous and docking in Earth orbit of a surplus Apollo Command/Service Module with a Soyuz spacecraft. The mission took place in July 1975. This was the last US manned space flight until the first orbital flight of the Space Shuttle in April 1981.[49] The mission included both joint and separate scientific experiments, and provided useful engineering experience for future joint US–Russian space flights, such as the Shuttle–Mir Program[50] and the International Space Station. Space Shuttle program (1972–2011) Main article: Space Shuttle program The Space Shuttle became the major focus of NASA in the late 1970s and the 1980s. Planned as a frequently launchable and mostly reusable vehicle, four space shuttle orbiters were built by 1985. The first to launch, Columbia, did so on April 12, 1981,[51] the 20th anniversary of the first known human space flight.[52]


98

CHAPTER 13. NASA While the 1986 loss was mitigated by building the Space Shuttle Endeavour from replacement parts, NASA did not build another orbiter to replace the second loss.[57] NASA’s Space Shuttle program had 135 missions when the program ended with the successful landing of the Space Shuttle Atlantis at the Kennedy Space Center on July 21, 2011. The program spanned 30 years with over 300 astronauts sent into space.[58] International Space Station (1993–present) Main article: International Space Station The International Space Station (ISS) combines NASA’s

Launch of the space shuttle

Its major components were a spaceplane orbiter with an external fuel tank and two solid-fuel launch rockets at its side. The external tank, which was bigger than the spacecraft itself, was the only major component that was not reused. The shuttle could orbit in altitudes of 185–643 km (115–400 miles)[53] and carry a maximum payload (to low orbit) of 24,400 kg (54,000 lb).[54] Missions could last from 5 to 17 days and crews could be from 2 to 8 astronauts.[53] On 20 missions (1983–98) the Space Shuttle carried Spacelab, designed in cooperation with the European Space Agency (ESA). Spacelab was not designed for independent orbital flight, but remained in the Shuttle’s cargo bay as the astronauts entered and left it through an airlock.[55] Another famous series of missions were the launch and later successful repair of the Hubble Space Telescope in 1990 and 1993, respectively.[56]

The International Space Station

Space Station Freedom project with the Soviet/Russian Mir-2 station, the European Columbus station, and the Japanese Kibō laboratory module.[59] NASA originally planned in the 1980s to develop Freedom alone, but US budget constraints led to the merger of these projects into a single multi-national program in 1993, managed by NASA, the Russian Federal Space Agency (RKA), the Japan Aerospace Exploration Agency (JAXA), the European Space Agency (ESA), and the Canadian Space Agency (CSA).[60][61] The station consists of pressurized modules, external trusses, solar arrays and other components, which have been launched by Russian Proton and Soyuz rockets, and the US Space Shuttles.[59] It is currently being assembled in Low Earth Orbit. The onorbit assembly began in 1998, the completion of the US Orbital Segment occurred in 2011 and the completion of the Russian Orbital Segment is expected by 2016.[62][63] The ownership and use of the space station is established in intergovernmental treaties and agreements[64] which divide the station into two areas and allow Russia to retain full ownership of the Russian Orbital Segment (with the exception of Zarya),[65][66] with the US Orbital Segment allocated between the other international partners.[64]

In 1995, Russian-American interaction resumed with the Shuttle-Mir missions (1995–1998). Once more an American vehicle docked with a Russian craft, this time a fullfledged space station. This cooperation has continued with Russia and the United States as two of the biggest partners in the largest space station built: the International Space Station (ISS). The strength of their cooperation on this project was even more evident when NASA began relying on Russian launch vehicles to service the ISS during the two-year grounding of the shuttle fleet following the Long duration missions to the ISS are referred to as ISS 2003 Space Shuttle Columbia disaster. Expeditions. Expedition crew members typically spend The Shuttle fleet lost two orbiters and 14 astronauts in two approximately six months on the ISS.[67] The initial expedisasters: Challenger in 1986, and Columbia in 2003.[57] dition crew size was three, temporarily decreased to two


13.2. SPACE FLIGHT PROGRAMS

99 hicles was under a fixed price milestone-based program, meaning that each company that received a funded award had a list of milestones with a dollar value attached to them that they didn't receive until after they had successful completed the milestone.[77] Private companies were also required to have some “skin in the game” which refers raising an unspecified amount of private investment for their proposal.[78]

On December 23, 2008, NASA awarded Commercial Resupply Services contracts to SpaceX and Orbital Sciences Corporation.[79] SpaceX uses its Falcon 9 rocket and Dragon spacecraft.[80] Orbital Sciences uses The STS-131 (light blue) and Expedition 23 (dark blue) crew its Antares rocket and Cygnus spacecraft. The first Dragon resupply mission occurred in May 2012.[81] The members in April 2010 first Cygnus resupply mission occurred in September 2013.[82] The CRS program now provides for all Amerfollowing the Columbia disaster. Since May 2009, expe- ica’s ISS cargo needs; with the exception of a few vehicledition crew size has been six crew members.[68] Crew size specific payloads that are delivered on the European ATV is expected to be increased to seven, the number the ISS and the Japanese HTV.[83] was designed for, once the Commercial Crew Program becomes operational.[69] The ISS has been continuously occupied for the past 15 years and 341 days, having exceeded the previous record held by Mir; and has been Commercial Crew Program (2010–present) Main visited by astronauts and cosmonauts from 15 different article: Commercial Crew Development nations.[70][71] The station can be seen from the Earth with the naked The Commercial Crew Development (CCDev) program eye and, as of 2016, is the largest artificial satellite in was initiated in 2010 with the purpose of creating AmeriEarth orbit with a mass and volume greater than that of can commercially operated crewed spacecraft capable of any previous space station.[72] The Soyuz spacecraft de- delivering at least four crew members to the ISS, staylivers crew members, stays docked for their half-year- ing docked for 180 days and then returning them back to [84] long missions and then returns them home. Several un- Earth. It is hoped that these vehicles could also transcrewed cargo spacecraft service the ISS, they are the port non-NASA customers to private space stations such [85] Like COTS, Russian Progress spacecraft which has done so since those planned by Bigelow Aerospace. CCDev is also a fixed price milestone-based developmen2000, the European Automated Transfer Vehicle (ATV) [77] tal program that requires some private investment. since 2008, the Japanese H-II Transfer Vehicle (HTV) since 2009, the American Dragon spacecraft since 2012, In 2010, NASA announced the winners of the first phase and the American Cygnus spacecraft since 2013. The of the program, a total of $50 million was divided among Space Shuttle, before its retirement, was also used for five American companies to foster research and developcargo transfer and would often switch out expedition crew ment into human spaceflight concepts and technologies members, although it did not have the capability to re- in the private sector. In 2011, the winners of the second main docked for the duration of their stay. Until another phase of the program were announced, $270 million was US manned spacecraft is ready, crew members will travel divided among four companies.[86] In 2012, the winners to and from the International Space Station exclusively of the third phase of the program were announced, NASA aboard the Soyuz.[73] The highest number of people occu- provided $1.1 billion divided among three companies to pying the ISS has been thirteen; this occurred three times further develop their crew transportation systems.[87] In during the late Shuttle ISS assembly missions.[74] 2014, the winners of the final round were announced.[88] The ISS program is expected to continue until at least SpaceX’s Dragon V2 (planned to be launched on a Falcon 9 v1.1) received a contract valued up to $2.6 billion and 2020, and may be extended beyond 2028.[75] Boeing’s CST-100 (to be launched on an Atlas V) received a contract valued up to $4.2 billion.[89] NASA exCommercial Resupply Services (2006–present) pects these vehicles to begin transporting humans to the ISS in 2017.[89] Main article: Commercial Resupply Services The development of the Commercial Resupply Services (CRS) vehicles began in 2006 with the purpose of creating American commercially operated uncrewed cargo vehicles to service the ISS.[76] The development of these ve-

• Dragon V2 • Computer rendering of CST-100 in orbit


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CHAPTER 13. NASA The Authorization Act required a newly designed HLV be chosen within 90 days of its passing; the launch vehicle was given the name “Space Launch System”. The new law also required the construction of a beyond low earth orbit spacecraft.[93] The Orion spacecraft, which was being developed as part of the Constellation program, was chosen to fulfill this role.[94] The Space Launch System is planned to launch both Orion and other necessary hardware for missions beyond low Earth orbit.[95] The SLS is to be upgraded over time with more powerful versions. The initial capability of SLS is required to be able to lift 70 mt into LEO. It is then planned to be upgraded to 105 mt and then eventually to 130 mt.[94][96] Exploration Flight Test 1 (EFT-1), an unmanned test flight of Orion’s crew module, was launched on December 5, 2014, atop a Delta IV Heavy rocket.[96] Exploration Mission-1 (EM-1) is the unmanned initial launch of SLS that would also send Orion on a circumlunar trajectory, which is planned for 2017.[96] The first manned flight of Orion and SLS, Exploration Mission 2 (EM-2) is to launch between 2019 and 2021; it is a 10- to 14-day mission planned to place a crew of four into Lunar orbit.[96] As of March 2012, the destination for EM-3 and the intermediate focus for this new program is still in-flux.[97]

Artist’s rendering of the 70 mt variant of SLS launching Orion

Beyond Low Earth Orbit program (2010–present) For missions beyond low Earth orbit (BLEO), NASA has been directed to develop the Space Launch System (SLS), a Saturn-V class rocket, and the two to six person, beyond low Earth orbit spacecraft, Orion. In February 2010, President Barack Obama's administration proposed eliminating public funds for the Constellation program and shifting greater responsibility of servicing the ISS to private companies.[90] During a speech at the Kennedy Space Center on April 15, 2010, Obama proposed a new heavy-lift vehicle (HLV) to replace the formerly planned Ares V.[91] In his speech, Obama called for a manned mission to an asteroid as soon as 2025, and a manned mission to Mars orbit by the mid-2030s.[91] The NASA Authorization Act of 2010 was passed by Congress and signed into law on October 11, 2010.[92] The act officially canceled the Constellation program.[92]

Orion spacecraft design as of January 2013

On June 5, 2016, NASA and DARPA announced plans to build a series of new X-planes over the next 10 years.[98] One of the planes will reportedly be a supersonic vehicle that burns low-carbon biofuels and generates quiet sonic booms.[98] NASA plans to build full scale deep space habitats as part of its Next Space Technologies for Exploration Partnerships (NextSTEP) program.[99]

13.2.2 Unmanned programs Main article: Unmanned NASA missions More than 1,000 unmanned missions have been designed to explore the Earth and the solar system.[100] Besides exploration, communication satellites have also been launched by NASA.[101] The missions have been launched directly from Earth or from orbiting space shuttles, which could either deploy the satellite itself, or with a rocket stage to take it farther. The first US unmanned satellite was Explorer 1, which started as an ABMA/JPL project during the early part of the Space Race. It was launched in January 1958, two months after Sputnik. At the creation of NASA the Explorer project was transferred to this agency and still continues to this day. Its missions have been focusing on the Earth and the Sun, measuring magnetic fields and the solar wind, among other aspects.[102] A more recent Earth mission, not related to the Explorer program, was the Hubble Space Telescope, which as mentioned above was brought into orbit in 1990.[103]


13.2. SPACE FLIGHT PROGRAMS

101 sages from the Earth to extraterrestrial life.[108][109] Communication can be difficult with deep space travel. For instance, it took about 3 hours for a radio signal to reach the New Horizons spacecraft when it was more than halfway to Pluto.[110] Contact with Pioneer 10 was lost in 2003. Both Voyager probes continue to operate as they explore the outer boundary between the Solar System and interstellar space.[111] On November 26, 2011, NASA’s Mars Science Laboratory mission was successfully launched for Mars. Curiosity successfully landed on Mars on August 6, 2012, and subsequently began its search for evidence of past or present life on Mars.[112][113][114]

13.2.3 Recent and planned activities NASA’s ongoing investigations include in-depth surveys of Mars (Mars 2020 and InSight) and Saturn and studies of the Earth and the Sun. Other active spacecraft missions are Juno for Jupiter, Cassini for Saturn, New Horizons (for Jupiter, Pluto, and beyond), and Dawn for the asteroid belt. NASA continued to support in situ exploration beyond the asteroid belt, including Pioneer and Voyager traverses into the unexplored trans-Pluto region, and Gas Giant orbiters Galileo (1989–2003), Cassini (1997–), and Juno (2011–). The New Horizons mission to Pluto was launched in 2006 and successfully performed a flyby of Pluto on July 14, Pioneer 3 and 4 launched in 1958 and 1959, respectively 2015. The probe received a gravity assist from Jupiter in February 2007, examining some of Jupiter’s inner moons and testing on-board instruments during the flyby. On the The inner Solar System has been made the goal of at least horizon of NASA’s plans is the MAVEN spacecraft as four unmanned programs. The first was Mariner in the part of the Mars Scout Program to study the atmosphere 1960s and '70s, which made multiple visits to Venus and of Mars.[115] Mars and one to Mercury. Probes launched under the Mariner program were also the first to make a planetary On December 4, 2006, NASA announced it was planflyby (Mariner 2), to take the first pictures from another ning a permanent moon base.[116] The goal was to start planet (Mariner 4), the first planetary orbiter (Mariner 9), building the moon base by 2020, and by 2024, have and the first to make a gravity assist maneuver (Mariner a fully functional base that would allow for crew rota10). This is a technique where the satellite takes advan- tions and in-situ resource utilization. However, in 2009, tage of the gravity and velocity of planets to reach its the Augustine Committee found the program to be on a “unsustainable trajectory.”[117] In 2010, President Barack destination.[104] Obama halted existing plans, including the Moon base, The first successful landing on Mars was made by Viking and directed a generic focus on manned missions to as1 in 1976. Twenty years later a rover was landed on Mars teroids and Mars, as well as extending support for the Inby Mars Pathfinder.[105] ternational Space Station.[118] Outside Mars, Jupiter was first visited by Pioneer 10 in Since 2011, NASA’s strategic goals have been[119] 1973. More than 20 years later Galileo sent a probe into the planet’s atmosphere, and became the first spacecraft • Extend and sustain human activities across the solar to orbit the planet.[106] Pioneer 11 became the first spacesystem craft to visit Saturn in 1979, with Voyager 2 making the first (and so far only) visits to Uranus and Neptune in 1986 • Expand scientific understanding of the Earth and the and 1989, respectively. The first spacecraft to leave the universe solar system was Pioneer 10 in 1983. For a time it was the most distant spacecraft, but it has since been surpassed by • Create innovative new space technologies both Voyager 1 and Voyager 2.[107] Pioneers 10 and 11 and both Voyager probes carry mes-

• Advance aeronautics research


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Curiosity’s wheel on Mars, 2012

Vision mission for an interstellar precursor spacecraft by NASA

• Enable program and institutional capabilities to conduct NASA’s aeronautics and space activities • Share NASA with the public, educators, and students to provide opportunities to participate In August 2011, NASA accepted the donation of two space telescopes from the National Reconnaissance Office. Despite being stored unused, the instruments are Radioisotope within a graphite shell that goes into the generator. superior to the Hubble Space Telescope.[120] In September 2011, NASA announced the start of the Space Launch System program to develop a human-rated heavy lift vehicle. The Space Launch System is intended to launch the Orion Multi-Purpose Crew Vehicle and other elements towards the Moon, near-Earth asteroids, and one day Mars.[121] The Orion MPCV conducted an unmanned test launch on a Delta IV Heavy rocket in December 2014.[122] The James Webb Space Telescope is currently scheduled to launch in late 2018.

NASA’s Aeronautics Research Mission Directorate conducts aeronautics research. NASA has made use of technologies such as the MultiMission Radioisotope Thermoelectric Generator (MMRTG), which is a type of Radioisotope thermoelectric generator used on space missions.[124]

13.4 Staff and leadership

On August 6, 2012, NASA landed the rover Curiosity on Mars. On August 27, 2012, Curiosity transmitted the first Main article: List of NASA Administrators pre-recorded message from the surface of Mars back to Earth, made by Administrator Charlie Bolden: The agency’s leader, NASA’s administrator, reports to the President of the United States and serves as the President’s senior space science adviser. Though the agency is 13.3 Scientific research independent, the survival or discontinuation of projects can depend directly on the will of the President.[125] The Main article: NASA research agency’s administration is located at NASA Headquarters For technologies funded or otherwise supported by in Washington, DC and provides overall guidance and NASA, see NASA spin-off technologies. direction.[126] Except under exceptional circumstances, NASA civil service employees are required to be citizens


13.5. FACILITIES

103

of the United States.[127]

the adjoining Cape Canaveral Air Force Station.

The first administrator was Dr. T. Keith Glennan, appointed by President Dwight D. Eisenhower. During his term he brought together the disparate projects in American space development research.[128]

Lyndon B. Johnson Space Center (JSC) in Houston is home to the Christopher C. Kraft Jr. Mission Control Center, where all flight control is managed for manned space missions. JSC is the lead NASA center for activities regarding the International Space Station and also houses the NASA Astronaut Corps that selects, trains, and provides astronauts as crew members for US and international space missions.

The third administrator was James E. Webb (served 1961–1968), appointed by President John F. Kennedy. In order to implement the Apollo program to achieve Kennedy’s Moon landing goal by the end of the 1960s, Webb directed major management restructuring and facility expansion, establishing the Houston Manned Spacecraft (Johnson) Center and the Florida Launch Operations (Kennedy) Center.

Another major facility is Marshall Space Flight Center in Huntsville, Alabama at which the Saturn 5 rocket and Skylab were developed.[130] The JPL worked together with ABMA, one of the agencies behind Explorer 1, the first American space mission. In 2009, President Barack Obama nominated Charles Bolden as NASA’s twelfth administrator.[129] Administrator Bolden is one of three NASA administrators who were astronauts, along with Richard H. Truly (served 1989–1992) and Frederick D. Gregory (acting, 2005).

13.5 Facilities

FCR 1 in 2009 during the STS-128 mission, JSC in Houston

The ten NASA field centers are: Jet Propulsion Laboratory complex in Pasadena, California

• John F. Kennedy Space Center, Florida • Ames Research Center, Moffett Field, California • Armstrong Flight Research Center (formerly Hugh L. Dryden Flight Research Facility), Edwards, California • Goddard Space Flight Center, Greenbelt, Maryland

Vehicle Assembly and Launch Control at Kennedy Space Center Main article: NASA facilities

• Jet Propulsion Laboratory, near Pasadena, California • Lyndon B. Johnson Space Center, Houston, Texas

NASA’s facilities are research, construction and communication centers to help its missions. Some facilities serve more than one application for historic or administrative reasons. NASA also operates a short-line railroad at the Kennedy Space Center and own special aircraft, for instance two Boeing 747 that transport Space Shuttle orbiter. John F. Kennedy Space Center (KSC), is one of the bestknown NASA facilities. It has been the launch site for every United States human space flight since 1968. Although such flights are currently on pause, KSC continues to manage and operate unmanned rocket launch facilities for America’s civilian space program from three pads at

• Langley Research Center, Hampton, Virginia • John H. Glenn Research Center, Cleveland, Ohio • George C. Marshall Space Flight Center, Huntsville, Alabama • John C. Stennis Space Center, Bay St. Louis, Mississippi Numerous other facilities are operated by NASA, including the Wallops Flight Facility in Wallops Island, Virginia; the Michoud Assembly Facility in New Orleans, Louisiana; the White Sands Test Facility in Las


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CHAPTER 13. NASA

Cruces, New Mexico; and Deep Space Network stations one where it has reclaimed its 20th century birthright to in Barstow, California; Madrid, Spain; and Canberra, dream of tomorrow.”[134][135] Australia. For Fiscal Year 2015, NASA received an appropriation of US$18.01 billion from Congress—$549 million more than requested and approximately $350 million more than the 2014 NASA budget passed by Congress.[136] 13.6 Budget

13.7 Environmental impact

NASA’s budget from 1958 to 2012 as a percentage of federal budget

An artist’s conception, from NASA, of an astronaut planting a US flag on Mars. A manned mission to Mars has been discussed as a possible NASA mission since the 1960s.

The exhaust gases produced by rocket propulsion systems, both in Earth’s atmosphere and in space, can adversely effect the Earth’s environment. Some hypergolic rocket propellants, such as hydrazine, are highly toxic prior to combustion, but decompose into less toxic compounds after burning. Rockets using hydrocarbon fuels, such as kerosene, release carbon dioxide and soot in their exhaust.[137] However, carbon dioxide emissions are insignificant compared to those from other sources; on average, the United States consumed 802,620,000 US gallons (3.0382×109 L) gallons of liquid fuels per day in 2014, while a single Falcon 9 rocket first stage burns around 25,000 US gallons (95,000 L) of kerosene fuel per launch.[138][139] Even if a Falcon 9 were launched every single day, it would only represent 0.006% of liquid fuel consumption (and carbon dioxide emissions) for that day. Additionally, the exhaust from LOx- and LH2- fueled engines, like the SSME, is almost entirely water vapor.[140] NASA addressed environmental concerns with its canceled Constellation program in accordance with the National Environmental Policy Act in 2011.[141] In contrast, ion engines use harmless noble gases like xenon for propulsion.[142][143] On May 8, 2003, Environmental Protection Agency recognized NASA as the first federal agency to directly use landfill gas to produce energy at one of its facilities—the Goddard Space Flight Center, Greenbelt, Maryland.[144]

An example of NASA’s environmental efforts is the NASA Sustainability Base. Additionally, the Exploration Sciences Building was awarded the LEED Gold rating in NASA’s budget has generally been approximately 1% 2010.[145] of the federal budget from the early 1970s on, after briefly peaking at approximately 4.41% in 1966 during the Apollo program.[125][131] Public perception of NASA’s budget has differed significantly from reality; a 13.8 Observations 1997 poll indicated that most Americans responded that 20% of the federal budget went to NASA.[132] • Plot of orbits of known Potentially Hazardous Asteroids (size over 460 feet (140 m) and passing within The percentage of federal budget that NASA has been 4.7 million miles (7.6×106 km) of Earth’s orbit) allocated has been steadily dropping since the Apollo program and in 2012 it was estimated at 0.48% of the • Various nebulae observed from a NASA space telefederal budget.[133] In a March 2012 meeting of the scope United States Senate Science Committee, Neil deGrasse Tyson testified that “Right now, NASA’s annual budget • 1 Ceres is half a penny on your tax dollar. For twice that—a penny on a dollar—we can transform the country from • Pluto and Charon a sullen, dispirited nation, weary of economic struggle, to Main article: Budget of NASA


13.13. REFERENCES

13.9 Spacecraft • Cassini-Huygens • Hubble Space Telescope

105

13.13 References [1] Lale Tayla & Figen Bingul (2007). “NASA stands “for the benefit of all.”—Interview with NASA’s Dr. Süleyman Gokoglu”. The Light Millennium.

• Curiosity rover

[2] US Centennial of Flight Commission, NACA. centennialofflight.net. Retrieved on November 3, 2011.

• James Webb Space Telescope

[3] “NASA workforce profile”. NASA. January 11, 2011. Retrieved December 17, 2012.

13.10 Examples of missions by target 13.11 See also • Astronomy Picture of the Day • Department of Defense Manned Space Flight Support Office • List of government space agencies • List of NASA aircraft • List of NASA missions • List of United States rockets • NASA Advanced Space Transportation Program • NASA awards and decorations • NASA insignia • NASA Research Park

[4] Dreier, Casey (18 December 2015). "[Updated] An Extraordinary Budget for NASA in 2016 - Congressional omnibus increases the space agency’s budget by $1.3 billion”. The Planetary Society. Retrieved 4 February 2016. [5] “Official US Executive Branch Web Sites - Newspaper and Current Periodical Reading Room (Serial and Government Publications Division, Library of Congress)". loc.gov. Retrieved 2016-05-24. [6] “Frequently Asked Questions”. hq.nasa.gov. Retrieved 2016-05-24. [7] “Ike in History: Eisenhower Creates NASA”. Eisenhower Memorial. 2013. Retrieved November 27, 2013. [8] “The National Aeronautics and Space Act”. NASA. 2005. Retrieved August 29, 2007. [9] Bilstein, Roger E. (1996). “From NACA to NASA”. NASA SP-4206, Stages to Saturn: A Technological History of the Apollo/Saturn Launch Vehicles. NASA. pp. 32–33. ISBN 978-0-16-004259-1. Retrieved May 6, 2013. [10] Netting, Ruth (June 30, 2009). “Earth—NASA Science”. Retrieved July 15, 2009. [11] Netting, Ruth (January 8, 2009). “Heliophysics—NASA Science”. Retrieved July 15, 2009. [12] Roston, Michael (August 28, 2015). “NASA’s Next Horizon in Space”. New York Times. Retrieved August 28, 2015.

• NASA TV

[13] Netting, Ruth (July 13, 2009). “Astrophysics—NASA Science”. Retrieved July 15, 2009.

• NASAcast

[14] “The NACA, NASA, and the Supersonic-Hypersonic Frontier” (PDF). NASA. Retrieved September 30, 2011.

• Small Explorer program

[15] Subcommittee On Military Construction, United States. Congress. Senate. Committee on Armed Services (January 21–24, 1958). Supplemental military construction authorization (Air Force).: Hearings, Eighty-fifth Congress, second session, on H.R. 9739.

• Space policy of the Barack Obama administration • TechPort (NASA)

[16] “T. KEITH GLENNAN”. NASA. August 4, 2006. Retrieved July 15, 2009.

13.12 Footnotes [1] NASA is an independent agency that is not a part of any executive department but reports directly to the President.[5][6]

[17] Executive Order 10849 (Wikisource) [18] von Braun, Werner (1963). “Recollections of Childhood: Early Experiences in Rocketry as Told by Werner Von Braun 1963”. MSFC History Office. NASA Marshall Space Flight Center. Retrieved July 15, 2009.


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[73] Chow, Denise (November 17, 2011). “U.S. Human Spaceflight Program Still Strong, NASA Chief Says”. Space.com. Retrieved July 2, 2012. [74] Potter, Ned (July 17, 2009). “Space Shuttle, Station Dock: 13 Astronauts Together”. ABC News. Retrieved September 7, 2012. [75] Leone, Dan (March 29, 2012). “Sen. Mikulski Questions NASA Commercial Crew Priority”. Space News. Retrieved June 30, 2012. [76] “NASA Selects Crew and Cargo Transportation to Orbit Partners” (Press release). NASA. August 18, 2006. Retrieved November 21, 2006. [77] “Moving Forward: Commercial Crew Development Building the Next Era in Spaceflight” (PDF). Rendezvous. NASA. 2010. pp. 10–17. Retrieved February 14, 2011. Just as in the COTS projects, in the CCDev project we have fixed-price, pay-for-performance milestones” Thorn said. “There’s no extra money invested by NASA if the projects cost more than projected. [78] McAlister, Phil (October 2010). “The Case for Commercial Crew” (PDF). NASA. Retrieved July 2, 2012. [79] “NASA Awards Space Station Commercial Resupply Services Contracts”. NASA, December 23, 2008. [80] “Space Exploration Technologies Corporation – Press”. Spacex.com. Retrieved July 17, 2009. [81] Clark, Stephen (June 2, 2012). “NASA expects quick start to SpaceX cargo contract”. SpaceFlightNow. Retrieved June 30, 2012. [82] Bergin, Chris (September 28, 2013). “Orbital’s Cygnus successfully berthed on the ISS”. NASASpaceFlight.com (not affiliated with NASA). Retrieved October 17, 2013. [83] “SpaceX/NASA Discuss launch of Falcon 9 rocket and Dragon capsule”. NASA. May 22, 2012. Retrieved June 23, 2012. [84] Berger, Brian (February 1, 2011). “Biggest CCDev Award Goes to Sierra Nevada”. Imaginova Corp. Retrieved December 13, 2011. [85] Morring, Frank (October 10, 2012). “Boeing Gets Most Money With Smallest Investment”. Aviation Week. Retrieved October 5, 2012. [86] Dean, James (April 18, 2011). “NASA awards $270 million for commercial crew efforts”. space.com. Archived from the original on April 19, 2011. Retrieved May 11, 2011. [87] “NASA Announces Next Steps in Effort to Launch Americans from U.S. Soil”. NASA. August 3, 2012. Retrieved August 3, 2012. [88] Bolden, Charlie. “American Companies Selected to Return Astronaut Launches to American Soil”. NASA.gov. Retrieved September 16, 2014.


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[89] Foust, Jeff (September 19, 2014). “NASA Commercial Crew Awards Leave Unanswered Questions”. Space News. Retrieved September 21, 2014. “We basically awarded based on the proposals that we were given,” Kathy Lueders, NASA commercial crew program manager, said in a teleconference with reporters after the announcement. “Both contracts have the same requirements. The companies proposed the value within which they were able to do the work, and the government accepted that.”

[107] “JPL Voyager”. JPL. Retrieved September 30, 2011. [108] “Pioneer 10 spacecraft send last signal”. NASA. Retrieved September 30, 2011. [109] “The golden record”. JPL. Retrieved September 30, 2011. [110] “New Horizon”. JHU/APL. Retrieved September 30, 2011. [111] “Voyages Beyond the Solar System: The Voyager Interstellar Mission”. NASA. Retrieved September 30, 2011.

[90] Achenbach, Joel (February 1, 2010). “NASA budget for 2011 eliminates funds for manned lunar missions”. Wash- [112] NASA Staff (November 26, 2011). “Mars Science Laboratory”. NASA. Retrieved November 26, 2011. ington Post. Retrieved February 1, 2010. [91] “President Barack Obama on Space Exploration in the [113] “NASA Launches Super-Size Rover to Mars: 'Go, Go!'". New York Times. Associated Press. November 26, 2011. 21st Century”. Office of the Press Secretary. April 15, Retrieved November 26, 2011. 2010. Retrieved July 4, 2012. [92] “Today – President Signs NASA 2010 Authorization Act”. Universetoday.com. Retrieved November 20, 2010.

[114] Kenneth Chang (August 6, 2012). “Curiosity Rover Lands Safely on Mars”. The New York Times. Retrieved August 6, 2012.

[93] Svitak, Amy (March 31, 2011). “Holdren: NASA Law [115] Wilson, Jim (September 15, 2008). “NASA Selects Doesn't Square with Budgetary Reality”. Space News. 'MAVEN' Mission to Study Mars Atmosphere”. NASA. Retrieved July 4, 2012. Retrieved July 15, 2009. [94] “Bill Text - 111th Congress (2009-2010) - THOMAS (Li[116] NASA Office of Public Affairs (December 4, 2006). brary of Congress)". loc.gov. “GLOBAL EXPLORATION STRATEGY AND LUNAR ARCHITECTURE” (PDF). NASA. Retrieved July [95] “NASA Announces Design for New Deep Space Explo15, 2009. ration System”. NASA. September 14, 2011. Retrieved April 28, 2012.

[117] “Review of United States Human Space Flight Plans Committee” (PDF). Office of Science and Technology Policy. [96] Bergin, Chris (February 23, 2012). “Acronyms to Ascent October 22, 2009. Retrieved December 13, 2011. – SLS managers create development milestone roadmap”. NASA. Retrieved April 29, 2012. [118] Goddard, Jacqui (February 2, 2010). “Nasa reduced to pipe dreams as Obama cancels Moon flights”. The Times. [97] Bergin, Chris (March 26, 2012). “NASA Advisory CounLondon. Retrieved May 19, 2010. cil: Select a Human Exploration Destination ASAP”. NasaSpaceflight (not affiliated with NASA). Retrieved [119] “NASA Strategic Plan, 2011” (PDF). NASA HeadquarApril 28, 2012. ters. [98] Grady, Mary (June 5, 2016). “NASA and DARPA plan [120] Boyle, Rebecca (June 5, 2012). “NASA Adopts Two to release new X-Planes”. Yahoo Tech. Retrieved June 8, Spare Spy Telescopes, Each Maybe More Powerful than 2016. Hubble”. Popular Science. Popular Science Technology Group. Retrieved June 5, 2012. [99] NextSTEP Program [121] “NASA Announces Design for New Deep Space Explo[100] “Launch History (Cumulative)" (PDF). NASA. Retrieved ration System”. NASA. September 14, 2011. Retrieved September 30, 2011. December 13, 2011. [101] “NASA Experimental Communications Satellites, 1958– [122] 1995”. NASA. Retrieved September 30, 2011. [123] [102] “NASA, Explorers program”. NASA. Retrieved September 20, 2011. [124] [103] NASA mission STS-31 (35) Archived 18 August 2011 at WebCite [125] [104] “JPL, Chapter 4. Interplanetary Trajectories”. NASA. Retrieved September 30, 2011. [105] “Missions to Mars”. September 30, 2011.

The Planet Society.

“NASA’s Orion Flight Test Yields Critical Data”. NASA. JPL, NASA. “First Recorded Voice from Mars”. nasa.gov. “Radioisotope Power Systems for Space Exploration” (PDF). March 2011. Retrieved March 13, 2015. Fouriezos, Nick (30 May 2016). “Your Presidential Candidates ... For the Milky Way”. OZY. Retrieved 30 May 2016.

Retrieved [126] Shouse, Mary (July 9, 2009). “Welcome to NASA Headquarters”. Retrieved July 15, 2009.

[106] “Missions to Jupiter”. The Planet Society. Retrieved [127] Information for Non U.S. Citizens, NASA (downloaded September 30, 2011. September 16, 2013)


13.14. EXTERNAL LINKS

[128] “T. Keith Glennan biography”. NASA. August 4, 2006. Retrieved July 5, 2008. [129] Cabbage, Michael (July 15, 2009). “Bolden and Garver Confirmed by U.S. Senate” (Press release). NASA. Retrieved July 16, 2009.

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13.14 External links General • Official NASA site

[130] “MSFC_Fact_sheet” (PDF). NASA. Retrieved October 1, 2011.

• NASA Engineering and Safety Center

[131] Rogers, Simon. (February 1, 2010) Nasa budgets: US spending on space travel since 1958 |Society. theguardian.com. Retrieved on August 26, 2013.

• NASA Launch Schedule

[132] Launius, Roger D. “Public opinion polls and perceptions of US human spaceflight”. Division of Space History, National Air and Space Museum, Smithsonian Institution. [133] “Fiscal Year 2013 Budget Estimates” (PDF). NASA. Retrieved February 13, 2013.

• NASA Photos and NASA Images • NASA Television and NASA podcasts • NASA on Google+ • NASA’s channel on YouTube • @NASA on Twitter • NASA on Facebook • NASA in the Federal Register

[134] “Past, Present, and Future of NASA — U.S. Senate Testimony”. Hayden Planetarium. March 7, 2012. Retrieved December 4, 2012.

• NASA Watch, an agency watchdog site

[135] “Past, Present, and Future of NASA — U.S. Senate Testimony (Video)". Hayden Planetarium. March 7, 2012. Retrieved December 4, 2012.

• NASA Documents relating to the Space Program, 1953–62, Dwight D. Eisenhower Presidential Library

[136] Clark, Stephen (December 14, 2014). “NASA gets budget hike in spending bill passed by Congress”. Spaceflight Now. Retrieved December 15, 2014.

• Online documents pertaining to the early history and development of NASA, Dwight D. Eisenhower Presidential Library

• The Gateway to Astronaut Photography of Earth

[137] “Rocket Soot Emissions and Climate Change”. The Aerospace Corporation. July 31, 2013. Retrieved January 7, 2014.

• NASA records available for research at the National Archives at Atlanta

[138] “Short-Term Energy Outlook” (PDF). U.S. Energy Information Administration. 2016-02-09. U.S. Petroleum and Other Liquids

• Technical Report Archive and Image Library (TRAIL) – historic technical reports from NASA and other federal agencies

[139] “Spaceflight Now - Dragon Mission Report - Mission Status Center”. Retrieved July 4, 2015.

• NASA Alumni League, NAL Florida Chapter, NAL JSC Chapter

[140] “Space Shuttle Main Engines”. NASA. July 16, 2009. Retrieved January 20, 2015.

• Works by NASA at Project Gutenberg

[141] “Constellation Programmatic Environmental Impact Statement”. NASA. August 1, 2011. Retrieved June 19, 2014.

• Works by or about NASA at Internet Archive Further reading

[142] Shiga, David (2007-09-28). “Next-generation ion engine sets new thrust record”. NewScientist. Retrieved 2011-0202.

• How NASA works on howstuffworks.com

[143] Goto, T; Nakata Y; Morita S (2003). “Will xenon be a stranger or a friend?: the cost, benefit, and future of xenon anesthesia”. Anesthesiology. 98 (1): 1– 2. doi:10.1097/00000542-200301000-00002. PMID 12502969. Retrieved 2010-09-15.

• Monthly look at Exploration events

[144] Michael K. Ewert (2006). “Johnson Space Center’s Role in a Sustainable Future” (PDF). NASA. Retrieved April 28, 2008. [145] “NASA - NASA’s New Building Awarded the U.S. Green Building Council LEED Gold Rating”. nasa.gov.

• NASA History Division

• NODIS: NASA Online Directives Information System • NTRS: NASA Technical Reports Server • NASA History and the Challenge of Keeping the Contemporary Past • Quest: The History of Spaceflight Quarterly


Chapter 14

Solar System This article is about the Sun and its planetary system. including comets, centaurs and interplanetary dust, freely For other similar systems, see Star system and Planetary travel between regions. Six of the planets, at least four system. of the dwarf planets, and many of the smaller bodies are orbited by natural satellites,[lower-alpha 6] usually termed The Solar System[lower-alpha 1] is the gravitationally bound “moons” after the Moon. Each of the outer planets is encircled by planetary rings of dust and other small system comprising the Sun and the objects that orbit [lower-alpha 2] it, either directly or indirectly. Of those ob- objects. jects that orbit the Sun directly, the largest eight are the planets,[lower-alpha 3] with the remainder being significantly smaller objects, such as dwarf planets and small Solar System bodies. Of the objects that orbit the Sun indirectly, the moons, two are larger than the smallest planet, Mercury.[lower-alpha 4]

The solar wind, a stream of charged particles flowing outwards from the Sun, creates a bubble-like region in the interstellar medium known as the heliosphere. The heliopause is the point at which pressure from the solar wind is equal to the opposing pressure of interstellar wind; it extends out to the edge of the scattered disc. The Oort cloud, which is thought to be the source for longperiod comets, may also exist at a distance roughly a thousand times further than the heliosphere. The Solar System is located in the Orion Arm, 26,000 light-years from the center of the Milky Way.

The Solar System formed 4.6 billion years ago from the gravitational collapse of a giant interstellar molecular cloud. The vast majority of the system’s mass is in the Sun, with most of the remaining mass contained in Jupiter. The four smaller inner planets, Mercury, Venus, Earth and Mars, are terrestrial planets, being primarily composed of rock and metal. The four outer planets are giant planets, being substantially more massive than the 14.1 Discovery and exploration terrestrials. The two largest, Jupiter and Saturn, are gas giants, being composed mainly of hydrogen and helium; Main article: Discovery and exploration of the Solar Systhe two outermost planets, Uranus and Neptune, are ice tem giants, being composed mostly of substances with relaFor most of history, humanity did not recognize or untively high melting points compared with hydrogen and helium, called ices, such as water, ammonia and methane. All planets have almost circular orbits that lie within a nearly flat disc called the ecliptic. The Solar System also contains smaller objects.[lower-alpha 5] The asteroid belt, which lies between the orbits of Mars and Jupiter, mostly contains objects composed, like the terrestrial planets, of rock and metal. Beyond Neptune’s orbit lie the Kuiper belt and scattered disc, which are populations of trans-Neptunian objects composed mostly of ices, and beyond them a newly discovered population of sednoids. Within these populations are several dozen to possibly tens of thousands of objects large enough that they have been rounded by their own gravity.[10] Such objects are categorized as dwarf planets. Identified dwarf planets include the asteroid Ceres and the trans-Neptunian objects Pluto and Eris.[lower-alpha 5] In addition to these Andreas Cellarius's illustration of the Copernican system, from two regions, various other small-body populations, the Harmonia Macrocosmica (1660) 110


14.2. STRUCTURE AND COMPOSITION derstand the concept of the Solar System. Most people up to the Late Middle Ages–Renaissance believed Earth to be stationary at the centre of the universe and categorically different from the divine or ethereal objects that moved through the sky. Although the Greek philosopher Aristarchus of Samos had speculated on a heliocentric reordering of the cosmos, Nicolaus Copernicus was the first to develop a mathematically predictive heliocentric system.[11][12] In the 17th century, Galileo Galilei, Johannes Kepler, and Isaac Newton developed an understanding of physics that led to the gradual acceptance of the idea that Earth moves around the Sun and that the planets are governed by the same physical laws that governed Earth. The invention of the telescope led to the discovery of further planets and moons. Improvements in the telescope and the use of unmanned spacecraft have enabled the investigation of geological phenomena, such as mountains, craters, seasonal meteorological phenomena, such as clouds, dust storms and ice caps on the other planets.

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The eight planets of the Solar System (by decreasing size) are Jupiter, Saturn, Uranus, Neptune, Earth, Venus, Mars and Mercury.

called natural satellites, or moons (two of which are larger than the planet Mercury), and, in the case of the four giant planets, by planetary rings, thin bands of tiny particles that orbit them in unison. Most of the largest natural satellites are in synchronous rotation, with one face permanently turned toward their parent.

14.2 Structure and composition The principal component of the Solar System is the Sun, a G2 main-sequence star that contains 99.86% of the system’s known mass and dominates it gravitationally.[13] The Sun’s four largest orbiting bodies, the giant planets, account for 99% of the remaining mass, with Jupiter and Saturn together comprising more than 90%. The remaining objects of the Solar System (including the four terrestrial planets, the dwarf planets, moons, asteroids, and comets) together comprise less than 0.002% of the Solar System’s total mass.[lower-alpha 7] Most large objects in orbit around the Sun lie near the plane of Earth’s orbit, known as the ecliptic. The planets are very close to the ecliptic, whereas comets and Kuiper belt objects are frequently at significantly greater angles to it.[17][18] All the planets and most other objects orbit the Sun in the same direction that the Sun is rotating (counterclockwise, as viewed from above Earth’s north pole).[19] There are exceptions, such as Halley’s Comet. The overall structure of the charted regions of the Solar System consists of the Sun, four relatively small inner planets surrounded by a belt of mostly rocky asteroids, and four giant planets surrounded by the Kuiper belt of mostly icy objects. Astronomers sometimes informally divide this structure into separate regions. The inner Solar System includes the four terrestrial planets and the asteroid belt. The outer Solar System is beyond the asteroids, including the four giant planets.[20] Since the discovery of the Kuiper belt, the outermost parts of the Solar System are considered a distinct region consisting of the objects beyond Neptune.[21]

All planets of the Solar System lie very close to the ecliptic. The closer they are to the Sun, the faster they travel (inner planets on the left, all planets except Neptune on the right). Kepler’s laws of planetary motion describe the orbits of objects about the Sun. Following Kepler’s laws, each object travels along an ellipse with the Sun at one focus. Objects closer to the Sun (with smaller semi-major axes) travel more quickly because they are more affected by the Sun’s gravity. On an elliptical orbit, a body’s distance from the Sun varies over the course of its year. A body’s closest approach to the Sun is called its perihelion, whereas its most distant point from the Sun is called its aphelion. The orbits of the planets are nearly circular, but many comets, asteroids, and Kuiper belt objects follow highly elliptical orbits. The positions of the bodies in the Solar System can be predicted using numerical models.

Although the Sun dominates the system by mass, it accounts for only about 2% of the angular momentum.[22][23] The planets, dominated by Jupiter, account for most of the rest of the angular momentum due to the combination of their mass, orbit, and distance from the Sun, with a possibly significant contribution from [22] Most of the planets in the Solar System have secondary comets. systems of their own, being orbited by planetary objects The Sun, which comprises nearly all the matter in the So-


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lar System, is composed of roughly 98% hydrogen and helium.[24] Jupiter and Saturn, which comprise nearly all the remaining matter, are also primarily composed of hydrogen and helium.[25][26] A composition gradient exists in the Solar System, created by heat and light pressure from the Sun; those objects closer to the Sun, which are more affected by heat and light pressure, are composed of elements with high melting points. Objects farther from the Sun are composed largely of materials with lower melting points.[27] The boundary in the Solar System beyond which those volatile substances could condense is known as the frost line, and it lies at roughly 5 AU from the Sun.[5] The objects of the inner Solar System are composed mostly of rock,[28] the collective name for compounds with high melting points, such as silicates, iron or nickel, that remained solid under almost all conditions in the protoplanetary nebula.[29] Jupiter and Saturn are composed mainly of gases, the astronomical term for materials with extremely low melting points and high vapour pressure, such as hydrogen, helium, and neon, which were always in the gaseous phase in the nebula.[29] Ices, like water, methane, ammonia, hydrogen sulfide and carbon dioxide,[28] have melting points up to a few hundred kelvins.[29] They can be found as ices, liquids, or gases in various places in the Solar System, whereas in the nebula they were either in the solid or gaseous phase.[29] Icy substances comprise the majority of the satellites of the giant planets, as well as most of Uranus and Neptune (the so-called "ice giants") and the numerous small objects that lie beyond Neptune’s orbit.[28][30] Together, gases and ices are referred to as volatiles.[31]

14.2.1

Some Solar System models attempt to convey the relative scales involved in the Solar System on human terms. Some are small in scale (and may be mechanical—called orreries)—whereas others extend across cities or regional areas.[33] The largest such scale model, the Sweden Solar System, uses the 110-metre (361-ft) Ericsson Globe in Stockholm as its substitute Sun, and, following the scale, Jupiter is a 7.5-metre (25-foot) sphere at Arlanda International Airport, 40 km (25 mi) away, whereas the farthest current object, Sedna, is a 10-cm (4-in) sphere in Luleå, 912 km (567 mi) away.[34][35] If the Sun–Neptune distance is scaled to 100 metres, then the Sun would be about 3 cm in diameter (roughly twothirds the diameter of a golf ball), the giant planets would be all smaller than about 3 mm, and Earth’s diameter along with that of the other terrestrial planets would be smaller than a flea (0.3 mm) at this scale.[36]

Distances and scales

The distance from Earth to the Sun is 1 astronomical unit (150,000,000 km), or AU. For comparison, the radius of the Sun is 0.0047 AU (700,000 km). Thus, the Sun occupies 0.00001% (10−5 %) of the volume of a sphere with a radius the size of Earth’s orbit, whereas Earth’s volume is roughly one millionth (10−6 ) that of the Sun. Jupiter, the largest planet, is 5.2 astronomical units (780,000,000 km) from the Sun and has a radius of 71,000 km (0.00047 AU), whereas the most distant planet, Neptune, is 30 AU (4.5×109 km) from the Sun. With a few exceptions, the farther a planet or belt is from the Sun, the larger the distance between its orbit and the orbit of the next nearer object to the Sun. For example, Venus is approximately 0.33 AU farther out from the Sun than Mercury, whereas Saturn is 4.3 AU out from Jupiter, and Neptune lies 10.5 AU out from Uranus. Attempts have been made to determine a relationship between these orbital distances (for example, the Titius–Bode law),[32] but no such theory has been accepted. The images at the beginning of this section show the orbits of the various constituents of the Solar System on different scales.

Solar System. Object sizes use one scale, orbit distances use another.

14.3 Formation and evolution Main article: Formation and evolution of the Solar System The Solar System formed 4.568 billion years ago from the gravitational collapse of a region within a large molecular cloud.[lower-alpha 8] This initial cloud was likely several light-years across and probably birthed several stars.[37] As is typical of molecular clouds, this one consisted mostly of hydrogen, with some helium, and small amounts of heavier elements fused by previous generations of stars. As the region that would become the Solar System, known as the pre-solar nebula,[38] collapsed, conservation of angular momentum caused it to rotate


14.4. SUN faster. The centre, where most of the mass collected, became increasingly hotter than the surrounding disc.[37] As the contracting nebula rotated faster, it began to flatten into a protoplanetary disc with a diameter of roughly 200 AU[37] and a hot, dense protostar at the centre.[39][40] The planets formed by accretion from this disc,[41] in which dust and gas gravitationally attracted each other, coalescing to form ever larger bodies. Hundreds of protoplanets may have existed in the early Solar System, but they either merged or were destroyed, leaving the planets, dwarf planets, and leftover minor bodies.

Artist’s concept of the early Solar System

113 lion years for all other phases of the Sun’s pre-remnant life combined.[44] Solar wind from the Sun created the heliosphere and swept away the remaining gas and dust from the protoplanetary disc into interstellar space, ending the planetary formation process. The Sun is growing brighter; early in its main-sequence life its brightness was 70% that of what it is today.[45] The Solar System will remain roughly as we know it today until the hydrogen in the core of the Sun has been entirely converted to helium, which will occur roughly 5 billion years from now. This will mark the end of the Sun’s main-sequence life. At this time, the core of the Sun will collapse, and the energy output will be much greater than at present. The outer layers of the Sun will expand to roughly 260 times its current diameter, and the Sun will become a red giant. Because of its vastly increased surface area, the surface of the Sun will be considerably cooler (2,600 K at its coolest) than it is on the main sequence.[44] The expanding Sun is expected to vaporize Mercury and Venus and render Earth uninhabitable as the habitable zone moves out to the orbit of Mars. Eventually, the core will be hot enough for helium fusion; the Sun will burn helium for a fraction of the time it burned hydrogen in the core. The Sun is not massive enough to commence the fusion of heavier elements, and nuclear reactions in the core will dwindle. Its outer layers will move away into space, leaving a white dwarf, an extraordinarily dense object, half the original mass of the Sun but only the size of Earth.[46] The ejected outer layers will form what is known as a planetary nebula, returning some of the material that formed the Sun—but now enriched with heavier elements like carbon—to the interstellar medium.

Due to their higher boiling points, only metals and silicates could exist in solid form in the warm inner Solar System close to the Sun, and these would eventually form the rocky planets of Mercury, Venus, Earth, and Mars. Because metallic elements only comprised a very small fraction of the solar nebula, the terrestrial planets could not grow very large. The giant planets (Jupiter, Saturn, Uranus, and Neptune) formed further out, be14.4 Sun yond the frost line, the point between the orbits of Mars and Jupiter where material is cool enough for volatile icy compounds to remain solid. The ices that formed these Main article: Sun planets were more plentiful than the metals and silicates The Sun is the Solar System’s star and by far its most that formed the terrestrial inner planets, allowing them to grow massive enough to capture large atmospheres of hydrogen and helium, the lightest and most abundant elements. Leftover debris that never became planets congregated in regions such as the asteroid belt, Kuiper belt, and Oort cloud. The Nice model is an explanation for the creation of these regions and how the outer planets could have formed in different positions and migrated to their current orbits through various gravitational interactions. Within 50 million years, the pressure and density of hydrogen in the centre of the protostar became great enough for it to begin thermonuclear fusion.[42] The temperature, reaction rate, pressure, and density increased until hydrostatic equilibrium was achieved: the thermal pressure equalled the force of gravity. At this point, the Sun became a main-sequence star.[43] The mainsequence phase, from beginning to end, will last about 10 billion years for the Sun compared to around two bil-

Size comparison of the Sun and the planets

massive component. Its large mass (332,900 Earth masses)[47] produces temperatures and densities in its core high enough to sustain nuclear fusion of hydrogen into helium, making it a main-sequence star.[48] This releases an enormous amount of energy, mostly radiated


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into space as electromagnetic radiation peaking in visible Earth’s magnetic field stops its atmosphere from being light.[49] stripped away by the solar wind.[59] Venus and Mars do The Sun is a G2-type main-sequence star. Hotter main- not have magnetic fields, and as a result the solar wind their atmospheres to gradually bleed away into sequence stars are more luminous. The Sun’s temperature is causing [60] space. Coronal mass ejections and similar events blow is intermediate between that of the hottest stars and that a magnetic field and huge quantities of material from the of the coolest stars. Stars brighter and hotter than the Sun surface of the Sun. The interaction of this magnetic field are rare, whereas substantially dimmer and cooler stars, and material with Earth’s magnetic field funnels charged known as red dwarfs, make up 85% of the stars in the particles into Earth’s upper atmosphere, where its inter[50][51] Milky Way. actions create aurorae seen near the magnetic poles. The Sun is a population I star; it has a higher abundance of elements heavier than hydrogen and helium The heliosphere and planetary magnetic fields (for those ("metals" in astronomical parlance) than the older pop- planets that have them) partially shield the Solar System ulation II stars.[52] Elements heavier than hydrogen and from high-energy interstellar particles called cosmic rays. helium were formed in the cores of ancient and explod- The density of cosmic rays in the interstellar medium ing stars, so the first generation of stars had to die before and the strength of the Sun’s magnetic field change on the Universe could be enriched with these atoms. The very long timescales, so the level of cosmic-ray penetraSolar System varies, though by how much is oldest stars contain few metals, whereas stars born later tion in the[61] unknown. have more. This high metallicity is thought to have been crucial to the Sun’s development of a planetary system be- The interplanetary medium is home to at least two disccause the planets form from the accretion of “metals”.[53] like regions of cosmic dust. The first, the zodiacal dust cloud, lies in the inner Solar System and causes the zodiacal light. It was likely formed by collisions within the asteroid belt brought on by gravitational interactions 14.5 Interplanetary medium with the planets.[62] The second dust cloud extends from about 10 AU to about 40 AU, and was probably created Main articles: Interplanetary medium and Solar wind by similar collisions within the Kuiper belt.[63][64] The vast majority of the Solar System consists of a near-

14.6 Inner Solar System The inner Solar System is the region comprising the terrestrial planets and the asteroid belt.[65] Composed mainly of silicates and metals, the objects of the inner Solar System are relatively close to the Sun; the radius of this entire region is less than the distance between the orbits of Jupiter and Saturn. This region is also within the frost line, which is a little less than 5 AU (about 700 million km) from the Sun.[66]

The heliospheric current sheet

14.6.1 Inner planets

vacuum known as the interplanetary medium. Along with light, the Sun radiates a continuous stream of charged particles (a plasma) known as the solar wind. This stream of particles spreads outwards at roughly 1.5 million kilometres per hour,[54] creating a tenuous atmosphere that permeates the interplanetary medium out to at least 100 AU (see § Heliosphere).[55] Activity on the Sun’s surface, such as solar flares and coronal mass ejections, disturb the heliosphere, creating space weather and causing geomagnetic storms.[56] The largest structure within the heliosphere is the heliospheric current sheet, a spiral form created by the actions of the Sun’s rotating magnetic field on the interplanetary medium.[57][58]

Main article: Terrestrial planet The four terrestrial or inner planets have dense, rocky compositions, few or no moons, and no ring systems. They are composed largely of refractory minerals, such as the silicates, which form their crusts and mantles, and metals, such as iron and nickel, which form their cores. Three of the four inner planets (Venus, Earth and Mars) have atmospheres substantial enough to generate weather; all have impact craters and tectonic surface features, such as rift valleys and volcanoes. The term inner planet should not be confused with inferior planet, which designates those planets that are closer to the Sun than Earth is (i.e. Mercury and Venus).


14.6. INNER SOLAR SYSTEM

115 Earth Main article: Earth

The inner planets. From left to right: Earth, Mars, Venus, and Mercury (sizes to scale).

Mercury Main article: Mercury (planet)

Mercury (0.4 AU from the Sun) is the closest planet to the Sun and the smallest planet in the Solar System (0.055 Earth masses). Mercury has no natural satellites; besides impact craters, its only known geological features are lobed ridges or rupes that were probably produced by a period of contraction early in its history.[67] Mercury’s very tenuous atmosphere consists of atoms blasted off its surface by the solar wind.[68] Its relatively large iron core and thin mantle have not yet been adequately explained. Hypotheses include that its outer layers were stripped off by a giant impact; or, that it was prevented from fully accreting by the young Sun’s energy.[69][70]

Venus Main article: Venus

Venus (0.7 AU from the Sun) is close in size to Earth (0.815 Earth masses) and, like Earth, has a thick silicate mantle around an iron core, a substantial atmosphere, and evidence of internal geological activity. It is much drier than Earth, and its atmosphere is ninety times as dense. Venus has no natural satellites. It is the hottest planet, with surface temperatures over 400 °C (752°F), most likely due to the amount of greenhouse gases in the atmosphere.[71] No definitive evidence of current geological activity has been detected on Venus, but it has no magnetic field that would prevent depletion of its substantial atmosphere, which suggests that its atmosphere is being replenished by volcanic eruptions.[72]

Earth (1 AU from the Sun) is the largest and densest of the inner planets, the only one known to have current geological activity, and the only place where life is known to exist.[73] Its liquid hydrosphere is unique among the terrestrial planets, and it is the only planet where plate tectonics has been observed. Earth’s atmosphere is radically different from those of the other planets, having been altered by the presence of life to contain 21% free oxygen.[74] It has one natural satellite, the Moon, the only large satellite of a terrestrial planet in the Solar System. Mars Main article: Mars

Mars (1.5 AU from the Sun) is smaller than Earth and Venus (0.107 Earth masses). It has an atmosphere of mostly carbon dioxide with a surface pressure of 6.1 millibars (roughly 0.6% of that of Earth).[75] Its surface, peppered with vast volcanoes, such as Olympus Mons, and rift valleys, such as Valles Marineris, shows geological activity that may have persisted until as recently as 2 million years ago.[76] Its red colour comes from iron oxide (rust) in its soil.[77] Mars has two tiny natural satellites (Deimos and Phobos) thought to be captured asteroids.[78]

14.6.2 Asteroid belt Main article: Asteroid belt Asteroids except for the largest, Ceres, are classified as small Solar System bodies[lower-alpha 5] and are composed mainly of refractory rocky and metallic minerals, with some ice.[79][80] They range from a few metres to hundreds of kilometres in size. Asteroids smaller than one meter are usually called meteoroids and micrometeoroids (grain-sized), depending on different, somewhat arbitrary definitions. The asteroid belt occupies the orbit between Mars and Jupiter, between 2.3 and 3.3 AU from the Sun. It is thought to be remnants from the Solar System’s formation that failed to coalesce because of the gravitational interference of Jupiter.[81] The asteroid belt contains tens of thousands, possibly millions, of objects over one kilometre in diameter.[82] Despite this, the total mass of the


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CHAPTER 14. SOLAR SYSTEM term “trojan” is also used for small bodies in any other planetary or satellite Lagrange point. Hilda asteroids are in a 2:3 resonance with Jupiter; that is, they go around the Sun three times for every two Jupiter orbits.[85] The inner Solar System also contains nearEarth asteroids, many of which cross the orbits of the inner planets.[86] Some of them are potentially hazardous objects.

14.7 Outer Solar System The outer region of the Solar System is home to the giant planets and their large moons. The centaurs and many short-period comets also orbit in this region. Due to their greater distance from the Sun, the solid objects The donut-shaped asteroid belt is located between the orbits of in the outer Solar System contain a higher proportion Mars and Jupiter. of volatiles, such as water, ammonia, and methane than those of the inner Solar System because the lower temasteroid belt is unlikely to be more than a thousandth of peratures allow these compounds to remain solid. that of Earth.[16] The asteroid belt is very sparsely populated; spacecraft routinely pass through without incident.

14.7.1 Outer planets

Ceres Main article: Ceres (dwarf planet)

Main articles: Outer planets and Giant planet The four outer planets, or giant planets (sometimes called

Ceres (2.77 AU) is the largest asteroid, a protoplanet, and a dwarf planet.[lower-alpha 5] It has a diameter of slightly under 1,000 km, and a mass large enough for its own gravity to pull it into a spherical shape. Ceres was considered a planet when it was discovered in 1801, and was reclassified to asteroid in the 1850s as further observations revealed additional asteroids.[83] It was classified as a dwarf planet in 2006 when the definition of a planet was created. Asteroid groups Asteroids in the asteroid belt are divided into asteroid groups and families based on their orbital characteristics. Asteroid moons are asteroids that orbit larger asteroids. They are not as clearly distinguished as planetary moons, sometimes being almost as large as their partners. The asteroid belt also contains main-belt comets, which may have been the source of Earth’s water.[84] Jupiter trojans are located in either of Jupiter’s L4 or L5 points (gravitationally stable regions leading and trailing a planet in its orbit); the

From top to bottom: Neptune, Uranus, Saturn, and Jupiter (Montage with approximate colour and relative size)

Jovian planets), collectively make up 99% of the mass known to orbit the Sun.[lower-alpha 7] Jupiter and Saturn


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are together over 400 times the mass of Earth and conthe planets, it orbits the Sun on its side; its sist overwhelmingly of hydrogen and helium; Uranus and axial tilt is over ninety degrees to the ecliptic. Neptune are far less massive (<20 Earth masses each) It has a much colder core than the other giant planets and radiates very little heat into and are composed primarily of ices. For these reasons, some astronomers suggest they belong in their own catespace.[91] Uranus has 27 known satellites, the [87] gory, “ice giants”. All four giant planets have rings, allargest ones being Titania, Oberon, Umbriel, though only Saturn’s ring system is easily observed from Ariel, and Miranda. Earth. The term superior planet designates planets outside Earth’s orbit and thus includes both the outer planets Neptune and Mars. Main article: Neptune Jupiter Main article: Jupiter

Jupiter (5.2 AU), at 318 Earth masses, is 2.5 times the mass of all the other planets put together. It is composed largely of hydrogen and helium. Jupiter’s strong internal heat creates semi-permanent features in its atmosphere, such as cloud bands and the Great Red Spot. Jupiter has 67 known satellites. The four largest, Ganymede, Callisto, Io, and Europa, show similarities to the terrestrial planets, such as volcanism and internal heating.[88] Ganymede, the largest satellite in the Solar System, is larger than Mercury. Saturn Main article: Saturn

Saturn (9.5 AU), distinguished by its extensive ring system, has several similarities to Jupiter, such as its atmospheric composition and magnetosphere. Although Saturn has 60% of Jupiter’s volume, it is less than a third as massive, at 95 Earth masses. Saturn is the only planet of the Solar System that is less dense than water.[89] The rings of Saturn are made up of small ice and rock particles. Saturn has 62 confirmed satellites composed largely of ice. Two of these, Titan and Enceladus, show signs of geological activity.[90] Titan, the secondlargest moon in the Solar System, is larger than Mercury and the only satellite in the Solar System with a substantial atmosphere. Uranus Main article: Uranus

Uranus (19.2 AU), at 14 Earth masses, is the lightest of the outer planets. Uniquely among

Neptune (30.1 AU), though slightly smaller than Uranus, is more massive (equivalent to 17 Earths) and hence more dense. It radiates more internal heat, but not as much as Jupiter or Saturn.[92] Neptune has 14 known satellites. The largest, Triton, is geologically active, with geysers of liquid nitrogen.[93] Triton is the only large satellite with a retrograde orbit. Neptune is accompanied in its orbit by several minor planets, termed Neptune trojans, that are in 1:1 resonance with it.

14.7.2 Centaurs Main article: Centaur (minor planet) The centaurs are icy comet-like bodies whose orbits have semi-major axes greater than Jupiter’s (5.5 AU) and less than Neptune’s (30 AU). The largest known centaur, 10199 Chariklo, has a diameter of about 250 km.[94] The first centaur discovered, 2060 Chiron, has also been classified as comet (95P) because it develops a coma just as comets do when they approach the Sun.[95]

14.8 Comets Main article: Comet Comets are small Solar System bodies,[lower-alpha 5] typically only a few kilometres across, composed largely of volatile ices. They have highly eccentric orbits, generally a perihelion within the orbits of the inner planets and an aphelion far beyond Pluto. When a comet enters the inner Solar System, its proximity to the Sun causes its icy surface to sublimate and ionise, creating a coma: a long tail of gas and dust often visible to the naked eye. Short-period comets have orbits lasting less than two hundred years. Long-period comets have orbits lasting thousands of years. Short-period comets are thought to originate in the Kuiper belt, whereas long-period comets, such as Hale–Bopp, are thought to originate in the Oort cloud. Many comet groups, such as the Kreutz Sungrazers, formed from the breakup of a single parent.[96]


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Known objects in the Kuiper belt

Hale–Bopp seen in 1997

Some comets with hyperbolic orbits may originate outside the Solar System, but determining their precise orbits is difficult.[97] Old comets that have had most of their volatiles driven out by solar warming are often categorised as asteroids.[98]

14.9 Trans-Neptunian region Beyond the orbit of Neptune lies the area of the "transNeptunian region", with the doughnut-shaped Kuiper belt, home of Pluto and several other dwarf planets, and an overlapping disc of scattered objects, which is tilted toward the plane of the Solar System and reaches much further out than the Kuiper belt. The entire region is still largely unexplored. It appears to consist overwhelmingly of many thousands of small worlds—the largest having a diameter only a fifth that of Earth and a mass far smaller than that of the Moon—composed mainly of rock and ice. This region is sometimes described as the “third zone of the Solar System”, enclosing the inner and the outer Solar System.[99]

14.9.1

Kuiper belt

Main article: Kuiper belt The Kuiper belt is a great ring of debris similar to the asteroid belt, but consisting mainly of objects composed primarily of ice.[100] It extends between 30 and 50 AU from the Sun. Though it is estimated to contain anything

Size comparison of some large TNOs with Earth: Pluto and its moons, Eris, Makemake, Haumea, Sedna, 2007 OR10, Quaoar, and Orcus.

from dozens to thousands of dwarf planets, it is composed mainly of small Solar System bodies. Many of the larger Kuiper belt objects, such as Quaoar, Varuna, and Orcus, may prove to be dwarf planets with further data. There are estimated to be over 100,000 Kuiper belt objects with a diameter greater than 50 km, but the total mass of the Kuiper belt is thought to be only a tenth or even a hundredth the mass of Earth.[15] Many Kuiper belt objects have multiple satellites,[101] and most have orbits that take them outside the plane of the ecliptic.[102] The Kuiper belt can be roughly divided into the "classical" belt and the resonances.[100] Resonances are orbits linked to that of Neptune (e.g. twice for every three Neptune orbits, or once for every two). The first resonance begins within the orbit of Neptune itself. The classical belt consists of objects having no resonance with Neptune, and extends from roughly 39.4 AU to 47.7 AU.[103] Members of the classical Kuiper belt are classified as cubewanos, after the first of their kind to be dis-


14.10. FARTHEST REGIONS

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covered, (15760) 1992 QB1, and are still in near primor- The scattered disc, which overlaps the Kuiper belt but dial, low-eccentricity orbits.[104] extends much further outwards, is thought to be the source of short-period comets. Scattered-disc objects are thought to have been ejected into erratic orbits by the Pluto and Charon gravitational influence of Neptune’s early outward migration. Most scattered disc objects (SDOs) have perihelia Main articles: Pluto and Charon (moon) within the Kuiper belt but aphelia far beyond it (some more than 150 AU from the Sun). SDOs’ orbits are also highly inclined to the ecliptic plane and are often almost The dwarf planet Pluto (39 AU average) is the perpendicular to it. Some astronomers consider the scatlargest known object in the Kuiper belt. When tered disc to be merely another region of the Kuiper belt discovered in 1930, it was considered to be and describe scattered disc objects as “scattered Kuiper the ninth planet; this changed in 2006 with the belt objects”.[109] Some astronomers also classify centaurs adoption of a formal definition of planet. Pluto as inward-scattered Kuiper belt objects along with the has a relatively eccentric orbit inclined 17 deoutward-scattered residents of the scattered disc.[110] grees to the ecliptic plane and ranging from 29.7 AU from the Sun at perihelion (within the orbit of Neptune) to 49.5 AU at aphelion. Eris Pluto has a 3:2 resonance with Neptune, meaning that Pluto orbits twice round the Sun for evMain article: Eris (dwarf planet) ery three Neptunian orbits. Kuiper belt objects whose orbits share this resonance are called plutinos.[105] Eris (68 AU average) is the largest known scatCharon, the largest of Pluto’s moons, is sometimes described as part of a binary system with Pluto, as the two bodies orbit a barycentre of gravity above their surfaces (i.e. they appear to “orbit each other”). Beyond Charon, four much smaller moons, Styx, Nix, Kerberos, and Hydra, orbit within the system. Makemake and Haumea

tered disc object, and caused a debate about what constitutes a planet, because it is 25% more massive than Pluto[111] and about the same diameter. It is the most massive of the known dwarf planets. It has one known moon, Dysnomia. Like Pluto, its orbit is highly eccentric, with a perihelion of 38.2 AU (roughly Pluto’s distance from the Sun) and an aphelion of 97.6 AU, and steeply inclined to the ecliptic plane.

Main articles: Makemake and Haumea

14.10 Farthest regions Makemake (45.79 AU average), although smaller than Pluto, is the largest known object in the classical Kuiper belt (that is, a Kuiper belt object not in a confirmed resonance with Neptune). Makemake is the brightest object in the Kuiper belt after Pluto. It was named and designated a dwarf planet in 2008.[7] Its orbit is far more inclined than Pluto’s, at 29°.[106] Haumea (43.13 AU average) is in an orbit similar to Makemake except that it is in a 7:12 orbital resonance with Neptune.[107] It is about the same size as Makemake and has two natural satellites. A rapid, 3.9-hour rotation gives it a flattened and elongated shape. It was named and designated a dwarf planet in 2008.[108]

14.9.2

Scattered disc

Main article: Scattered disc

From the Sun to the nearest star: The Solar System on a logarithmic scale in astronomical units (AU)

The point at which the Solar System ends and interstellar space begins is not precisely defined because its outer boundaries are shaped by two separate forces: the solar wind and the Sun’s gravity. The limit of the solar wind’s influence is roughly four times Pluto’s distance from the Sun; this heliopause, the outer boundary of the


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heliosphere, is considered the beginning of the interstellar medium.[55] The Sun’s Hill sphere, the effective range of its gravitational dominance, is thought to extend up to a thousand times farther and encompasses the theorized Oort cloud.[112]

14.10.1

Heliosphere

Sedna Kuiper Belt

Jupiter

Neptune

Mars Earth Venus Mercury

Uranus Saturn Jupiter

Asteroids

Pluto

Inner Solar System

Outer Solar System

Inner extent of Oort Cloud

Orbit of Sedna

Main article: Heliosphere The heliosphere is a stellar-wind bubble, a region of

Zooming out the Solar System: • inner Solar System and Jupiter • outer Solar System and Pluto The bubble-like heliosphere with its various transitional regions moving through the interstellar medium

• orbit of Sedna (detached object) • inner part of the Oort Cloud

space dominated by the Sun, which radiates at roughly 400 km/s its solar wind, a stream of charged particles, Due to a lack of data, conditions in local interstellar until it collides with the wind of the interstellar medium. space are not known for certain. It is expected that The collision occurs at the termination shock, which is NASA's Voyager spacecraft, as they pass the heliopause, data on radiation levels and soroughly 80–100 AU from the Sun upwind of the in- will transmit valuable [119] lar wind to Earth. How well the heliosphere shields terstellar medium and roughly 200 AU from the Sun the Solar System from cosmic rays is poorly understood. [113] downwind. Here the wind slows dramatically, conA NASA-funded team has developed a concept of a [113] denses and becomes more turbulent, forming a great “Vision Mission” dedicated to sending a probe to the oval structure known as the heliosheath. This structure is [120][121] heliosphere. thought to look and behave very much like a comet’s tail, extending outward for a further 40 AU on the upwind side but tailing many times that distance downwind; ev14.10.2 Detached objects idence from Cassini and Interstellar Boundary Explorer spacecraft has suggested that it is forced into a bubble Main articles: Detached object and Sednoid shape by the constraining action of the interstellar magnetic field.[114] 90377 Sedna (520 AU average) is a large, reddish object The outer boundary of the heliosphere, the heliopause, is with a gigantic, highly elliptical orbit that takes it from the point at which the solar wind finally terminates and about 76 AU at perihelion to 940 AU at aphelion and is the beginning of interstellar space.[55] Voyager 1 and takes 11,400 years to complete. Mike Brown, who disVoyager 2 are reported to have passed the termination covered the object in 2003, asserts that it cannot be part shock and entered the heliosheath, at 94 and 84 AU from of the scattered disc or the Kuiper belt because its perithe Sun, respectively.[115][116] Voyager 1 is reported to helion is too distant to have been affected by Neptune’s have crossed the heliopause in August 2012.[117] migration. He and other astronomers consider it to be The shape and form of the outer edge of the heliosphere is the first in an entirely new population, sometimes termed likely affected by the fluid dynamics of interactions with “distant detached objects” (DDOs), which also may inthe interstellar medium as well as solar magnetic fields clude the object 2000 CR105 , which has a perihelion of prevailing to the south, e.g. it is bluntly shaped with 45 AU, an aphelion of 415 AU, and an orbital period of the northern hemisphere extending 9 AU farther than 3,420 years.[122] Brown terms this population the “inner the southern hemisphere.[113] Beyond the heliopause, at Oort cloud” because it may have formed through a similar around 230 AU, lies the bow shock, a plasma “wake” left process, although it is far closer to the Sun.[123] Sedna is by the Sun as it travels through the Milky Way.[118] very likely a dwarf planet, though its shape has yet to be


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determined. The second unequivocally detached object, Currently, the furthest known objects, such as Comet with a perihelion farther than Sedna’s at roughly 81 AU, West have aphelia around 70,000 AU from the Sun, but as is 2012 VP113, discovered in 2012. Its aphelion is only the Oort cloud becomes better known, this may change. half that of Sedna’s, at 400–500 AU.[124][125]

14.11 Galactic context

Main article: Oort cloud The Oort cloud is a hypothetical spherical cloud of up to

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Kuiper Belt and outer solar system planetary orbits

(Vela)

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Orbit of binary Kuiper belt object 1998 WW31

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150

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240

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180

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14.10.3

30

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(Sagittarius)

Diagram of the Milky Way with the position of the Solar System marked by a yellow arrow observation shadow of galactic core

The Oort cloud (comprising many billions of comets)

Schematic of the hypothetical Oort cloud, with a spherical outer cloud and a disc-shaped inner cloud

a trillion icy objects that is thought to be the source for all long-period comets and to surround the Solar System at roughly 50,000 AU (around 1 light-year (ly)), and possibly to as far as 100,000 AU (1.87 ly). It is thought to be composed of comets that were ejected from the inner Solar System by gravitational interactions with the outer planets. Oort cloud objects move very slowly, and can be perturbed by infrequent events, such as collisions, the gravitational effects of a passing star, or the galactic tide, the tidal force exerted by the Milky Way.[126][127]

14.10.4

Boundaries

See also: Vulcanoid, Planets beyond Neptune, and Planet Nine Much of the Solar System is still unknown. The Sun’s gravitational field is estimated to dominate the gravitational forces of surrounding stars out to about two light years (125,000 AU). Lower estimates for the radius of the Oort cloud, by contrast, do not place it farther than 50,000 AU.[128] Despite discoveries such as Sedna, the region between the Kuiper belt and the Oort cloud, an area tens of thousands of AU in radius, is still virtually unmapped. There are also ongoing studies of the region between Mercury and the Sun.[129] Objects may yet be discovered in the Solar System’s uncharted regions.

The Solar System is located in the Milky Way, a barred spiral galaxy with a diameter of about 100,000 light-years containing about 200 billion stars.[130] The Sun resides in one of the Milky Way’s outer spiral arms, known as the Orion–Cygnus Arm or Local Spur.[131] The Sun lies between 25,000 and 28,000 light-years from the Galactic Centre,[132] and its speed within the Milky Way is about 220 km/s, so that it completes one revolution every 225– 250 million years. This revolution is known as the Solar System’s galactic year.[133] The solar apex, the direction of the Sun’s path through interstellar space, is near the constellation Hercules in the direction of the current location of the bright star Vega.[134] The plane of the ecliptic lies at an angle of about 60° to the galactic plane.[lower-alpha 9] The Solar System’s location in the Milky Way is a factor in the evolutionary history of life on Earth. Its orbit is close to circular, and orbits near the Sun are at roughly the same speed as that of the spiral arms.[136][137] Therefore, the Sun passes through arms only rarely. Because spiral arms are home to a far larger concentration of supernovae, gravitational instabilities, and radiation that could disrupt the Solar System, this has given Earth long periods of stability for life to evolve.[136] The Solar System also lies well outside the star-crowded environs of the galactic centre. Near the centre, gravitational tugs from nearby stars could perturb bodies in the Oort cloud and send many comets into the inner Solar System, producing collisions with potentially catastrophic implications for life on Earth. The intense radiation of the galactic centre could also interfere with the development of complex life.[136] Even at the Solar System’s current location, some scientists have speculated that recent supernovae may have adversely affected life in the last 35,000


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years, by flinging pieces of expelled stellar core towards light-years are the binary red-dwarf system Luyten 726-8 the Sun, as radioactive dust grains and larger, comet-like (8.7 ly) and the solitary red dwarf Ross 154 (9.7 ly).[143] bodies.[138] The closest solitary Sun-like star to the Solar System is Tau Ceti at 11.9 light-years. It has roughly 80% of the Sun’s mass but only 60% of its luminosity.[144] The clos14.11.1 Neighbourhood est known free-floating planetary-mass object to the Sun is WISE 0855−0714,[145] an object with a mass less than 10 Jupiter masses roughly 7 light-years away.

Beyond the heliosphere is the interstellar medium, consisting of various clouds of gases. The Solar System currently moves through the Local Interstellar Cloud.

The Solar System is in the Local Interstellar Cloud or Local Fluff. It is thought to be near the neighbouring G-Cloud but it is not known if the Solar System is embedded in the Local Interstellar Cloud, or if it is in the region where the Local Interstellar Cloud and G-Cloud are interacting.[139][140] The Local Interstellar Cloud is an area of denser cloud in an otherwise sparse region known as the Local Bubble, an hourglass-shaped cavity in the interstellar medium roughly 300 light-years (ly) across. The bubble is suffused with high-temperature plasma, that suggests it is the product of several recent supernovae.[141]

diagram of Earth’s location in the observable Universe. (Click here for an alternate image.)

14.11.2 Comparison with other planetary systems Compared to other planetary systems the Solar System stands out in lacking planets interior to the orbit of Mercury.[146][147] The known Solar System also lacks super-Earths (Planet Nine could be a super-Earth beyond the known Solar System).[146] Uncommonly, it has only small rocky planets and large gas giants; elsewhere planets of intermediate size are typical—both rocky and gas—so there is no “gap” as seen between the size of Earth and of Neptune (with a radius 3.8 times as large). Also, these super-Earths have closer orbits than Mercury.[146] This led to hypothesis that all planetary systems start with many close-in planets, and that typically a sequence of their collisions causes consolidation of mass into few larger planets, but in case of the Solar System the collisions caused their destruction and ejection.[148][149]

There are relatively few stars within ten light-years of the Sun. The closest is the triple star system Alpha Centauri, which is about 4.4 light-years away. Alpha Centauri A and B are a closely tied pair of Sun-like stars, whereas the small red dwarf, Proxima Centauri, orbits the pair at a distance of 0.2 light-year. In 2016, a potentially habitable exoplanet was confirmed to be orbiting Proxima Centauri, called Proxima Centauri b, the closest confirmed exoplanet to the Sun.[142] The stars next closest to the Sun are the red dwarfs Barnard’s Star (at 5.9 ly), Wolf 359 (7.8 ly), and Lalande 21185 (8.3 ly). The orbits of Solar System planets are nearly circular. The largest nearby star is Sirius, a bright main-sequence Compared to other systems, they have smaller orbital ecstar roughly 8.6 light-years away and roughly twice the centricity.[146] Although there are attempts to explain it Sun’s mass and that is orbited by a white dwarf, Sir- partly with a bias in the radial-velocity detection method ius B. The nearest brown dwarfs are the binary Luhman and partly with long interactions of a quite high number of 16 system at 6.6 light-years. Other systems within ten planets, the exact causes remain undetermined.[146][150]


14.15. REFERENCES

14.12 Visual summary This section is a sampling of Solar System bodies, selected for size and quality of imagery, and sorted by volume. Some omitted objects are larger than the ones included here, notably Eris, because these have not been imaged in high quality.

14.13 See also • Outline of the Solar System • Astronomical symbols • HIP 11915 (a solar analog whose planetary system contains a Jupiter analog) • Lists of geological features of the Solar System • List of gravitationally rounded objects of the Solar System • List of Solar System extremes • Planetary mnemonic • Solar System in fiction

14.14 Notes [1] Capitalization of the name varies. The IAU, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects, but uses mixed “Solar System” and “solar system” in their naming guidelines document. The name is commonly rendered in lower case ("solar system"), as, for example, in the Oxford English Dictionary and MerriamWebster’s 11th Collegiate Dictionary. [2] The moons orbiting the Solar System’s planets are an example of the latter. [3] Historically, several other bodies were once considered planets, including, from its discovery in 1930 until 2006, Pluto. See Former planets. [4] The two moons larger than Mercury are Ganymede which orbits Jupiter, and Titan which orbits Saturn. Although bigger than Mercury, each of those two moons has less than half the mass of Mercury. [5] According to current definitions, objects orbiting the Sun are classified dynamically and physically into three categories: planets, dwarf planets, and small Solar System bodies. A planet is any body orbiting the Sun whose mass is sufficient for gravity to have pulled it into a (near-)spherical shape and that has cleared its immediate neighbourhood of all smaller objects. By this definition, the Solar System has eight planets: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. Because it has

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not cleared its neighbourhood of other Kuiper belt objects, Pluto does not fit this definition.[6] Instead, Pluto is a dwarf planet, a body orbiting the Sun that is massive enough to be made near-spherical by its own gravity but that has not cleared planetesimals from its neighbourhood and is also not a satellite.[6] In addition to Pluto, the IAU has recognized four other dwarf planets in the Solar System: Ceres, Haumea, Makemake, and Eris.[7] Other objects commonly (but not officially) treated as dwarf planets include 2007 OR10, Sedna, Orcus, and Quaoar.[8] In a reference to Pluto, other dwarf planets orbiting in the trans-Neptunian region are sometimes called "plutoids".[9] The remaining objects orbiting the Sun are known as small Solar System bodies.[6] [6] See List of natural satellites of the Solar System for the full list of natural satellites of the eight planets and first five dwarf planets [7] The mass of the Solar System excluding the Sun, Jupiter and Saturn can be determined by adding together all the calculated masses for its largest objects and using rough calculations for the masses of the Oort cloud (estimated at roughly 3 Earth masses),[14] the Kuiper belt (estimated at roughly 0.1 Earth mass)[15] and the asteroid belt (estimated to be 0.0005 Earth mass)[16] for a total, rounded upwards, of ~37 Earth masses, or 8.1% of the mass in orbit around the Sun. With the combined masses of Uranus and Neptune (~31 Earth masses) subtracted, the remaining ~6 Earth masses of material comprise 1.3% of the total orbiting mass. [8] The date is based on the oldest inclusions found to date in meteorites, 4568.2+0.2 −0.4 million years, and is thought to be the date of the formation of the first solid material in the collapsing nebula. A. Bouvier and M. Wadhwa. “The age of the Solar System redefined by the oldest Pb–Pb age of a meteoritic inclusion”. Nature Geoscience, 3, 637–641, 2010. doi:10.1038/NGEO941 [9] If ψ is the angle between the north pole of the ecliptic and the north galactic pole then: cos ψ = cos(βg ) cos(βe ) cos(αg −αe )+sin(βg ) sin(βe ) where βg = 27° 07′ 42.01″ and αg = 12h 51m 26.282 are the declination and right ascension of the north galactic pole,[135] whereas βe = 66° 33′ 38.6″ and αe = 18h 0m 00 are those for the north pole of the ecliptic. (Both pairs of coordinates are for J2000 epoch.) The result of the calculation is 60.19°.

14.15 References [1] Mike Brown (23 August 2011). “Free the dwarf planets!". “Mike Brown’s Planets (self-published)". [2] Sheppard, Scott S. “The Giant Planet Satellite and Moon Page”. Departament of Terrestrial Magnetism at Carniege Institution for science. Retrieved 7 March 2016. [3] Wm. Robert Johnston (6 March 2016). “Asteroids with Satellites”. Johnston’s Archive. Retrieved 7 March 2016.


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14.16. EXTERNAL LINKS

14.16 External links • A Cosmic History of the Solar System • A Tediously Accurate Map of the Solar System (web based scroll map scaled to the Moon being 1 pixel) • NASA’s Solar System Simulator • NASA/JPL Solar System main page • Solar System Profile by NASA’s Solar System Exploration

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Sun This article is about the star. For other uses, see Sun (disambiguation). The Sun is the star at the center of the Solar System. It is a nearly perfect sphere of hot plasma,[13][14] with internal convective motion that generates a magnetic field via a dynamo process.[15] It is by far the most important source of energy for life on Earth. Its diameter is about 109 times that of Earth, and its mass is about 330,000 times that of Earth, accounting for about 99.86% of the total mass of the Solar System.[16] About three quarters of the Sun’s mass consists of hydrogen; the rest is mostly helium, with much smaller quantities of heavier elements, including oxygen, carbon, neon, and iron.[17] The Sun is a G-type main-sequence star (G2V) based on its spectral class, and is informally referred to as a yellow dwarf. It formed approximately 4.6 billion[lower-alpha 1][9][18] years ago from the gravitational collapse of matter within a region of a large molecular cloud. Most of this matter gathered in the center, whereas the rest flattened into an orbiting disk that became the Solar System. The central mass became so hot and dense that it eventually initiated nuclear fusion in its core. It is thought that almost all stars form by this process. The Sun is roughly middle-aged: it has not changed dramatically for more than four billion[lower-alpha 1] years, and will remain fairly stable for more than another five billion years. After hydrogen fusion in its core has stopped, the Sun will undergo severe changes and become a red giant. It is calculated that the Sun will become sufficiently large to engulf the current orbits of Mercury, Venus, and possibly Earth. The enormous effect of the Sun on Earth has been recognized since prehistoric times, and the Sun has been regarded by some cultures as a deity. The synodic rotation of Earth and its orbit around the Sun are the basis of the solar calendar, which is the predominant calendar in use today.

15.1 Name and etymology The English proper name Sun developed from Old English sunne and may be related to south. Cognates to English sun appear in other Germanic languages, including Old Frisian sunne, sonne, Old Saxon sunna, Middle Dutch sonne, modern Dutch zon, Old High German sunna, modern German Sonne, Old Norse sunna, and Gothic sunnō. All Germanic terms for the Sun stem from ProtoGermanic *sunnōn.[19][20] The English weekday name Sunday stems from Old English (Sunnandæg; “Sun’s day”, from before 700) and is ultimately a result of a Germanic interpretation of Latin dies solis, itself a translation of the Greek ἡμέρα ἡλίου (hēméra hēlíou).[21] The Latin name for the Sun, Sol, is not common in general English language use; the adjectival form is the related word solar.[22][23] The term sol is also used by planetary astronomers to refer to the duration of a solar day on another planet, such as Mars.[24] A mean Earth solar day is approximately 24 hours, whereas a mean Martian 'sol' is 24 hours, 39 minutes, and 35.244 seconds.[25]

15.1.1 Religious aspects Main article: Solar deity Solar deities and Sun worship can be found throughout most of recorded history in various forms, including the Egyptian Ra, the Hindu Surya, the Japanese Amaterasu, the Germanic Sól, and the Aztec Tonatiuh, among others. From at least the 4th Dynasty of Ancient Egypt, the Sun was worshipped as the god Ra, portrayed as a falconheaded divinity surmounted by the solar disk, and surrounded by a serpent. In the New Empire period, the Sun became identified with the dung beetle, whose spherical ball of dung was identified with the Sun. In the form of the Sun disc Aten, the Sun had a brief resurgence during the Amarna Period when it again became the preeminent, if not only, divinity for the Pharaoh Akhenaton.[26][27] The Sun is viewed as a goddess in Germanic paganism, Sól/Sunna.[20] Scholars theorize that the Sun, as

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15.3. SUNLIGHT a Germanic goddess, may represent an extension of an earlier Proto-Indo-European Sun deity because of IndoEuropean linguistic connections between Old Norse Sól, Sanskrit Surya, Gaulish Sulis, Lithuanian Saulė, and Slavic Solntse.[20] In ancient Roman culture, Sunday was the day of the Sun god. It was adopted as the Sabbath day by Christians who did not have a Jewish background. The symbol of light was a pagan device adopted by Christians, and perhaps the most important one that did not come from Jewish traditions. In paganism, the Sun was a source of life, giving warmth and illumination to mankind. It was the center of a popular cult among Romans, who would stand at dawn to catch the first rays of sunshine as they prayed. The celebration of the winter solstice (which influenced Christmas) was part of the Roman cult of the unconquered Sun (Sol Invictus). Christian churches were built with an orientation so that the congregation faced toward the sunrise in the East.[28]

131 creasing distance from its center.[37] For the purpose of measurement, however, the Sun’s radius is considered to be the distance from its center to the edge of the photosphere, the apparent visible surface of the Sun.[38] By this measure, the Sun is a near-perfect sphere with an oblateness estimated at about 9 millionths,[39] which means that its polar diameter differs from its equatorial diameter by only 10 kilometres (6.2 mi).[40] The tidal effect of the planets is weak and does not significantly affect the shape of the Sun.[41] The Sun rotates faster at its equator than at its poles. This differential rotation is caused by convective motion due to heat transport and the Coriolis force due to the Sun’s rotation. In a frame of reference defined by the stars, the rotational period is approximately 25.6 days at the equator and 33.5 days at the poles. Viewed from Earth as it orbits the Sun, the apparent rotational period of the Sun at its equator is about 28 days.[42]

15.3 Sunlight 15.2 Characteristics

Main article: Sunlight

The Sun is a G-type main-sequence star that comprises about 99.86% of the mass of the Solar System. The Sun has an absolute magnitude of +4.83, estimated to be brighter than about 85% of the stars in the Milky Way, most of which are red dwarfs.[29][30] The Sun is a Population I, or heavy-element-rich,[lower-alpha 2] star.[31] The formation of the Sun may have been triggered by shockwaves from one or more nearby supernovae.[32] This is suggested by a high abundance of heavy elements in the Solar System, such as gold and uranium, relative to the abundances of these elements in so-called Population II, heavy-element-poor, stars. The heavy elements could most plausibly have been produced by endothermic nuclear reactions during a supernova, or by transmutation through neutron absorption within a massive secondgeneration star.[31]

The solar constant is the amount of power that the Sun deposits per unit area that is directly exposed to sunlight. The solar constant is equal to approximately 1,368 W/m2 (watts per square meter) at a distance of one astronomical unit (AU) from the Sun (that is, on or near Earth).[43] Sunlight on the surface of Earth is attenuated by Earth’s atmosphere, so that less power arrives at the surface (closer to 1,000 W/m2 ) in clear conditions when the Sun is near the zenith.[44] Sunlight at the top of Earth’s atmosphere is composed (by total energy) of about 50% infrared light, 40% visible light, and 10% ultraviolet light.[45] The atmosphere in particular filters out over 70% of solar ultraviolet, especially at the shorter wavelengths.[46] Solar ultraviolet radiation ionizes Earth’s dayside upper atmosphere, creating the electrically conducting ionosphere.[47]

The Sun is by far the brightest object in the sky, with an apparent magnitude of −26.74.[33][34] This is about 13 billion times brighter than the next brightest star, Sirius, which has an apparent magnitude of −1.46. The mean distance of the Sun’s center to Earth’s center is approximately 1 astronomical unit (about 150,000,000 km; 93,000,000 mi), though the distance varies as Earth moves from perihelion in January to aphelion in July.[35] At this average distance, light travels from the Sun’s horizon to Earth’s horizon in about 8 minutes and 19 seconds, while light from the closest points of the Sun and Earth takes about two seconds less. The energy of this sunlight supports almost all life[lower-alpha 3] on Earth by photosynthesis,[36] and drives Earth’s climate and weather.

The Sun’s color is white, with a CIE color-space index near (0.3, 0.3), when viewed from space or when the Sun is high in the sky. When measuring all the photons emitted, the Sun is actually emitting more photons in the green portion of the spectrum than any other.[48][49] When the Sun is low in the sky, atmospheric scattering renders the Sun yellow, red, orange, or magenta. Despite its typical whiteness, most people mentally picture the Sun as yellow; the reasons for this are the subject of debate.[50] The Sun is a G2V star, with G2 indicating its surface temperature of approximately 5,778 K (5,505 °C, 9,941 °F), and V that it, like most stars, is a mainsequence star.[51][52] The average luminance of the Sun is about 1.88 giga candela per square metre, but as viewed through Earth’s atmosphere, this is lowered to about 1.44 The Sun does not have a definite boundary, and in its Gcd/m2 .[lower-alpha 4] However, the luminance is not conouter parts its density decreases exponentially with in- stant across the disk of the Sun (limb darkening).


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15.4 Composition See also: Molecules in stars The Sun is composed primarily of the chemical elements hydrogen and helium; they account for 74.9% and 23.8% of the mass of the Sun in the photosphere, respectively.[53] All heavier elements, called metals in astronomy, account for less than 2% of the mass, with oxygen (roughly 1% of the Sun’s mass), carbon (0.3%), neon (0.2%), and iron (0.2%) being the most abundant.[54] The Sun inherited its chemical composition from the interstellar medium out of which it formed. The hydrogen and helium in the Sun were produced by Big Bang nucleosynthesis, and the heavier elements were produced by stellar nucleosynthesis in generations of stars that completed their stellar evolution and returned their material to the interstellar medium before the formation of the Sun.[55] The chemical composition of the photosphere is normally considered representative of the composition of the primordial Solar System.[56] However, since the Sun formed, some of the helium and heavy elements have gravitationally settled from the photosphere. Therefore, in today’s photosphere the helium fraction is reduced, and the metallicity is only 84% of what it was in the protostellar phase (before nuclear fusion in the core started). The protostellar Sun’s composition is believed to have been 71.1% hydrogen, 27.4% helium, and 1.5% heavier elements.[53]

CHAPTER 15. SUN nificant research was done, until 1978 it was difficult to determine the abundances of some iron-group elements (e.g. cobalt and manganese) via spectrography because of their hyperfine structures.[59] The first largely complete set of oscillator strengths of singly ionized iron-group elements were made available in the 1960s,[61] and these were subsequently improved.[62] In 1978, the abundances of singly ionized elements of the iron group were derived.[59]

15.4.2 Isotopic composition Various authors have considered the existence of a gradient in the isotopic compositions of solar and planetary noble gases,[63] e.g. correlations between isotopic compositions of neon and xenon in the Sun and on the planets.[64] Prior to 1983, it was thought that the whole Sun has the same composition as the solar atmosphere.[65] In 1983, it was claimed that it was fractionation in the Sun itself that caused the isotopic-composition relationship between the planetary and solar-wind-implanted noble gases.[65]

15.5 Structure 15.5.1 Core

Today, nuclear fusion in the Sun’s core has modified the Main article: Solar core composition by converting hydrogen into helium, so the The core of the Sun extends from the center to about 20– innermost portion of the Sun is now roughly 60% helium, with the abundance of heavier elements unchanged. Because heat is transferred from the Sun’s core by radiation rather than by convection (see Radiative zone below), none of the fusion products from the core have risen to the photosphere.[57] The reactive core zone of “hydrogen burning”, where hydrogen is converted into helium, is starting to surround an inner core of “helium ash”. This development will continue and will eventually cause the Sun to leave the main sequence, to become a red giant.[58] The structure of the Sun The solar heavy-element abundances described above are typically measured both using spectroscopy of the Sun’s 25% of the solar radius.[66] It has a density of up to 150 photosphere and by measuring abundances in meteorites g/cm3[67][68] (about 150 times the density of water) and that have never been heated to melting temperatures. a temperature of close to 15.7 million kelvins (K).[68] By These meteorites are thought to retain the composition contrast, the Sun’s surface temperature is approximately of the protostellar Sun and are thus not affected by set- 5,800 K. Recent analysis of SOHO mission data favors a tling of heavy elements. The two methods generally agree faster rotation rate in the core than in the radiative zone well.[17] above.[66] Through most of the Sun’s life, energy is produced by nuclear fusion in the core region through a series of steps called the p–p (proton–proton) chain; this pro15.4.1 Singly ionized iron-group elements cess converts hydrogen into helium.[69] Only 0.8% of the energy generated in the Sun comes from the CNO cycle, In the 1970s, much research focused on the abundances though this proportion is expected to increase as the Sun of iron-group elements in the Sun.[59][60] Although sig- becomes older.[70]


15.5. STRUCTURE

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The core is the only region in the Sun that produces an appreciable amount of thermal energy through fusion; 99% of the power is generated within 24% of the Sun’s radius, and by 30% of the radius, fusion has stopped nearly entirely. The remainder of the Sun is heated by this energy as it is transferred outwards through many successive layers, finally to the solar photosphere where it escapes into space as sunlight or the kinetic energy of particles.[51][71]

where the sharp regime change between the uniform rotation of the radiative zone and the differential rotation of the convection zone results in a large shear between the two—a condition where successive horizontal layers slide past one another.[77] The fluid motion of the convection zone above, slowly disappears from the top of this layer to its bottom where it matches that of the radiative zone. Presently, it is hypothesized (see Solar dynamo) that a magnetic dynamo within this layer generates the 37 The proton–proton chain occurs around 9.2×10 times [68] 38 each second in the core, converting about 3.7×10 pro- Sun’s magnetic field. tons into alpha particles (helium nuclei) every second (out of a total of ~8.9×1056 free protons in the Sun), or about 6.2×1011 kg/s.[51] Fusing four free protons (hydrogen nu- 15.5.4 Convective zone clei) into a single alpha particle (helium nuclei) releases around 0.7% of the fused mass as energy,[72] so the Sun Main article: Convection zone releases energy at the mass–energy conversion rate of 4.26 million metric tons per second, for 384.6 yottawatts The Sun’s convection zone extends from 0.7 solar radii (3.846×1026 W),[1] or 9.192×1010 megatons of TNT per (200,000 km) to near the surface. In this layer, the temsecond. Theoretical models of the Sun’s interior indicate perature is lower than in the radiative zone and heavier a power density of approximately 276.5 W/m3 ,[73] a value atoms are not fully ionized. As a result, radiative heat that more nearly approximates reptile metabolism than a transport is less effective and convection moves the Sun’s thermonuclear bomb.[lower-alpha 5] energy outward through this layer. The density of the The fusion rate in the core is in a self-correcting equilib- plasma is low enough to allow convective currents to derium: a slightly higher rate of fusion would cause the core velop. Material heated at the tachocline picks up heat to heat up more and expand slightly against the weight of and expands, thereby reducing its density and allowing it the outer layers, reducing the density and hence the fu- to rise. As a result, an orderly motion of the mass desion rate and correcting the perturbation; and a slightly velops into thermal cells that carry the majority of the lower rate would cause the core to cool and shrink slightly, heat outward to the Sun’s photosphere above. Once the increasing the density and increasing the fusion rate and material diffusively and radiatively cools just beneath the photospheric surface, its density increases, and it sinks again reverting it to its present rate.[74][75] to the base of the convection zone, where it again picks up heat from the top of the radiative zone and the convective cycle continues. At the photosphere, the temperature 15.5.2 Radiative zone has dropped to 5,700 K and the density to only 0.2 g/m3 (about 1/6,000 the density of air at sea level).[68] Main article: Radiative zone The thermal columns of the convection zone form an imFrom the core out to about 0.7 solar radii, thermal ra- print on the surface of the Sun giving it a granular apdiation is the primary means of energy transfer.[76] The pearance called the solar granulation at the smallest scale transfer of energy through this zone is by radiation not and supergranulation at larger scales. Turbulent convecby thermal convection. The temperature drops from ap- tion in this outer part of the solar interior sustains “smallproximately 7 million to 2 million kelvins with increasing scale” dynamo action over the near-surface volume of the [68] distance from the core.[68] This temperature gradient is Sun. The Sun’s thermal columns are Bénard cells and take the shape of hexagonal prisms.[78] less than the value of the adiabatic lapse rate and hence cannot drive convection, hence, energy is transferred by radiation.[68] Ions of hydrogen and helium emit photons, which travel only a brief distance before being reabsorbed 15.5.5 Photosphere by other ions.[76] The density drops a hundredfold (from 20 g/cm3 to only 0.2 g/cm3 ) from 0.25 solar radii to the Main article: Photosphere 0.7 radii, the top of the radiative zone.[76] The visible surface of the Sun, the photosphere, is the layer below which the Sun becomes opaque to visi15.5.3 Tachocline ble light.[79] Above the photosphere visible sunlight is free to propagate into space, and its energy escapes the Main article: Tachocline Sun entirely. The change in opacity is due to the decreasing amount of H− ions, which absorb visible light The radiative zone and the convective zone are separated easily.[79] Conversely, the visible light we see is produced by a transition layer, the tachocline. This is a region as electrons react with hydrogen atoms to produce H−


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CHAPTER 15. SUN

The effective temperature, or black body temperature, of the Sun (5,777 K) is the temperature a black body of the same size must have to yield the same total emissive power.

ions.[80][81] The photosphere is tens to hundreds of kilometers thick, and is slightly less opaque than air on Earth. Because the upper part of the photosphere is cooler than the lower part, an image of the Sun appears brighter in the center than on the edge or limb of the solar disk, in a phenomenon known as limb darkening.[79] The spectrum of sunlight has approximately the spectrum of a blackbody radiating at about 6,000 K, interspersed with atomic absorption lines from the tenuous layers above the photosphere. The photosphere has a particle density of ~1023 m−3 (about 0.37% of the particle number per volume of Earth’s atmosphere at sea level). The photosphere is not fully ionized—the extent of ionization is about 3%, leaving almost all of the hydrogen in atomic form.[82]

During a total solar eclipse, the solar corona can be seen with the naked eye, during the brief period of totality.

is not well understood, but evidence suggests that Alfvén waves may have enough energy to heat the corona.[85]

Above the temperature minimum layer is a layer about 2,000 km thick, dominated by a spectrum of emission and absorption lines.[79] It is called the chromosphere from the Greek root chroma, meaning color, because the chromosphere is visible as a colored flash at the beginning and end of total solar eclipses.[76] The temperature of the chromosphere increases gradually with altitude, ranging up to around 20,000 K near the top.[79] In the upper part of the chromosphere helium becomes partially During early studies of the optical spectrum of the photoionized.[86] sphere, some absorption lines were found that did not correspond to any chemical elements then known on Earth. In 1868, Norman Lockyer hypothesized that these absorption lines were caused by a new element that he dubbed helium, after the Greek Sun god Helios. Twentyfive years later, helium was isolated on Earth.[83]

15.5.6

Atmosphere

See also: Corona and Coronal loop During a total solar eclipse, when the disk of the Sun is covered by that of the Moon, parts of the Sun’s surrounding atmosphere can be seen. It is composed of four distinct parts: the chromosphere, the transition region, the Taken by Hinode's Solar Optical Telescope on 12 January 2007, corona and the heliosphere. The coolest layer of the Sun is a temperature minimum region extending to about 500 km above the photosphere, and has a temperature of about 4,100 K.[79] This part of the Sun is cool enough to allow the existence of simple molecules such as carbon monoxide and water, which can be detected via their absorption spectra.[84]

this image of the Sun reveals the filamentary nature of the plasma connecting regions of different magnetic polarity.

Above the chromosphere, in a thin (about 200 km) transition region, the temperature rises rapidly from around 20,000 K in the upper chromosphere to coronal temperatures closer to 1,000,000 K.[87] The temThe chromosphere, transition region, and corona are perature increase is facilitated by the full ionization of much hotter than the surface of the Sun.[79] The reason helium in the transition region, which significantly re-


15.6. MAGNETISM AND ACTIVITY

The corona is the next layer of the Sun. The low corona, near the surface of the Sun, has a particle density around 1015 m−3 to 1016 m−3 .[86][lower-alpha 6] The average temperature of the corona and solar wind is about 1,000,000–2,000,000 K; however, in the hottest regions it is 8,000,000–20,000,000 K.[87] Although no complete theory yet exists to account for the temperature of the corona, at least some of its heat is known to be from magnetic reconnection.[87][89] The corona is the extended atmosphere of the Sun, which has a volume much larger than the volume enclosed by the Sun’s photosphere. A flow of plasma outward from the Sun into interplanetary space is the solar wind.[89]

with matter, the time scale of energy transport in the Sun is longer, on the order of 30,000,000 years. This is the time it would take the Sun to return to a stable state, if the rate of energy generation in its core were suddenly changed.[96] Neutrinos are also released by the fusion reactions in the core, but, unlike photons, they rarely interact with matter, so almost all are able to escape the Sun immediately. For many years measurements of the number of neutrinos produced in the Sun were lower than theories predicted by a factor of 3. This discrepancy was resolved in 2001 through the discovery of the effects of neutrino oscillation: the Sun emits the number of neutrinos predicted by the theory, but neutrino detectors were missing 2 ⁄3 of them because the neutrinos had changed flavor by the time they were detected.[97]

15.6 Magnetism and activity 15.6.1 Magnetic field

Latitude

The heliosphere, the tenuous outermost atmosphere of the Sun, is filled with the solar wind plasma. This outSee also: Stellar magnetic field, Sunspots, List of solar ermost layer of the Sun is defined to begin at the discycles, and Solar phenomena tance where the flow of the solar wind becomes superPosition and area of sunspots 90N alfvénic—that is, where the flow becomes faster than the 30N speed of Alfvén waves,[90] at approximately 20 solar radii EQ (0.1 AU). Turbulence and dynamic forces in the helio30S sphere cannot affect the shape of the solar corona within, because the information can only travel at the speed of 90S 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020 Date Alfvén waves. The solar wind travels outward continArea in relation to the visible hemisphere < 80 ppm < 600 ppm ≥ 600 ppm [91][92] uously through the heliosphere, forming the solar [89] magnetic field into a spiral shape, until it impacts the heliopause more than 50 AU from the Sun. In December 2004, the Voyager 1 probe passed through a shock front that is thought to be part of the heliopause.[93] In late 2012 Voyager 1 recorded a marked increase in cosmic ray collisions and a sharp drop in lower energy particles from the solar wind, which suggested that the probe had passed through the heliopause and entered the interstellar medium.[94]

15.5.7

Photons and neutrinos

High-energy gamma-ray photons initially released with fusion reactions in the core are almost immediately absorbed by the solar plasma of the radiative zone, usually after traveling only a few millimeters. Re-emission happens in a random direction and usually at a slightly lower energy. With this sequence of emissions and absorptions, it takes a long time for radiation to reach the Sun’s surface. Estimates of the photon travel time range between 10,000 and 170,000 years.[95] In contrast, it takes only 2.3 seconds for the neutrinos, which account for about 2% of the total energy production of the Sun, to reach the surface. Because energy transport in the Sun is a process that involves photons in thermodynamic equilibrium

Visible light photograph of sunspot, 13 December 2006

diagram showing paired sunspot pattern. Graph is of sunspot area. The Sun has a magnetic field that varies across the surface of the Sun. Its polar field is 1–2 gauss (0.0001– 0.0002 T), whereas the field is typically 3,000 gauss (0.3 T) in features on the Sun called sunspots and 10–100 gauss (0.001–0.01 T) in solar prominences.[1] The magnetic field also varies in time and location. The quasi-periodic 11-year solar cycle is the most prominent variation in which the number and size of sunspots waxes

% of Sun's visible hemisphere

duces radiative cooling of the plasma.[86] The transition region does not occur at a well-defined altitude. Rather, it forms a kind of nimbus around chromospheric features such as spicules and filaments, and is in constant, chaotic motion.[76] The transition region is not easily visible from Earth’s surface, but is readily observable from space by instruments sensitive to the extreme ultraviolet portion of the spectrum.[88]

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0.5 0.4 0.3 0.2 0.1

11 0 1870 18


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CHAPTER 15. SUN lar magnetic fields. At solar-cycle maximum, the external poloidal dipolar magnetic field is near its dynamo-cycle minimum strength, but an internal toroidal quadrupolar field, generated through differential rotation within the tachocline, is near its maximum strength. At this point in the dynamo cycle, buoyant upwelling within the convective zone forces emergence of toroidal magnetic field through the photosphere, giving rise to pairs of sunspots, roughly aligned east–west and having footprints with opposite magnetic polarities. The magnetic polarity of sunspot pairs alternates every solar cycle, a phenomenon known as the Hale cycle.[102][103]

During the solar cycle’s declining phase, energy shifts from the internal toroidal magnetic field to the external poloidal field, and sunspots diminish in number. At solarcycle minimum, the toroidal field is, correspondingly, at In this false-color ultraviolet image, the Sun shows a C3-class minimum strength, sunspots are relatively rare, and the solar flare (white area on upper left), a solar tsunami (wave-like poloidal field is at its maximum strength. With the rise of structure, upper right) and multiple filaments of plasma following the next 11-year sunspot cycle, differential rotation shifts a magnetic field, rising from the stellar surface. magnetic energy back from the poloidal to the toroidal field, but with a polarity that is opposite to the previous cycle. The process carries on continuously, and in an idealized, simplified scenario, each 11-year sunspot cycle corresponds to a change, then, in the overall polarity of the Sun’s large-scale magnetic field.[104][105]

The heliospheric current sheet extends to the outer reaches of the Solar System, and results from the influence of the Sun’s rotating magnetic field on the plasma in the interplanetary medium.[98]

and wanes.[15][99][100]

The solar magnetic field extends well beyond the Sun itself. The electrically conducting solar wind plasma carries the Sun’s magnetic field into space, forming what is called the interplanetary magnetic field.[89] In an approximation known as ideal magnetohydrodynamics, plasma particles only move along the magnetic field lines. As a result, the outward-flowing solar wind stretches the interplanetary magnetic field outward, forcing it into a roughly radial structure. For a simple dipolar solar magnetic field, with opposite hemispherical polarities on either side of the solar magnetic equator, a thin current sheet is formed in the solar wind.[89] At great distances, the rotation of the Sun twists the dipolar magnetic field and corresponding current sheet into an Archimedean spiral structure called the Parker spiral.[89] The interplanetary magnetic field is much stronger than the dipole component of the solar magnetic field. The Sun’s dipole magnetic field of 50–400 μT (at the photosphere) reduces with the inverse-cube of the distance to about 0.1 nT at the distance of Earth. However, according to spacecraft observations the interplanetary field at Earth’s location is around 5 nT, about a hundred times greater.[106] The difference is due to magnetic fields generated by electrical currents in the plasma surrounding the Sun.

Sunspots are visible as dark patches on the Sun’s photosphere, and correspond to concentrations of magnetic field where the convective transport of heat is inhibited from the solar interior to the surface. As a result, sunspots are slightly cooler than the surrounding photosphere, and, so, they appear dark. At a typical solar minimum, few sunspots are visible, and occasionally none can be seen at all. Those that do appear are at high solar latitudes. As the solar cycle progresses towards its maximum, sunspots tend form closer to the so15.6.2 Variation in activity lar equator, a phenomenon known as Spörer’s law. The largest sunspots can be tens of thousands of kilometers The Sun’s magnetic field leads to many effects that are across.[101] collectively called solar activity. Solar flares and coronalAn 11-year sunspot cycle is half of a 22-year Babcock– mass ejections tend to occur at sunspot groups. Slowly Leighton dynamo cycle, which corresponds to an oscilla- changing high-speed streams of solar wind are emitted tory exchange of energy between toroidal and poloidal so- from coronal holes at the photospheric surface. Both


15.7. LIFE PHASES

137 four billion[lower-alpha 1] years, and will remain fairly stable for more than five billion more. However, after hydrogen fusion in its core has stopped, the Sun will undergo severe changes, both internally and externally.

15.7.1 Formation

Measurements of solar cycle variation during the last 30 years

coronal-mass ejections and high-speed streams of solar wind carry plasma and interplanetary magnetic field outward into the Solar System.[107] The effects of solar activity on Earth include auroras at moderate to high latitudes and the disruption of radio communications and electric power. Solar activity is thought to have played a large role in the formation and evolution of the Solar System. With solar-cycle modulation of sunspot number comes a corresponding modulation of space weather conditions, including those surrounding Earth where technological systems can be affected.

15.6.3

Long-term change

The Sun formed about 4.6 billion years ago from the collapse of part of a giant molecular cloud that consisted mostly of hydrogen and helium and that probably gave birth to many other stars.[114] This age is estimated using computer models of stellar evolution and through nucleocosmochronology.[9] The result is consistent with the radiometric date of the oldest Solar System material, at 4.567 billion years ago.[115][116] Studies of ancient meteorites reveal traces of stable daughter nuclei of short-lived isotopes, such as iron-60, that form only in exploding, short-lived stars. This indicates that one or more supernovae must have occurred near the location where the Sun formed. A shock wave from a nearby supernova would have triggered the formation of the Sun by compressing the matter within the molecular cloud and causing certain regions to collapse under their own gravity.[117] As one fragment of the cloud collapsed it also began to rotate because of conservation of angular momentum and heat up with the increasing pressure. Much of the mass became concentrated in the center, whereas the rest flattened out into a disk that would become the planets and other Solar System bodies. Gravity and pressure within the core of the cloud generated a lot of heat as it accreted more matter from the surrounding disk, eventually triggering nuclear fusion. Thus, the Sun was born.

A recent theory claims that there are magnetic instabilities in the core of the Sun that cause fluctuations with periods of either 41,000 or 100,000 years. These could provide a better explanation of the ice ages than the Milankovitch cycles.[112][113]

Ratio with current Sun

Long-term secular change in sunspot number is thought, by some scientists, to be correlated with long-term change in solar irradiance,[108] which, in turn, might influence Earth’s long-term climate.[109] For example, in the 17th century, the solar cycle appeared to have stopped 15.7.2 entirely for several decades; few sunspots were observed 2.0 during a period known as the Maunder minimum. This coincided in time with the era of the Little Ice Age, when 1.8 Europe experienced unusually cold temperatures.[110] Earlier extended minima have been discovered through 1.6 analysis of tree rings and appear to have coincided with 1.4 lower-than-average global temperatures.[111]

Main sequence

Luminosity Radius Temperature

1.2

Now 1.0

0.8

0.6

1

2

3

4

5

6

7

8

9

10

11

12

Age (billions of years)

15.7 Life phases

Evolution of the Sun’s luminosity, radius and effective temperature compared to the present Sun. After Ribas (2010)[118]

Main articles: Formation and evolution of the Solar The Sun is about halfway through its main-sequence System and Stellar evolution stage, during which nuclear fusion reactions in its core fuse hydrogen into helium. Each second, more than four The Sun today is roughly halfway through the most stable million tonnes of matter are converted into energy within part of its life. It has not changed dramatically for over the Sun’s core, producing neutrinos and solar radiation.


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15.7.3

After core hydrogen exhaustion

The Sun as a red giant (diameter ≈ 2 AU)

The Sun as a main-sequence star (diameter ≈ 0.01 AU)

The size of the current Sun (now in the main sequence) compared to its estimated size during its red-giant phase in the future

The Sun does not have enough mass to explode as a supernova. Instead it will exit the main sequence in approximately 5 billion years and start to turn into a red giant.[122][123] As a red giant, the Sun will grow so large that it will engulf Mercury, Venus, and probably Earth.[123][124] Even before it becomes a red giant, the luminosity of the Sun will have nearly doubled, and Earth will be hotter than Venus is today. Once the core hydrogen is exhausted in 5.4 billion years, the Sun will expand into a subgiant phase and slowly double in size over about half a billion years. It will then expand more rapidly over about half a billion years until it is over two hundred times larger than today and a couple of thousand times more luminous. This then starts the red-giant-branch phase where the Sun will spend around a billion years and lose around a third of its mass.[123]

Evolution of the Sun from main sequence to end of fusion 10,000

Fusion ends Planetary nebula Towards white dwarf

Helium shell burning Asymptotic Giant Branch (<1 million years)

1,000

Luminosity [L⊙]

At this rate, the Sun has so far converted around 100 times the mass of Earth into energy, about 0.03% of the total mass of the Sun. The Sun will spend a total of approximately 10 billion years as a main-sequence star.[119] The Sun is gradually becoming hotter during its time on the main sequence, because the helium atoms in the core occupy less volume than the hydrogen atoms that were fused. The core is therefore shrinking, allowing the outer layers of the Sun to move closer to the centre and experience a stronger gravitational force, according to the inverse-square law. This stronger force increases the pressure on the core, which is resisted by a gradual increase in the rate at which fusion occurs. This process speeds up as the core gradually becomes denser. It is estimated that the Sun has become 30% brighter in the last 4.5 billion years.[120] At present, it is increasing in brightness by about 1% every 100 million years.[121]

Core helium ignition (flash) 100

Core helium burning Horizontal branch (100 million years)

Shell hydrogen burning Red Giant (1 billion years)

10

Zero

1

Core hydrogen burning (9 billion years)

Age

Mai n

Seq

uen ce

0.1 8,000

7,000

6,000

5,000

4,000

Temperature [K]

Evolution of a Sun-like star. The track of a one solar mass star on the Hertzsprung–Russell diagram is shown from the main sequence to the post-asymptotic-giant-branch stage.

After the red-giant branch the Sun has approximately 120 million years of active life left, but much happens. First, the core, full of degenerate helium ignites violently in the helium flash, where it is estimated that 6% of the core, itself 40% of the Sun’s mass, will be converted into carbon within a matter of minutes through the triple-alpha process.[125] The Sun then shrinks to around 10 times its current size and 50 times the luminosity, with a temperature a little lower than today. It will then have reached the red clump or horizontal branch, but a star of the Sun’s mass does not evolve blueward along the horizontal branch. Instead, it just becomes moderately larger and more luminous over about 100 million years as it continues to burn helium in the core.[123] When the helium is exhausted, the Sun will repeat the expansion it followed when the hydrogen in the core was exhausted, except that this time it all happens faster, and the Sun becomes larger and more luminous. This is the asymptotic-giant-branch phase, and the Sun is alternately burning hydrogen in a shell or helium in a deeper shell. After about 20 million years on the early asymptotic giant branch, the Sun becomes increasingly unstable, with rapid mass loss and thermal pulses that increase the size and luminosity for a few hundred years every 100,000 years or so. The thermal pulses become larger each time, with the later pulses pushing the luminosity to as much as 5,000 times the current level and the radius to over 1 AU.[126] According to a 2008 model, Earth’s orbit is shrinking due to tidal forces (and, eventually, drag from the lower chromosphere), so that it is engulfed by the Sun near the end of the asymptotic-giant-branch phase. Models vary depending on the rate and timing of mass loss. Models that have higher mass loss on the red-giant branch produce smaller, less luminous stars at the tip of the asymptotic giant branch, perhaps only 2,000 times the luminosity and less than 200 times the radius.[123]

3,000


15.9. THEORETICAL PROBLEMS For the Sun, four thermal pulses are predicted before it completely loses its outer envelope and starts to make a planetary nebula. By the end of that phase – lasting approximately 500,000 years – the Sun will only have about half of its current mass. The post-asymptotic-giant-branch evolution is even faster. The luminosity stays approximately constant as the temperature increases, with the ejected half of the Sun’s mass becoming ionised into a planetary nebula as the exposed core reaches 30,000 K. The final naked core, a white dwarf, will have a temperature of over 100,000 K, and contain an estimated 54.05% of the Sun’s present day mass.[123] The planetary nebula will disperse in about 10,000 years, but the white dwarf will survive for trillions of years before fading to a hypothetical black.[127][128]

15.8 Motion and location 15.8.1

Orbit in Milky Way

139 ing the red dwarf Proxima Centauri at approximately 4.2 light-years), the Sun ranks fourth in mass.[137] The Sun is orbiting the center of the Milky Way, going in the direction of Cygnus. The Sun’s orbit around the Milky Way is expected to be roughly elliptical with the addition of perturbations due to the galactic spiral arms and non-uniform mass distributions. In addition the Sun oscillates up and down relative to the galactic plane approximately 2.7 times per orbit.[138] It has been argued that the Sun’s passage through the higher density spiral arms often coincides with mass extinctions on Earth, perhaps due to increased impact events.[139] It takes the Solar System about 225–250 million years to complete one orbit through the Milky Way (a galactic year),[140] so it is thought to have completed 20–25 orbits during the lifetime of the Sun. The orbital speed of the Solar System about the center of the Milky Way is approximately 251 km/s (156 mi/s).[141] At this speed, it takes around 1,190 years for the Solar System to travel a distance of 1 lightyear, or 7 days to travel 1 AU.[142] The Milky Way is moving with respect to the cosmic microwave background radiation (CMB) in the direction of the constellation Hydra with a speed of 550 km/s, and the Sun’s resultant velocity with respect to the CMB is about 370 km/s in the direction of Crater or Leo.[143]

15.9 Theoretical problems

Illustration of the Milky Way, showing the location of the Sun

The Sun lies close to the inner rim of the Milky Way's Orion Arm, in the Local Interstellar Cloud or the Gould Belt, at a distance of 7.5–8.5 kpc (25,000–28,000 lightyears) from the Galactic Center.[129][130] [131][132][133][134] The Sun is contained within the Local Bubble, a space of rarefied hot gas, possibly produced by the supernova remnant Geminga.[135] The distance between the local arm and the next arm out, the Perseus Arm, is about 6,500 light-years.[136] The Sun, and thus the Solar System, is found in what scientists call the galactic habitable zone. The Apex of the Sun’s Way, or the solar apex, is the direction that the Sun travels relative to other nearby stars. This motion is towards a point in the constellation Hercules, near the star Vega. Of the 50 nearest stellar systems within 17 light-years from Earth (the closest be-

Map of the full Sun by STEREO and SDO spacecraft

15.9.1 Coronal heating problem Main article: Corona The temperature of the photosphere is approximately 6,000 K, whereas the temperature of the corona reaches 1,000,000–2,000,000 K.[87] The high temperature of the corona shows that it is heated by something other than direct heat conduction from the photosphere.[89] It is thought that the energy necessary to heat the corona is provided by turbulent motion in the convection zone below the photosphere, and two main mechanisms have been proposed to explain coronal heating.[87] The first is


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wave heating, in which sound, gravitational or magnetohydrodynamic waves are produced by turbulence in the convection zone.[87] These waves travel upward and dissipate in the corona, depositing their energy in the ambient matter in the form of heat.[144] The other is magnetic heating, in which magnetic energy is continuously built up by photospheric motion and released through magnetic reconnection in the form of large solar flares and myriad similar but smaller events—nanoflares.[145] Currently, it is unclear whether waves are an efficient heating mechanism. All waves except Alfvén waves have been found to dissipate or refract before reaching the corona.[146] In addition, Alfvén waves do not easily dissipate in the corona. Current research focus has therefore The Trundholm sun chariot pulled by a horse is a sculpture beshifted towards flare heating mechanisms.[87] lieved to be illustrating an important part of Nordic Bronze Age mythology. The sculpture is probably from around 1350 BC. It is displayed at the National Museum of Denmark.

15.9.2

Faint young Sun problem

Main article: Faint young Sun paradox Theoretical models of the Sun’s development suggest that 3.8 to 2.5 billion years ago, during the Archean period, the Sun was only about 75% as bright as it is today. Such a weak star would not have been able to sustain liquid water on Earth’s surface, and thus life should not have been able to develop. However, the geological record demonstrates that Earth has remained at a fairly constant temperature throughout its history, and that the young Earth was somewhat warmer than it is today. The consensus among scientists is that the atmosphere of the young Earth contained much larger quantities of greenhouse gases (such as carbon dioxide, methane and/or ammonia) than are present today, which trapped enough heat to compensate for the smaller amount of solar energy reaching it.[147]

what is now Mexico. In religions such as Hinduism, the Sun is still considered a god. Many ancient monuments were constructed with solar phenomena in mind; for example, stone megaliths accurately mark the summer or winter solstice (some of the most prominent megaliths are located in Nabta Playa, Egypt; Mnajdra, Malta and at Stonehenge, England); Newgrange, a prehistoric humanbuilt mount in Ireland, was designed to detect the winter solstice; the pyramid of El Castillo at Chichén Itzá in Mexico is designed to cast shadows in the shape of serpents climbing the pyramid at the vernal and autumnal equinoxes.

The Egyptians portrayed the god Ra as being carried across the sky in a solar barque, accompanied by lesser gods, and to the Greeks, he was Helios, carried by a chariot drawn by fiery horses. From the reign of Elagabalus in the late Roman Empire the Sun’s birthday was a holiday celebrated as Sol Invictus (literally “Unconquered Sun”) soon after the winter solstice, which may have been an 15.10 History of observation antecedent to Christmas. Regarding the fixed stars, the Sun appears from Earth to revolve once a year along the The enormous effect of the Sun on Earth has been rec- ecliptic through the zodiac, and so Greek astronomers ognized since prehistoric times, and the Sun has been considered it to be one of the seven planets (Greek planregarded by some cultures as a deity. etes, “wanderer”), after which the seven days of the week are named in some languages.[148][149][150]

15.10.1

Early understanding

See also: The Sun in culture The Sun has been an object of veneration in many cultures throughout human history. Humanity’s most fundamental understanding of the Sun is as the luminous disk in the sky, whose presence above the horizon creates day and whose absence causes night. In many prehistoric and ancient cultures, the Sun was thought to be a solar deity or other supernatural entity. Worship of the Sun was central to civilizations such as the ancient Egyptians, the Inca of South America and the Aztecs of

15.10.2 Development of scientific understanding In the early first millennium BC, Babylonian astronomers observed that the Sun’s motion along the ecliptic is not uniform, though they did not know why; it is today known that this is due to the movement of Earth in an elliptic orbit around the Sun, with Earth moving faster when it is nearer to the Sun at perihelion and moving slower when it is farther away at aphelion.[151] One of the first people to offer a scientific or philosoph-


15.10. HISTORY OF OBSERVATION

141

ical explanation for the Sun was the Greek philosopher Anaxagoras, who reasoned that it is a giant flaming ball of metal even larger than the Peloponnesus rather than the chariot of Helios, and that the Moon reflected the light of the Sun.[152] For teaching this heresy, he was imprisoned by the authorities and sentenced to death, though he was later released through the intervention of Pericles. Eratosthenes estimated the distance between Earth and the Sun in the 3rd century BC as “of stadia myriads 400 and 80000”, the translation of which is ambiguous, implying either 4,080,000 stadia (755,000 km) or 804,000,000 stadia (148 to 153 million kilometers or 0.99 to 1.02 AU); the latter value is correct to within a few percent. In the 1st century AD, Ptolemy estimated Sol, the Sun, from a 1550 edition of Guido Bonatti's Liber asthe distance as 1,210 times the radius of Earth, approxi- tronomiae. mately 7.71 million kilometers (0.0515 AU).[153] The theory that the Sun is the center around which the planets orbit was first proposed by the ancient Greek Aristarchus of Samos in the 3rd century BC, and later adopted by Seleucus of Seleucia (see Heliocentrism). This view was developed in a more detailed mathematical model of a heliocentric system in the 16th century by Nicolaus Copernicus. Observations of sunspots were recorded during the Han Dynasty (206 BC–AD 220) by Chinese astronomers, who maintained records of these observations for centuries. Averroes also provided a description of sunspots in the 12th century.[154] The invention of the telescope in the early 17th century permitted detailed observations of sunspots by Thomas Harriot, Galileo Galilei and other astronomers. Galileo posited that sunspots were on the surface of the Sun rather than small objects passing between Earth and the Sun.[155] Arabic astronomical contributions include Albatenius' discovery that the direction of the Sun’s apogee (the place in the Sun’s orbit against the fixed stars where it seems to be moving slowest) is changing.[156] (In modern heliocentric terms, this is caused by a gradual motion of the aphelion of the Earth’s orbit). Ibn Yunus observed more than 10,000 entries for the Sun’s position for many years using a large astrolabe.[157] From an observation of a transit of Venus in 1032, the Persian astronomer and polymath Avicenna concluded that Venus is closer to Earth than the Sun.[158] In 1672 Giovanni Cassini and Jean Richer determined the distance to Mars and were thereby able to calculate the distance to the Sun.

tific era, the source of the Sun’s energy was a significant puzzle. Lord Kelvin suggested that the Sun is a gradually cooling liquid body that is radiating an internal store of heat.[161] Kelvin and Hermann von Helmholtz then proposed a gravitational contraction mechanism to explain the energy output, but the resulting age estimate was only 20 million years, well short of the time span of at least 300 million years suggested by some geological discoveries of that time.[161][162] In 1890 Joseph Lockyer, who discovered helium in the solar spectrum, proposed a meteoritic hypothesis for the formation and evolution of the Sun.[163] Not until 1904 was a documented solution offered. Ernest Rutherford suggested that the Sun’s output could be maintained by an internal source of heat, and suggested radioactive decay as the source.[164] However, it would be Albert Einstein who would provide the essential clue to the source of the Sun’s energy output with his mass-energy equivalence relation E = mc2 .[165] In 1920, Sir Arthur Eddington proposed that the pressures and temperatures at the core of the Sun could produce a nuclear fusion reaction that merged hydrogen (protons) into helium nuclei, resulting in a production of energy from the net change in mass.[166] The preponderance of hydrogen in the Sun was confirmed in 1925 by Cecilia Payne using the ionization theory developed by Meghnad Saha, an Indian physicist. The theoretical concept of fusion was developed in the 1930s by the astrophysicists Subrahmanyan Chandrasekhar and Hans Bethe. Hans Bethe calculated the details of the two main energyproducing nuclear reactions that power the Sun.[167][168] In 1957, Margaret Burbidge, Geoffrey Burbidge, William Fowler and Fred Hoyle showed that most of the elements in the universe have been synthesized by nuclear reactions inside stars, some like the Sun.[169]

In 1666, Isaac Newton observed the Sun’s light using a prism, and showed that it is made up of light of many colors.[159] In 1800, William Herschel discovered infrared radiation beyond the red part of the solar spectrum.[160] The 19th century saw advancement in spectroscopic studies of the Sun; Joseph von Fraunhofer 15.10.3 Solar space missions recorded more than 600 absorption lines in the spectrum, the strongest of which are still often referred to as See also: Solar observatory Fraunhofer lines. In the early years of the modern scienThe first satellites designed to observe the Sun were


142

CHAPTER 15. SUN transients”, and of coronal holes, now known to be intimately associated with the solar wind.[173] In 1980, the Solar Maximum Mission was launched by NASA. This spacecraft was designed to observe gamma rays, X-rays and UV radiation from solar flares during a time of high solar activity and solar luminosity. Just a few months after launch, however, an electronics failure caused the probe to go into standby mode, and it spent the next three years in this inactive state. In 1984 Space Shuttle Challenger mission STS-41C retrieved the satellite and repaired its electronics before re-releasing it into orbit. The Solar Maximum Mission subsequently acquired thousands of images of the solar corona before reentering Earth’s atmosphere in June 1989.[174]

The Sun giving out a large geomagnetic storm on 1:29 pm, EST, 13 March 2012

Launched in 1991, Japan’s Yohkoh (Sunbeam) satellite observed solar flares at X-ray wavelengths. Mission data allowed scientists to identify several different types of flares, and demonstrated that the corona away from regions of peak activity was much more dynamic and active than had previously been supposed. Yohkoh observed an entire solar cycle but went into standby mode when an annular eclipse in 2001 caused it to lose its lock on the Sun. It was destroyed by atmospheric re-entry in 2005.[175]

One of the most important solar missions to date has been the Solar and Heliospheric Observatory, jointly built by the European Space Agency and NASA and launched on 2 December 1995.[88] Originally intended to serve a two-year mission, a mission extension through 2012 was approved in October 2009.[176] It has proven so useful that a follow-on mission, the Solar Dynamics Observatory (SDO), was launched in February 2010.[177] Situated at the Lagrangian point between Earth and the Sun (at which the gravitational pull from both is equal), SOHO has proA lunar transit of the Sun captured during calibration of STEREO vided a constant view of the Sun at many wavelengths since its launch.[88] Besides its direct solar observation, B’s ultraviolet imaging cameras[170] SOHO has enabled the discovery of a large number of comets, mostly tiny sungrazing comets that incinerate as NASA's Pioneers 5, 6, 7, 8 and 9, which were launched they pass the Sun.[178] between 1959 and 1968. These probes orbited the Sun at a distance similar to that of Earth, and made the first detailed measurements of the solar wind and the solar magnetic field. Pioneer 9 operated for a particularly long time, transmitting data until May 1983.[171][172] In the 1970s, two Helios spacecraft and the Skylab Apollo Telescope Mount provided scientists with significant new data on solar wind and the solar corona. The Helios 1 and 2 probes were U.S.–German collaborations that studied the solar wind from an orbit carrying the spacecraft inside Mercury's orbit at perihelion.[173] The Skylab space station, launched by NASA in 1973, included a solar observatory module called the Apollo Telescope Mount that was operated by astronauts resident on the station.[88] Skylab made the first time-resolved observations of the solar transition region and of ultraviolet emissions from the solar corona.[88] Discoveries included the first observations of coronal mass ejections, then called “coronal

A solar prominence erupts in August 2012, as captured by SDO

All these satellites have observed the Sun from the plane of the ecliptic, and so have only observed its equatorial regions in detail. The Ulysses probe was launched in 1990 to study the Sun’s polar regions. It first travelled


15.11. OBSERVATION AND EFFECTS

143

to Jupiter, to “slingshot” into an orbit that would take it far above the plane of the ecliptic. Once Ulysses was in its scheduled orbit, it began observing the solar wind and magnetic field strength at high solar latitudes, finding that the solar wind from high latitudes was moving at about 750 km/s, which was slower than expected, and that there were large magnetic waves emerging from high latitudes that scattered galactic cosmic rays.[179] Elemental abundances in the photosphere are well known from spectroscopic studies, but the composition of the interior of the Sun is more poorly understood. A solar wind sample return mission, Genesis, was designed to allow astronomers to directly measure the composition of The Sun, as seen from low Earth orbit overlooking the solar material.[180] International Space Station. This sunlight is not filtered by the The Solar Terrestrial Relations Observatory (STEREO) mission was launched in October 2006. Two identical spacecraft were launched into orbits that cause them to (respectively) pull further ahead of and fall gradually behind Earth. This enables stereoscopic imaging of the Sun and solar phenomena, such as coronal mass ejections.[181][182]

lower atmosphere, which blocks much of the solar spectrum

UV, and not whether one looks directly at the Sun.[188] Long-duration viewing of the direct Sun with the naked eye can begin to cause UV-induced, sunburn-like lesions on the retina after about 100 seconds, particularly under conditions where the UV light from the Sun is intense and The Indian Space Research Organisation has scheduled well focused;[189][190] conditions are worsened by young the launch of a 100 kg satellite named Aditya for 2017– eyes or new lens implants (which admit more UV than 18. Its main instrument will be a coronagraph for studyaging natural eyes), Sun angles near the zenith, and obing the dynamics of the Solar corona.[183] serving locations at high altitude. Viewing the Sun through light-concentrating optics such as binoculars may result in permanent damage to the 15.11 Observation and effects retina without an appropriate filter that blocks UV and substantially dims the sunlight. When using an attenuating filter to view the Sun, the viewer is cautioned to use a filter specifically designed for that use. Some improvised filters that pass UV or IR rays, can actually harm the eye at high brightness levels.[191] Herschel wedges, also called Solar Diagonals, are effective and inexpensive for small telescopes. The sunlight that is destined for the eyepiece is reflected from an unsilvered surface of a piece of glass. Only a very small fraction of the incident light is reflected. The rest passes through the glass and leaves the instrument. If the glass breaks because of the heat, no light at all is reflected, making the device fail-safe. Simple filters made of darkened glass allow the full intensity of sunlight During certain atmospheric conditions, the Sun becomes clearly to pass through if they break, endangering the observer’s visible to the naked eye, and can be observed without stress to the eyes. Click on this photo to see the full cycle of a sunset, as eyesight. Unfiltered binoculars can deliver hundreds of times as much energy as using the naked eye, possibly observed from the high plains of the Mojave Desert. causing immediate damage. It is claimed that even brief an unfiltered telescope The brightness of the Sun can cause pain from looking at glances at the midday Sun through [192] can cause permanent damage. it with the naked eye; however, doing so for brief periods is not hazardous for normal non-dilated eyes.[184][185] Partial solar eclipses are hazardous to view because the Looking directly at the Sun causes phosphene visual ar- eye’s pupil is not adapted to the unusually high visual contifacts and temporary partial blindness. It also delivers trast: the pupil dilates according to the total amount of about 4 milliwatts of sunlight to the retina, slightly heat- light in the field of view, not by the brightest object in the ing it and potentially causing damage in eyes that can- field. During partial eclipses most sunlight is blocked by not respond properly to the brightness.[186][187] UV expo- the Moon passing in front of the Sun, but the uncovered sure gradually yellows the lens of the eye over a period parts of the photosphere have the same surface brightness of years, and is thought to contribute to the formation of as during a normal day. In the overall gloom, the pupil cataracts, but this depends on general exposure to solar expands from ~2 mm to ~6 mm, and each retinal cell ex-


144

CHAPTER 15. SUN Ultraviolet light from the Sun has antiseptic properties and can be used to sanitize tools and water. It also causes sunburn, and has other biological effects such as the production of vitamin D and sun tanning. Ultraviolet light is strongly attenuated by Earth’s ozone layer, so that the amount of UV varies greatly with latitude and has been partially responsible for many biological adaptations, including variations in human skin color in different regions of the globe.[197]

15.12 See also Halo with sun dogs

• Advanced Composition Explorer • Antisolar point

posed to the solar image receives up to ten times more light than it would looking at the non-eclipsed Sun. This can damage or kill those cells, resulting in small permanent blind spots for the viewer.[193] The hazard is insidious for inexperienced observers and for children, because there is no perception of pain: it is not immediately obvious that one’s vision is being destroyed.

• List of brightest stars • Solar energy • Solar System • Sun dogs • Sun path • Sun-Earth Day • Sunday • Sungazing • Timeline of the far future

15.13 Notes A sunrise

During sunrise and sunset, sunlight is attenuated because of Rayleigh scattering and Mie scattering from a particularly long passage through Earth’s atmosphere,[194] and the Sun is sometimes faint enough to be viewed comfortably with the naked eye or safely with optics (provided there is no risk of bright sunlight suddenly appearing through a break between clouds). Hazy conditions, atmospheric dust, and high humidity contribute to this atmospheric attenuation.[195] An optical phenomenon, known as a green flash, can sometimes be seen shortly after sunset or before sunrise. The flash is caused by light from the Sun just below the horizon being bent (usually through a temperature inversion) towards the observer. Light of shorter wavelengths (violet, blue, green) is bent more than that of longer wavelengths (yellow, orange, red) but the violet and blue light is scattered more, leaving light that is perceived as green.[196]

[1] All numbers in this article are short scale. One billion is 109 , or 1,000,000,000. [2] In astronomical sciences, the term heavy elements (or metals) refers to all elements except hydrogen and helium. [3] Hydrothermal vent communities live so deep under the sea that they have no access to sunlight. Bacteria instead use sulfur compounds as an energy source, via chemosynthesis. [4] 1.88 Gcd/m2 is calculated from the solar illuminance of 128000 lux (see sunlight) times the square of the distance to the center of the Sun, divided by the cross sectional area of the Sun. 1.44 Gcd/m2 is calculated using 98000 lux. [5] A 50 kg adult human has a volume of about 0.05 m3 , which corresponds to 13.8 watts, at the volumetric power of the solar center. This is 285 kcal/day, about 10% of the actual average caloric intake and output for humans in non-stressful conditions. [6] Earth’s atmosphere near sea level has a particle density of about 2×1025 m−3 .


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[153] Goldstein, B.R. (1967). “The Arabic Version of [171] Wade, M. (2008). “Pioneer 6-7-8-9-E”. Encyclopedia Ptolemy’s Planetary Hypotheses”. Transactions of Astronautica. Retrieved 22 March 2006. the American Philosophical Society. 57 (4): 9–12. [172] “Solar System Exploration: Missions: By Target: Our Sodoi:10.2307/1006040. JSTOR 1006040. lar System: Past: Pioneer 9”. NASA. Retrieved 30 Octo[154] Ead, Hamed A. Averroes As A Physician. University of ber 2010. NASA maintained contact with Pioneer 9 until Cairo. May 1983 [155] “Galileo Galilei (1564–1642)". March 2006.

BBC. Retrieved 22 [173] Burlaga, L.F. (2001). “Magnetic Fields and plasmas in the inner heliosphere: Helios results”. Planetary and Space Science. 49 (14–15): 1619–27. [156] A short History of scientific ideas to 1900, C. Singer, OxBibcode:2001P&SS...49.1619B. doi:10.1016/S0032ford University Press, 1959, p. 151. 0633(01)00098-8. [157] The Arabian Science, C. Ronan, pp. 201–244 in The [174] Burkepile, C.J. (1998). “Solar Maximum Mission Cambridge Illustrated History of the World’s Science, CamOverview”. Archived from the original on 5 April 2006. bridge University Press, 1983; at pp. 213–214. Retrieved 22 March 2006. [158] Goldstein, Bernard R. (March 1972). “Theory and Ob- [175] “Result of Re-entry of the Solar X-ray Observatory servation in Medieval Astronomy”. Isis. University of “Yohkoh” (SOLAR-A) to the Earth’s Atmosphere” (Press Chicago Press. 63 (1): 39–47 [44]. doi:10.1086/350839. release). Japan Aerospace Exploration Agency. 2005. Retrieved 22 March 2006. [159] “Sir Isaac Newton (1643–1727)". BBC. Retrieved 22 March 2006. [176] “Mission extensions approved for science missions”. ESA [160] “Herschel Discovers Infrared Light”. Cool Cosmos. Retrieved 22 March 2006.

Science and Technology. 7 October 2009. Retrieved 16 February 2010.

[161] Thomson, W. (1862). “On the Age of the Sun’s Heat”. [177] “NASA Successfully Launches a New Eye on the Sun”. NASA Press Release Archives. 11 February 2010. ReMacmillan’s Magazine. 5: 388–393. trieved 16 February 2010. [162] Stacey, Frank D. (2000). “Kelvin’s age of the Earth paradox revisited”. Journal of Geophysical Research. 105 [178] “Sungrazing Comets”. LASCO (US Naval Research Laboratory). Retrieved 19 March 2009. (B6): 13155–13158. Bibcode:2000JGR...10513155S. doi:10.1029/2000JB900028. [179] JPL/CALTECH (2005). “Ulysses: Primary Mission Results”. NASA. Retrieved 22 March 2006. [163] Lockyer, J.N. (1890). The meteoritic hypothesis; a statement of the results of a spectroscopic inquiry into [180] Calaway, M.J.; Stansbery, Eileen K.; Keller, Lindthe origin of cosmical systems. Macmillan and Co. say P. (2009). “Genesis capturing the Sun: SoBibcode:1890mhsr.book.....L. lar wind irradiation at Lagrange 1”. Nuclear Instruments and Methods in Physics Research B. 267 [164] Darden, L. (1998). “The Nature of Scientific Inquiry”. (7): 1101–1108. Bibcode:2009NIMPB.267.1101C. doi:10.1016/j.nimb.2009.01.132. [165] Hawking, S. W. (2001). The Universe in a Nutshell. Bantam Books. ISBN 0-553-80202-X. [181] “STEREO Spacecraft & Instruments”. NASA Missions. 8 March 2006. Retrieved 30 May 2006. [166] “Studying the stars, testing relativity: Sir Arthur Eddington”. Space Science. European Space Agency. 2005. Re[182] Howard, R. A.; Moses, J. D.; Socker, D. G.; Dere, trieved 1 August 2007. K. P.; Cook, J. W. (2002). “Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI)". [167] Bethe, H.; Critchfield, C. (1938). “On the Formation Advances in Space Research. 29 (12): 2017–2026. of Deuterons by Proton Combination”. Physical Review. Bibcode:2008SSRv..136...67H. doi:10.1007/s1121454 (10): 862–862. Bibcode:1938PhRv...54Q.862B. 008-9341-4. doi:10.1103/PhysRev.54.862.2. [168] Bethe, H. (1939). “Energy Produc- [183] Laxman, Srinivas; Rhik Kundu, TNN (9 September 2012). “Aditya 1 launch delayed to 2015–16”. The Times tion in Stars”. Physical Review. 55 (1): of India. Bennett, Coleman & Co. Ltd. Bibcode:1939PhRv...55..434B. 434–456. doi:10.1103/PhysRev.55.434. [184] White, T.J.; Mainster, M.A.; Wilson, P.W.; Tips, J.H. (1971). “Chorioretinal temperature increases from solar [169] Burbidge, E.M.; Burbidge, G.R.; Fowler, W.A.; observation”. Bulletin of Mathematical Biophysics. 33 (1): Hoyle, F. (1957). “Synthesis of the Elements 1–17. doi:10.1007/BF02476660. Reviews of Modern Physics. 29 in Stars”. (4): 547–650. Bibcode:1957RvMP...29..547B. [185] Tso, M.O.M.; La Piana, F.G. (1975). “The Human Fovea doi:10.1103/RevModPhys.29.547. After Sungazing”. Transactions of the American Academy [170] Phillips, T. (2007). “Stereo Eclipse”. Science@NASA. of Ophthalmology and Otolaryngology. 79 (6): OP788– NASA. Retrieved 19 June 2008. 95. PMID 1209815.


15.15. FURTHER READING

[186] Hope-Ross, M.W.; Mahon, GJ; Gardiner, TA; Archer, DB (1993). “Ultrastructural findings in solar retinopathy”. Eye. 7 (4): 29–33. doi:10.1038/eye.1993.7. PMID 8325420. [187] Schatz, H.; Mendelblatt, F. (1973). “Solar Retinopathy from Sun-Gazing Under Influence of LSD”. British Journal of Ophthalmology. 57 (4): 270–3. doi:10.1136/bjo.57.4.270. PMC 1214879 . PMID 4707624. [188] Chou, B.R. (2005). “Eye Safety During Solar Eclipses”. "While environmental exposure to UV radiation is known to contribute to the accelerated aging of the outer layers of the eye and the development of cataracts, the concern over improper viewing of the Sun during an eclipse is for the development of “eclipse blindness” or retinal burns."

151

15.15 Further reading • Cohen, Richard (2010). Chasing the Sun: the Epic Story of the Star that Gives us Life. Simon & Schuster. ISBN 1-4000-6875-4. • Thompson, M. J. (2004). “Solar interior: Helioseismology and the Sun’s interior”. Astronomy & Geophysics. 45 (4): 21–25. • Solar Activity Scholarpedia Hugh Hudson 3(3):3967. doi:10.4249/scholarpedia.3967

15.16 External links

[189] Ham, W.T. Jr.; Mueller, H.A.; Sliney, D.H. (1976). “Retinal sensitivity to damage from short wavelength light”. Nature. 260 (5547): 153–155. Bibcode:1976Natur.260..153H. doi:10.1038/260153a0.

• Nasa SOHO (Solar & Heliospheric Observatory) satellite

[190] Ham, W.T. Jr.; Mueller, H.A.; Ruffolo, J.J. Jr.; Guerry, D. III (1980). “Solar Retinopathy as a function of Wavelength: its Significance for Protective Eyewear”. In Williams, T.P.; Baker, B.N. The Effects of Constant Light on Visual Processes. Plenum Press. pp. 319–346. ISBN 0-306-40328-5.

• Astronomy Cast: The Sun

[191] Kardos, T. (2003). Earth science. J.W. Walch. p. 87. ISBN 978-0-8251-4500-1.

• Sun|Trek, an educational website about the Sun

[192] Macdonald, Lee (2012). “2. Equipment for Observing the Sun”. How to Observe the Sun Safely. New York: Springer Science + Business Media. p. 17. doi:10.1007/978-14614-3825-0_2. NEVER LOOK DIRECTLY AT THE SUN THROUGH ANY FORM OF OPTICAL EQUIPMENT, EVEN FOR AN INSTANT. A brief glimpse of the Sun through a telescope is enough to cause permanent eye damage, or even blindness. Even looking at the Sun with the naked eye for more than a second or two is not safe. Do not assume that it is safe to look at the Sun through a filter, no matter how dark the filter appears to be. [193] Espenak, Fred (26 April 1996). “Eye Safety During Solar Eclipses”. NASA. [194] Haber, Jorg; Magnor, Marcus; Seidel, Hans-Peter (2005). “Physically based Simulation of Twilight Phenomena”. ACM Transactions on Graphics. 24 (4): 1353–1373. doi:10.1145/1095878.1095884. CiteSeerX: 10.1.1.67.2567. [195] Piggin, I. G. (1972). “Diurnal asymmetries in global radiation”. Springer. 20 (1): Bibcode:1972AMGBB..20...41P. 41–48. doi:10.1007/BF02243313. [196] “The Green Flash”. BBC. Archived from the original on 16 December 2008. Retrieved 10 August 2008. [197] Barsh, G.S. (2003). “What Controls Variation in Human Skin Color?". PLoS Biology. 1 (1): e7. doi:10.1371/journal.pbio.0000027. PMC 212702 . PMID 14551921.

• National Solar Observatory

• A collection of spectacular images of the Sun from various institutions (The Boston Globe) • Satellite observations of solar luminosity

• The Swedish 1-meter Solar Telescope, SST • An animated explanation of the structure of the Sun (University of Glamorgan) • Animation – The Future of the Sun • Solar Conveyor Belt Speeds Up – NASA – images, link to report on Science • NASA 5-year timelapse video of the Sun • Sun in Ultra High Definition NASA 11/1/2015


Chapter 16

Nicolaus Copernicus “Copernicus” redirects here. Copernicus (disambiguation).

For other uses, see 16.1.1

Father’s family

Nicolaus Copernicus (/koʊˈpɜːrnɪkəs, kə-/;[1][2][3] Polish: Mikołaj Kopernik [miˈkɔwaj kɔˈpɛrɲik]; German: Nikolaus Kopernikus; 19 February 1473 – 24 May 1543) was a Renaissance mathematician and astronomer who formulated a model of the universe that placed the Sun rather than the Earth at the center of the universe.[lower-alpha 1] The publication of this model in his book De revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres) just before his death in 1543 is considered a major event in the history of science, triggering the Copernican Revolution and making an important contribution to the Scientific Revolution. Copernicus was born and died in Royal Prussia, a region that had been a part of the Kingdom of Poland since 1466. He was a polyglot and polymath who obtained a doctorate in canon law and also practiced as a physician, classics scholar, translator, governor, diplomat, and economist. Like the rest of his family, he was a thirdorder Dominican.[5] In 1517 he derived a quantity theory of money – a key concept in economics – and in 1519 he formulated a version of what later became known as Gresham’s law.[6]

Toruń birthplace (ul. Kopernika 15, left). Together with the house at no. 17 (right), it forms the Muzeum Mikołaja Kopernika.

16.1 Life Nicolaus Copernicus was born on 19 February 1473 in the city of Toruń (Thorn), in the province of Royal Prussia, in the Crown of the Kingdom of Poland.[7][8] His father was a merchant from Kraków and his mother was the daughter of a wealthy Toruń merchant.[9] Nicolaus was the youngest of four children. His brother Andreas (Andrew) became an Augustinian canon at Frombork (Frauenburg).[9] His sister Barbara, named after her mother, became a Benedictine nun and, in her final years, prioress of a convent in Chełmno (Kulm); she died after 1517.[9] His sister Katharina married the businessman and Toruń city councilor Barthel Gertner and left five children, whom Copernicus looked after to the end of his life.[9] Copernicus never married or had children.

The father’s family can be traced to a village in Silesia near Nysa (Neiße). The village’s name has been variously spelled Kopernik,[10] Copernik, Copernic, Kopernic, Coprirnik, and today Koperniki.[11] In the 14th century, members of the family began moving to various other Silesian cities, to the Polish capital, Kraków (1367), and to Toruń (1400).[11] The father, Mikołaj the Elder, likely the son of Jan, came from the Kraków line.[11] Nicolaus was named after his father, who appears in records for the first time as a well-to-do merchant who dealt in copper, selling it mostly in Danzig (Gdańsk).[12][13] He moved from Kraków to Toruń around 1458.[14] Toruń, situated on the Vistula River,

152


16.1. LIFE was at that time embroiled in the Thirteen Years’ War, in which the Kingdom of Poland and the Prussian Confederation, an alliance of Prussian cities, gentry and clergy, fought the Teutonic Order over control of the region. In this war, Hanseatic cities like Danzig and Toruń, Nicolaus Copernicus’s hometown, chose to support the Polish King, Casimir IV Jagiellon, who promised to respect the cities’ traditional vast independence, which the Teutonic Order had challenged. Nicolaus’ father was actively engaged in the politics of the day and supported Poland and the cities against the Teutonic Order.[15] In 1454 he mediated negotiations between Poland’s Cardinal Zbigniew Oleśnicki and the Prussian cities for repayment of war loans.[11] In the Second Peace of Thorn (1466), the Teutonic Order formally relinquished all claims to its western province, which as Royal Prussia remained a region of the Crown of the Kingdom of Poland until the First (1772) and Second (1793) Partitions of Poland.

153 and after 1360 had settled in Toruń. They soon became one of the wealthiest and most influential patrician families.[9] Through the Watzenrodes’ extensive family relationships by marriage, Copernicus was related to wealthy families of Toruń (Thorn), Gdańsk (Danzig) and Elbląg (Elbing), and to prominent Polish noble families of Prussia: the Czapskis, Działyńskis, Konopackis and Kościeleckis.[9] Lucas and Katherine had three children: Lucas Watzenrode the Younger (1447–1512), who would become Bishop of Warmia and Copernicus’s patron; Barbara, the astronomer’s mother (deceased after 1495); and Christina (deceased before 1502), who in 1459 married the Toruń merchant and mayor, Tiedeman von Allen.[9]

Lucas Watzenrode the Elder, a wealthy merchant and in 1439–62 president of the judicial bench, was a decided opponent of the Teutonic Knights.[9] In 1453 he was the delegate from Toruń at the Grudziądz (Graudenz) conference that planned the uprising against them.[9] DurCopernicus’s father married Barbara Watzenrode, the as- ing the ensuing Thirteen Years’ War (1454–66), he actronomer’s mother, between 1461 and 1464.[11] He died tively supported the Prussian cities’ war effort with substantial monetary subsidies (only part of which he later about 1483.[9] re-claimed), with political activity in Toruń and Danzig, and by personally fighting in battles at Łasin (Lessen) and 16.1.2 Mother’s family Malbork (Marienburg).[9] He died in 1462.[9] Lucas Watzenrode the Younger, the astronomer’s maternal uncle and patron, was educated at the University of Kraków (now Jagiellonian University) and at the universities of Cologne and Bologna. He was a bitter opponent of the Teutonic Order,[17][18] and its Grand Master once referred to him as “the devil incarnate”.[19] In 1489 Watzenrode was elected Bishop of Warmia (Ermeland, Ermland) against the preference of King Casimir IV, who had hoped to install his own son in that seat. As a result, Watzenrode quarreled with the king until Casimir IV’s death three years later.[20] Watzenrode was then able to form close relations with three successive Polish monarchs: John I Albert, Alexander Jagiellon, and Sigismund I the Old. He was a friend and key advisor to each ruler, and his influence greatly strengthened the ties between Warmia and Poland proper.[19][21] Watzenrode came to be considered the most powerful man in Warmia, and his wealth, connections and influence allowed him to secure Copernicus’ education and career as a canon at Frombork Cathedral.[22][23]

Copernicus’ maternal uncle, Lucas Watzenrode the Younger

16.1.3 Languages

Nicolaus’ mother, Barbara Watzenrode, was the daughter of a wealthy Toruń patrician and city councillor, Lucas Watzenrode the Elder (deceased 1462), and Katarzyna (widow of Jan Peckau), mentioned in other sources as Katarzyna Rüdiger gente Modlibóg (deceased 1476).[9] The Modlibógs were a prominent Polish family who had been well known in Poland’s history since 1271.[16] The Watzenrode family, like the Kopernik family, had come from Silesia from near Świdnica (Schweidnitz),

Copernicus is postulated to have spoken Latin and German with equal fluency. He also spoke Polish,[24] Greek and Italian.[25][26][27][lower-alpha 2] The vast majority of Copernicus’s surviving works are in Latin, which in his lifetime was the language of academia in Europe. Latin was also the official language of the Roman Catholic Church and of Poland’s royal court, and thus all of Copernicus’s correspondence with the Church and with Polish leaders was in Latin.


154

CHAPTER 16. NICOLAUS COPERNICUS local Silesian copper-mining industry,[30] though some scholars assert that it may have been inspired by the dill plant (in Polish, "koperek" or "kopernik") that grows wild in Silesia.[37] As was to be the case with William Shakespeare a century later,[38] numerous variant spellings of the name are documented for the astronomer and his relatives. The name first appeared as a place name in Silesia in the 13th century, where it was spelled variously in Latin documents. Copernicus “was rather indifferent about orthography".[39] During his childhood, about 1480, the name of his father (and thus of the future astronomer) was recorded in Thorn as Niclas Koppernigk.[40] At Kraków he signed himself, in Latin, Nicolaus Nicolai de Torunia (Nicolaus, son of Nicolaus, of Toruń).[41] At Bologna, in 1496, he registered in the Matricula Nobilissimi Germanorum Collegii, resp. Annales Clarissimae Nacionis Germanorum, of the Natio Germanica Bononiae, as Dominus Nicolaus Kopperlingk de Thorn – IX grosseti.[42][43] At Padua he signed himself “Nicolaus Copernik”, later “Coppernicus”.[39] The astronomer thus Latinized his name to Coppernicus, generally with two “p"s (in 23 of 31 documents studied),[44] but later in life he used a single “p”. On the title page of De revolutionibus, Rheticus published the name as (in the genitive, or possessive, case) "Nicolai Copernici".[lower-alpha 3]

German-language letter from Copernicus to Duke Albert of Prussia, giving medical advice for George von Kunheim (1541)

16.1.5 Education In Poland

There survive a few documents written by Copernicus in German. The German philosophy professor Martin Carrier mentions this as a reason to consider Copernicus’s native language to have been German.[31] Other arguments for German being Copernicus’s native tongue are that he was born in a predominantly German-speaking city and that, while studying canon law at Bologna in 1496, he signed into the German natio (Natio Germanorum)— a student organization which, according to its 1497 bylaws, was open to students of all kingdoms and states whose mother-tongue was German.[32] However, according to French philosopher Alexandre Koyré, Copernicus’s registration with the Natio Germanorum does not in itself imply that Copernicus considered himself German, since students from Prussia and Silesia were routinely so cat- Collegium Maius, Kraków egorized, which carried certain privileges that made it a natural choice for German-speaking students, regardless Upon his father’s death, young Nicolaus’ maternal unof their ethnicity or self-identification.[32][33][34][35][36] cle, Lucas Watzenrode the Younger (1447–1512), took the boy under his wing and saw to his education and career.[9] Watzenrode maintained contacts with leading 16.1.4 Name intellectual figures in Poland and was a friend of the influential Italian-born humanist and Kraków courtier, In Copernicus’s time, people were often called after the Filippo Buonaccorsi.[45] There are no surviving primary places where they lived. Like the Silesian village that documents on the early years of Copernicus’s childhood inspired it, Copernicus’s surname has been spelled var- and education.[9] Copernicus biographers assume that iously. The surname likely had something to do with the Watzenrode first sent young Copernicus to St. John’s


16.1. LIFE School, at Toruń, where he himself had been a master.[9] Later, according to Armitage,[lower-alpha 4] the boy attended the Cathedral School at Włocławek, up the Vistula River from Toruń, which prepared pupils for entrance to the University of Kraków, Watzenrode’s alma mater in Poland’s capital.[46]

155 ical and natural-science writings of Aristotle (De coelo, Metaphysics), stimulated his interest in learning, and made him conversant with humanistic culture.[22] Copernicus broadened the knowledge that he took from the university lecture halls with independent reading of books that he acquired during his Kraków years (Euclid, Haly Abenragel, the Alfonsine Tables, Johannes Regiomontanus' Tabulae directionum); to this period, probably, also date his earliest scientific notes, now preserved partly at Uppsala University.[22] At Kraków Copernicus began collecting a large library on astronomy; it would later be carried off as war booty by the Swedes during the Deluge in the 1650s and is now at the Uppsala University Library. Copernicus’s four years at Kraków played an important role in the development of his critical faculties and initiated his analysis of the logical contradictions in the two most popular systems of astronomy—Aristotle’s theory of homocentric spheres, and Ptolemy's mechanism of eccentrics and epicycles—the surmounting and discarding of which constituted the first step toward the creation of Copernicus’s own doctrine of the structure of the universe.[22]

Without taking a degree, probably in the fall of 1495, Copernicus left Kraków for the court of his uncle Watzenrode, who in 1489 had been elevated to Prince-Bishop of Warmia and soon (before November 1495) sought to place his nephew in the Warmia canonry vacated by the 26 August 1495 death of its previous tenant, Jan Czanow. For unclear reasons—probably due to opposition from part of the chapter, who appealed to Rome— Copernicus’s installation was delayed, inclining WatzenNicolaus Copernicus Monument in Kraków rode to send both his nephews to study canon law in Italy, In the winter semester of 1491–92 Copernicus, as “Nico- seemingly with a view to furthering their ecclesiastic castrengthening his own influence in laus Nicolai de Thuronia”, matriculated together with reers and thereby also [22] the Warmia chapter. his brother Andrew at the University of Kraków (now Jagiellonian University).[9] Copernicus began his studies Leaving Warmia in mid-1496—possibly with the retinue in the Department of Arts (from the fall of 1491, pre- of the chapter’s chancellor, Jerzy Pranghe, who was gosumably until the summer or fall of 1495) in the hey- ing to Italy—in the fall, possibly in October, of that year day of the Kraków astronomical-mathematical school, Copernicus arrived in Bologna and a few months later acquiring the foundations for his subsequent mathemati- (after 6 January 1497) signed himself into the register cal achievements.[9] According to a later but credible tra- of the Bologna University of Jurists’ “German nation”, dition (Jan Brożek), Copernicus was a pupil of Albert which also included young Poles from Silesia, Prussia and Brudzewski, who by then (from 1491) was a profes- Pomerania, as well as students of other nationalities.[22] sor of Aristotelian philosophy but taught astronomy privately outside the university; Copernicus became familiar with Brudzewski’s widely read commentary to Georg von In Italy Peuerbach's Theoricæ novæ planetarum and almost certainly attended the lectures of Bernard of Biskupie and It was only on 20 October 1497 that Copernicus, by Wojciech Krypa of Szamotuły, and probably other astro- proxy, formally succeeded to the Warmia canonry which nomical lectures by Jan of Głogów, Michał of Wrocław had been granted to him two years earlier. To this, by a (Breslau), Wojciech of Pniewy, and Marcin Bylica of document dated 10 January 1503 at Padua, he would add Olkusz.[47] a sinecure at the Collegiate Church of the Holy Cross in Copernicus’s Kraków studies gave him a thorough grounding in the mathematical-astronomical knowledge taught at the university (arithmetic, geometry, geometric optics, cosmography, theoretical and computational astronomy), a good knowledge of the philosoph-

Wrocław, Silesia, Bohemia. Despite having been granted a papal indult on 29 November 1508 to receive further benefices, through his ecclesiastic career Copernicus not only did not acquire further prebends and higher stations (prelacies) at the chapter, but in 1538 he relinquished the


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“Here, where stood the house of Domenico Maria Novara, professor of the ancient Studium of Bologna, NICOLAUS COPERNICUS, the Polish mathematician and astronomer who would revolutionize concepts of the universe, conducted brilliant celestial observations with his teacher in 1497–1500. Placed on the 5th centenary of [Copernicus’s] birth by the City, the University, the Academy of Sciences of the Institute of Bologna, the Polish Academy of Sciences. 1473 [—] 1973.”

Wrocław sinecure. It is unclear whether he was ever ordained a priest. Author Ed Rosen asserts that he was not.[48][49] He did take minor orders, which sufficed for assuming a chapter canonry.[22] The Catholic encyclope- Via Galliera 65, Bologna, site of house of Domenico Maria Novara. Plaque on portico commemorates Copernicus. dia proposes that his ordination was probable, as he was one of four candidates for the episcopal seat of Ermland, a position which required ordination.[5] During his three-year stay at Bologna, between fall 1496 at Bologna, observing, for example, a lunar eclipse on the and spring 1501, Copernicus seems to have devoted him- night of 5–6 November 1500. According to a later acself less keenly to studying canon law (he received his count by Rheticus, Copernicus also—probably privately, doctorate in law only after seven years, following a second rather than at the Roman Sapienza—as a "Professor return to Italy in 1503) than to studying the humanities— Mathematum" (professor of astronomy) delivered, “to nuprobably attending lectures by Filippo Beroaldo, Antonio merous... students and... leading masters of the science”, the mathUrceo, called Codro, Giovanni Garzoni, and Alessandro public lectures devoted probably to a critique of [51] ematical solutions of contemporary astronomy. Achillini—and to studying astronomy. He met the famous astronomer Domenico Maria Novara da Ferrara and became his disciple and assistant. Copernicus was developing new ideas inspired by reading the “Epitome of the Almagest” (Epitome in Almagestum Ptolemei) by George von Peuerbach and Johannes Regiomontanus (Venice, 1496). He verified its observations about certain peculiarities in Ptolemy’s theory of the Moon’s motion, by conducting on 9 March 1497 at Bologna a memorable observation of the occultation of Aldebaran, the brightest star in the Taurus constellation, by the moon. Copernicus the humanist sought confirmation for his growing doubts through close reading of Greek and Latin authors (Pythagoras, Aristarchos of Samos, Cleomedes, Cicero, Pliny the Elder, Plutarch, Philolaus, Heraclides, Ecphantos, Plato), gathering, especially while at Padua, fragmentary historic information about ancient astronomical, cosmological and calendar systems.[50] Copernicus spent the jubilee year 1500 in Rome, where he arrived with his brother Andrew that spring, doubtless to perform an apprenticeship at the Papal Curia. Here, too, however, he continued his astronomical work begun

On his return journey doubtless stopping briefly at Bologna, in mid-1501 Copernicus arrived back in Warmia. After on 28 July receiving from the chapter a two-year extension of leave in order to study medicine (since “he may in future be a useful medical advisor to our Reverend Superior [Bishop Lucas Watzenrode] and the gentlemen of the chapter”), in late summer or in the fall he returned again to Italy, probably accompanied by his brother Andrew and by Canon B. Sculteti. This time he studied at the University of Padua, famous as a seat of medical learning, and—except for a brief visit to Ferrara in May–June 1503 to pass examinations for, and receive, his doctorate in canon law—he remained at Padua from fall 1501 to summer 1503.[51] Copernicus studied medicine probably under the direction of leading Padua professors—Bartolomeo da Montagnana, Girolamo Fracastoro, Gabriele Zerbi, Alessandro Benedetti—and read medical treatises that he acquired at this time, by Valescus de Taranta, Jan Mesue, Hugo Senensis, Jan Ketham, Arnold de Villa Nova, and Michele Savonarola, which would form the embryo of his


16.1. LIFE later medical library.[51] One of the subjects that Copernicus must have studied was astrology, since it was considered an important part of a medical education.[52] However, unlike most other prominent Renaissance astronomers, he appears never to have practiced or expressed any interest in astrology.[53] As at Bologna, Copernicus did not limit himself to his official studies. It was probably the Padua years that saw the beginning of his Hellenistic interests. He familiarized himself with Greek language and culture with the aid of Theodorus Gaza's grammar (1495) and J.B. Chrestonius’ dictionary (1499), expanding his studies of antiquity, begun at Bologna, to the writings of Basilius Bessarion, Lorenzo Valla and others. There also seems to be evidence that it was during his Padua stay that the idea finally crystallized, of basing a new system of the world on the movement of the Earth.[51] As the time approached for Copernicus to return home, in spring 1503 he journeyed to Ferrara where, on 31 May 1503, having passed the obligatory examinations, he was granted the degree of doctor of canon law (Nicolaus Copernich de Prusia, Jure Canonico ... et doctoratus[54] ). No doubt it was soon after (at latest, in fall 1503) that he left Italy for good to return to Warmia.[51]

16.1.6

157 1503 to 1510 (or perhaps till his uncle’s death on 29 March 1512) and resided in the Bishop’s castle at Lidzbark (Heilsberg), where he began work on his heliocentric theory. In his official capacity, he took part in nearly all his uncle’s political, ecclesiastic and administrative-economic duties. From the beginning of 1504, Copernicus accompanied Watzenrode to sessions of the Royal Prussian diet held at Malbork and Elbląg and, write Dobrzycki and Hajdukiewicz, “participated... in all the more important events in the complex diplomatic game that ambitious politician and statesman played in defense of the particular interests of Prussia and Warmia, between hostility to the [Teutonic] Order and loyalty to the Polish Crown.”[51]

Work

Astronomer Copernicus, or Conversations with God, by Matejko. In background: Frombork Cathedral.

Having completed all his studies in Italy, 30-yearold Copernicus returned to Warmia, where he would live out the remaining 40 years of his life, apart from brief journeys to Kraków and to nearby Prussian cities: Toruń (Thorn), Gdańsk (Danzig), Elbląg (Elbing), Grudziądz (Graudenz), Malbork (Marienburg), Königsberg (Królewiec).[51]

Copernicus’s translation of Theophylact Simocatta's Epistles. Cover shows coats-of-arms of (clockwise from top) Poland, Lithuania and Kraków.

In 1504–12 Copernicus made numerous journeys as part of his uncle’s retinue—in 1504, to Toruń and Gdańsk, to a session of the Royal Prussian Council in the presence of Poland’s King Alexander Jagiellon; to sessions of the Prussian diet at Malbork (1506), Elbląg (1507) and Sztum (Stuhm) (1512); and he may have attended a Poznań (Posen) session (1510) and the coronation of Poland’s King Sigismund I the Old in Kraków (1507). Watzenrode’s itinerary suggests that in spring 1509 Copernicus may have attended the Kraków sejm.[51]

The Prince-Bishopric of Warmia enjoyed substantial autonomy, with its own diet (parliament) and monetary It was probably on the latter occasion, in Kraków, that unit (the same as in the other parts of Royal Prussia) and Copernicus submitted for printing at Jan Haller's press his treasury.[55] translation, from Greek to Latin, of a collection, by the Copernicus was his uncle’s secretary and physician from 7th-century Byzantine historian Theophylact Simocatta,


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of 85 brief poems called Epistles, or letters, supposed to have passed between various characters in a Greek story. They are of three kinds—"moral,” offering advice on how people should live; “pastoral”, giving little pictures of shepherd life; and “amorous”, comprising love poems. They are arranged to follow one another in a regular rotation of subjects. Copernicus had translated the Greek verses into Latin prose, and he now published his version as Theophilacti scolastici Simocati epistolae morales, rurales et amatoriae interpretatione latina, which he dedicated to his uncle in gratitude for all the benefits he had received from him. With this translation, Copernicus declared himself on the side of the humanists in the struggle over the question whether Greek literature should be revived.[28] Copernicus’s first poetic work was a Greek epigram, composed probably during a visit to Kraków, for Johannes Dantiscus' epithalamium for Barbara Zapolya's 1512 wedding to King Zygmunt I the Old.[56] Some time before 1514, Copernicus wrote an initial outline of his heliocentric theory known only from later transcripts, by the title (perhaps given to it by a copyist), Nicolai Copernici de hypothesibus motuum coelestium a se constitutis commentariolus—commonly referred to as the Commentariolus. It was a succinct theoretical description of the world’s heliocentric mechanism, without mathematical apparatus, and differed in some important details of geometric construction from De revolutionibus; but it was already based on the same assumptions regarding Earth’s triple motions. The Commentariolus, which Copernicus consciously saw as merely a first sketch for his planned book, was not intended for printed distribution. He made only a very few manuscript copies available to his closest acquaintances, including, it seems, several Kraków astronomers with whom he collaborated in 1515–30 in observing eclipses. Tycho Brahe would include a fragment from the Commentariolus in his own treatise, Astronomiae instauratae progymnasmata, published in Prague in 1602, based on a manuscript that he had received from the Bohemian physician and astronomer Tadeáš Hájek, a friend of Rheticus. The Commentariolus would appear complete in print for the first time only in 1878.[56] In 1510 or 1512 Copernicus moved to Frombork, a town to the northwest at the Vistula Lagoon on the Baltic Sea coast. There, in April 1512, he participated in the election of Fabian of Lossainen as Prince-Bishop of Warmia. It was only in early June 1512 that the chapter gave Copernicus an “external curia”—a house outside the defensive walls of the cathedral mount. In 1514 he purchased the northwestern tower within the walls of the Frombork stronghold. He would maintain both these residences to the end of his life, despite the devastation of the chapter’s buildings by a raid against Frauenburg carried out by the Teutonic Order in January 1520, during which Copernicus’s astronomical instruments were probably destroyed. Copernicus conducted astronomical observations in 1513–16 presumably from his external cu-

Copernicus’s tower at Frombork, where he lived and worked; rebuilt recently

ria; and in 1522–43, from an unidentified “small tower” (turricula), using primitive instruments modeled on ancient ones—the quadrant, triquetrum, armillary sphere. At Frombork Copernicus conducted over half of his more than 60 registered astronomical observations.[56] Having settled permanently at Frombork, where he would reside to the end of his life, with interruptions in 1516–19 and 1520–21, Copernicus found himself at the Warmia chapter’s economic and administrative center, which was also one of Warmia’s two chief centers of political life. In the difficult, politically complex situation of Warmia, threatened externally by the Teutonic Order's aggressions (attacks by Teutonic bands; the Polish-Teutonic War of 1519–21; Albert’s plans to annex Warmia), internally subject to strong separatist pressures (the selection of the prince-bishops of Warmia; currency reform), he, together with part of the chapter, represented a program of strict cooperation with the Polish Crown and demonstrated in all his public activities (the defense of his country against the Order’s plans of conquest; proposals to unify its monetary system with the Polish Crown’s; support for Poland’s interests in the Warmia dominion’s ecclesiastic administration) that he was consciously a citizen of the Polish-Lithuanian Republic. Soon after the death of uncle Bishop Watzenrode, he participated in the signing of the Second Treaty of Piotrków Trybunalski (7 December 1512), governing the appointment of the Bishop


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of Warmia, declaring, despite opposition from part of the chapter, for loyal cooperation with the Polish Crown.[56]

Olsztyn Castle

Frombork Cathedral mount and fortifications. In foreground: statue of Copernicus

That same year (before 8 November 1512) Copernicus assumed responsibility, as magister pistoriae, for administering the chapter’s economic enterprises (he would hold this office again in 1530), having already since 1511 fulfilled the duties of chancellor and visitor of the chapter’s estates.[56] His administrative and economic dutes did not distract Copernicus, in 1512–15, from intensive observational activity. The results of his observations of Mars and Saturn in this period, and especially a series of four observations of the Sun made in 1515, led to discovery of the variability of Earth's eccentricity and of the movement of the solar apogee in relation to the fixed stars, which in 1515– 19 prompted his first revisions of certain assumptions of his system. Some of the observations that he made in this period may have had a connection with a proposed reform of the Julian calendar made in the first half of 1513 at the request of the Bishop of Fossombrone, Paul of Middelburg. Their contacts in this matter in the period of the Fifth Lateran Council were later memorialized in a complimentary mention in Copernicus’s dedicatory epistle in Dē revolutionibus orbium coelestium and in a treatise by Paul of Middelburg, Secundum compendium correctionis Calendarii (1516), which mentions Copernicus among the learned men who had sent the Council proposals for the calendar’s emendation.[57] During 1516–21, Copernicus resided at Olsztyn (Allenstein) Castle as economic administrator of Warmia, including Olsztyn (Allenstein) and Pieniężno (Mehlsack). While there, he wrote a manuscript, Locationes mansorum desertorum (Locations of Deserted Fiefs), with a view to populating those fiefs with industrious farmers and so bolstering the economy of Warmia. When Olsztyn was besieged by the Teutonic Knights during the Polish–Teutonic War, Copernicus directed the defense of Olsztyn and Warmia by Royal Polish forces. He also represented the Polish side in the ensuing peace negotiations.[58]

Copernicus for years advised the Royal Prussian sejmik on monetary reform, particularly in the 1520s when that was a major question in regional Prussian politics.[59] In 1526 he wrote a study on the value of money, Monetae cudendae ratio. In it he formulated an early iteration of the theory, now called Gresham’s law, that “bad” (debased) coinage drives “good” (un-debased) coinage out of circulation—several decades before Thomas Gresham. He also, in 1517, set down a quantity theory of money, a principal concept in economics to the present day. Copernicus’s recommendations on monetary reform were widely read by leaders of both Prussia and Poland in their attempts to stabilize currency.[60]

Copernicus Monument in Warsaw designed by the Danish sculptor Bertel Thorvaldsen

In 1533, Johann Widmanstetter, secretary to Pope Clement VII, explained Copernicus’s heliocentric sys-


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tem to the Pope and two cardinals. The Pope was so Duke Albert and, by letter, the Polish Royal Physician.[63] pleased that he gave Widmanstetter a valuable gift.[61] In 1535 Bernard Wapowski wrote a letter to a gentleman in Vienna, urging him to publish an enclosed almanac, which he claimed had been written by Copernicus. This is the only mention of a Copernicus almanac in the historical records. The “almanac” was likely Copernicus’s tables of planetary positions. Wapowski’s letter mentions Copernicus’s theory about the motions of the earth. Nothing came of Wapowski’s request, because he died a couple of weeks later.[61] Following the death of Prince-Bishop of Warmia Mauritius Ferber (1 July 1537), Copernicus participated in the election of his successor, Johannes Dantiscus (20 September 1537). Copernicus was one of four candidates for the post, written in at the initiative of Tiedemann Giese; but his candidacy was actually pro forma, since Dantiscus had earlier been named coadjutor bishop to Ferber.[62] At first Copernicus maintained friendly relations with the new Prince-Bishop, assisting him medically in spring 1538 and accompanying him that summer on an inspection tour of Chapter holdings. But that autumn, their friendship was strained by suspicions over Copernicus’s housekeeper, Anna Schilling, whom Dantiscus removed from Frombork in 1539.[62] "Nicolaus Copernicus Tornaeus Borussus Mathemat.", 1597

In the spring of 1541, Duke Albert summoned Copernicus to Königsberg to attend the Duke’s counselor, George von Kunheim, who had fallen seriously ill, and for whom the Prussian doctors seemed unable to do anything. Copernicus went willingly; he had met von Kunheim during negotiations over reform of the coinage. And Copernicus had come to feel that Albert himself was not such a bad person; the two had many intellectual interests in common. The Chapter readily gave Copernicus permission to go, as it wished to remain on good terms with the Duke, despite his Lutheran faith. In about a month the patient recovered, and Copernicus returned to Frombork. For a time, he continued to receive reports on von Kunheim’s condition, and to send him medical advice by letter.[64] Throughout this period of his life, Copernicus continued making astronomical observations and calculations, but only as his other responsibilities permitted and never in a professional capacity.

Copernicus with medicinal plant

Some of Copernicus’s close friends turned Protestant, but Copernicus never showed a tendency in that direction. The first attacks on him came from Protestants. Wilhelm Gnapheus, a Dutch refugee settled in Elbląg, wrote a comedy in Latin, Morosophus (The Foolish Sage), and staged it at the Latin school that he had established there. In the play, Copernicus was caricatured as a haughty, cold, aloof man who dabbled in astrology, considered himself inspired by God, and was rumored to have written a large work that was moldering in a chest.[45]

In his younger days, Copernicus the physician had treated his uncle, brother and other chapter members. In later years he was called upon to attend the elderly bishops who in turn occupied the see of Warmia—Mauritius Ferber and Johannes Dantiscus – and, in 1539, his old friend Tiedemann Giese, Bishop of Chełmno (Kulm). In treating such important patients, he sometimes sought consul- Elsewhere Protestants were the first to react to news of tations from other physicians, including the physician to Copernicus’s theory. Melanchthon wrote:


16.1. LIFE Some people believe that it is excellent and correct to work out a thing as absurd as did that Sarmatian [i.e., Polish] astronomer who moves the earth and stops the sun. Indeed, wise rulers should have curbed such light-mindedness.[45]

161 confessed—to risk the scorn “to which he would expose himself on account of the novelty and incomprehensibility of his theses.”[62]

In 1533, Johann Albrecht Widmannstetter delivered a series of lectures in Rome outlining Copernicus’s theory. Pope Clement VII and several Catholic cardinals Nevertheless, in 1551, eight years after Copernicus’s heard the lectures and were interested in the theory. On death, astronomer Erasmus Reinhold published, under 1 November 1536, Cardinal Nikolaus von Schönberg, the sponsorship of Copernicus’s former military adver- Archbishop of Capua, wrote to Copernicus from Rome: sary, the Protestant Duke Albert, the Prussian Tables, a set of astronomical tables based on Copernicus’s work. Some years ago word reached me concernAstronomers and astrologers quickly adopted it in place ing your proficiency, of which everybody conof its predecessors.[65] stantly spoke. At that time I began to have a very high regard for you... For I had learned that you had not merely mastered the discov16.1.7 Heliocentrism eries of the ancient astronomers uncommonly well but had also formulated a new cosmology. In it you maintain that the earth moves; that the sun occupies the lowest, and thus the central, place in the universe... Therefore with the utmost earnestness I entreat you, most learned sir, unless I inconvenience you, to communicate this discovery of yours to scholars, and at the earliest possible moment to send me your writings on the sphere of the universe together with the tables and whatever else you have that is relevant to this subject ...[67] By then Copernicus’s work was nearing its definitive form, and rumors about his theory had reached educated people all over Europe. Despite urgings from many quarters, Copernicus delayed publication of his book, perhaps from fear of criticism—a fear delicately expressed in the subsequent dedication of his masterpiece to Pope Paul III. Scholars disagree on whether Copernicus’s concern was limited to possible astronomical and philosophical objections, or whether he was also concerned about religious objections.[lower-alpha 6]

16.1.8 The book Photograph of a 16th-century portrait of Copernicus — the original painting was looted, and possibly destroyed, by the Germans in World War II during the occupation of Poland.

Some time before 1514 Copernicus made available to friends his "Commentariolus" (“Little Commentary”), a forty-page manuscript describing his ideas about the heliocentric hypothesis.[lower-alpha 5] It contained seven basic assumptions (detailed below).[66] Thereafter he continued gathering data for a more detailed work.

Copernicus was still working on De revolutionibus orbium coelestium (even if not certain that he wanted to publish it) when in 1539 Georg Joachim Rheticus, a Wittenberg mathematician, arrived in Frombork. Philipp Melanchthon, a close theological ally of Martin Luther, had arranged for Rheticus to visit several astronomers and study with them. Rheticus became Copernicus’s pupil, staying with him for two years and writing a book, Narratio prima (First Account), outlining the essence of Copernicus’s theory. In 1542 Rheticus published a treatise on trigonometry by Copernicus (later included in the second book of De revolutionibus).

About 1532 Copernicus had basically completed his work on the manuscript of Dē revolutionibus orbium Under strong pressure from Rheticus, and having seen the coelestium; but despite urging by his closest friends, he favorable first general reception of his work, Copernicus resisted openly publishing his views, not wishing—as he finally agreed to give De revolutionibus to his close friend,


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Frombork Cathedral

De revolutionibus, 1543, title page

Tiedemann Giese, bishop of Chełmno (Kulm), to be delivered to Rheticus for printing by the German printer Johannes Petreius at Nuremberg (Nürnberg), Germany. While Rheticus initially supervised the printing, he had to leave Nuremberg before it was completed, and he handed over the task of supervising the rest of the printing to a Lutheran theologian, Andreas Osiander.[68]

Casket with Copernicus’ remains, St. James’ Cathedral Basilica, Olsztyn, March 2010

gust 2005, however, a team led by Jerzy Gąssowski, head of an archaeology and anthropology institute in Pułtusk, after scanning beneath the cathedral floor, discovered Osiander added an unauthorised and unsigned preface, what they believed to be Copernicus’s remains.[71] defending the work against those who might be offended by the novel hypotheses. He explained that astronomers The find came after a year of searching, and the discovery may find different causes for observed motions, and was announced only after further research, on 3 Novemchoose whatever is easier to grasp. As long as a hypothe- ber 2008. Gąssowski said he was “almost 100 percent [72] sis allows reliable computation, it does not have to match sure it is Copernicus”. Forensic expert Capt. Dariusz Zajdel of the Polish Police Central Forensic Laboratory what a philosopher might seek as the truth. used the skull to reconstruct a face that closely resembled the features—including a broken nose and a scar above the left eye—on a Copernicus self-portrait.[72] The expert 16.1.9 Death also determined that the skull belonged to a man who had age 70—Copernicus’s age at the time of his Toward the close of 1542, Copernicus was seized with died around [71] death. apoplexy and paralysis, and he died at age 70 on 24 May 1543. Legend has it that he was presented with the final printed pages of his Dē revolutionibus orbium coelestium on the very day that he died, allowing him to take farewell of his life’s work.[69] He is reputed to have awoken from a stroke-induced coma, looked at his book, and then died peacefully.[70]

The grave was in poor condition, and not all the remains of the skeleton were found; missing, among other things, was the lower jaw.[73] The DNA from the bones found in the grave matched hair samples taken from a book owned by Copernicus which was kept at the library of the University of Uppsala in Sweden.[74][75]

Copernicus was reportedly buried in Frombork Cathedral, where archaeologists for over two centuries searched in vain for his remains. Efforts to locate the remains in 1802, 1909, 1939 and 2004 had come to nought. In Au-

On 22 May 2010 Copernicus was given a second funeral in a Mass led by Józef Kowalczyk, the former papal nuncio to Poland and newly named Primate of Poland. Copernicus’s remains were reburied in the same spot in


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163

Copernicus’ 2010 grave, Frombork Cathedral

Frombork Cathedral where part of his skull and other bones had been found. A black granite tombstone now identifies him as the founder of the heliocentric theory and also a church canon. The tombstone bears a representation of Copernicus’s model of the solar system—a 1735 epitaph, Frombork Cathedral. A 1580 epitaph had been golden sun encircled by six of the planets.[76] destroyed.

16.2 Copernican system Main article: Copernican heliocentrism

16.2.1

Predecessors

Philolaus (c. 480–385 BCE) described an astronomical system in which a Central Fire (different from the Sun) occupied the centre of the universe, and a counter-Earth, the Earth, Moon, the Sun itself, planets, and stars all revolved around it, in that order outward from the centre.[77] Heraclides Ponticus (387–312 BCE) proposed that the Earth rotates on its axis.[78] Aristarchus of Samos (310 BCE – c. 230 BCE) was the first to advance a theory that the earth orbited the sun.[79] Further mathematical details of Aristarchus’ heliocentric system were worked out around 150 BC by the Hellenistic astronomer Seleucus of Seleucia. Though Aristarchus’ original text has been lost, a reference in Archimedes' book The Sand Reckoner (Archimedis Syracusani Arenarius & Dimensio Circuli) describes a work by Aristarchus in which he advanced

the heliocentric model. Archimedes wrote: You (King Gelon) are aware the 'universe' is the name given by most astronomers to the sphere the center of which is the center of the Earth, while its radius is equal to the straight line between the center of the Sun and the center of the Earth. This is the common account as you have heard from astronomers. But Aristarchus has brought out a book consisting of certain hypotheses, wherein it appears, as a consequence of the assumptions made, that the universe is many times greater than the 'universe' just mentioned. His hypotheses are that the fixed stars and the Sun remain unmoved, that the Earth revolves about the Sun on the circumference of a circle, the Sun lying in the middle of the Floor, and that the sphere of the fixed stars, situated about the same center as the Sun, is so great that the circle in which he supposes the Earth to revolve bears such a proportion to the distance of the fixed stars as the center of the sphere bears to its surface.[80]


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CHAPTER 16. NICOLAUS COPERNICUS — The Sand Reckoner

Copernicus cited Aristarchus of Samos in an early (unpublished) manuscript of De Revolutionibus (which still survives), though he removed the reference from his final published manuscript.[4]

etary system, which was mathematically more accurate at predicting the heliocentric orbits of the interior planets than both the Tychonic and Copernican models. The prevailing theory in Europe during Copernicus’s lifetime was the one that Ptolemy published in his Almagest circa 150 CE; the Earth was the stationary center of the universe. Stars were embedded in a large outer sphere which rotated rapidly, approximately daily, while each of the planets, the Sun, and the Moon were embedded in their own, smaller spheres. Ptolemy’s system employed devices, including epicycles, deferents and equants, to account for observations that the paths of these bodies differed from simple, circular orbits centered on the Earth.[82]

Some technical details of Copernicus’s system[lower-alpha 7] closely resembled those developed earlier by the Islamic astronomers Naṣīr al-Dīn al-Ṭūsī and Ibn al-Shāṭir, both of whom retained a geocentric model. Aryabhata (476–550), in his magnum opus Aryabhatiya (499), propounded a planetary model in which the Earth was taken to be spinning on its axis and the periods of the planets were given with respect to the Sun. He accurately calculated many astronomical constants, such as the periods of 16.2.2 the planets, times of the solar and lunar eclipses, and the instantaneous motion of the Moon.

Tusi couple

At the Maragha observatory, Najm al-Dīn al-Qazwīnī alKātibī (died 1277), in his Hikmat al-'Ain, wrote an argument for a heliocentric model, but later abandoned the model. Qutb al-Din Shirazi (born 1236) also discussed the possibility of heliocentrism, but rejected it.[41] Ibn al-Shatir (born 1304) developed a geocentric system that employed mathematical techniques, such as the Tusi couple and Urdi lemma, that were almost identical to those Nicolaus Copernicus later employed in his heliocentric system, implying that its mathematical model was influenced by the Maragha school.[81] Nilakantha Somayaji (1444–1544), in his Aryabhatiyabhasya, a commentary on Aryabhata’s Aryabhatiya, developed a computational system for a partially heliocentric planetary model, in which the planets orbit the Sun, which in turn orbits the Earth, similar to the Tychonic system later proposed by Tycho Brahe in the late 16th century. In the Tantrasangraha (1500), he further revised his plan-

Copernicus

Copernicus’s vision of the universe in Dē revolutionibus orbium coelestium

Copernicus’s major theory was published in Dē revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres), in the year of his death, 1543, though he had formulated the theory several decades earlier. Copernicus’s “Commentariolus” summarized his heliocentric theory. It listed the “assumptions” upon which the theory was based, as follows:[83] 1. There is no one center of all the celestial circles or spheres. 2. The center of the earth is not the center of the universe, but only of gravity and of the lunar sphere. 3. All the spheres revolve about the sun as their midpoint, and therefore the sun is the center of the universe. 4. The ratio of the earth’s distance from the sun to the height of the firmament (outermost


16.3. CONTROVERSY celestial sphere containing the stars) is so much smaller than the ratio of the earth’s radius to its distance from the sun that the distance from the earth to the sun is imperceptible in comparison with the height of the firmament. 5. Whatever motion appears in the firmament arises not from any motion of the firmament, but from the earth’s motion. The earth together with its circumjacent elements performs a complete rotation on its fixed poles in a daily motion, while the firmament and highest heaven abide unchanged. 6. What appear to us as motions of the sun arise not from its motion but from the motion of the earth and our sphere, with which we revolve about the sun like any other planet. The earth has, then, more than one motion. 7. The apparent retrograde and direct motion of the planets arises not from their motion but from the earth’s. The motion of the earth alone, therefore, suffices to explain so many apparent inequalities in the heavens. De revolutionibus itself was divided into six parts, called “books": 1. General vision of the heliocentric theory, and a summarized exposition of his idea of the World 2. Mainly theoretical, presents the principles of spherical astronomy and a list of stars (as a basis for the arguments developed in the subsequent books) 3. Mainly dedicated to the apparent motions of the Sun and to related phenomena 4. Description of the Moon and its orbital motions 5. Exposition of the motions in longitude of the nonterrestrial planets

165 on. Scholars hold that sixty years after the publication of The Revolutions there were only around 15 astronomers espousing Copernicanism in all of Europe: "Thomas Digges and Thomas Harriot in England; Giordano Bruno and Galileo Galilei in Italy; Diego Zuniga in Spain; Simon Stevin in the Low Countries; and in Germany, the largest group – Georg Joachim Rheticus, Michael Maestlin, Christoph Rothmann (who may have later recanted),[84] and Johannes Kepler.”[84] Additional possibilities are Englishman William Gilbert, along with Achilles Gasser, Georg Vogelin, Valentin Otto, and Tiedemann Giese.[84] Arthur Koestler, in his popular book The Sleepwalkers, asserted that Copernicus’s book had not been widely read on its first publication.[85] This claim was trenchantly criticised by Edward Rosen,[lower-alpha 8] and has been decisively disproved by Owen Gingerich, who examined nearly every surviving copy of the first two editions and found copious marginal notes by their owners throughout many of them. Gingerich published his conclusions in 2004 in The Book Nobody Read.[86] The intellectual climate of the time “remained dominated by Aristotelian philosophy and the corresponding Ptolemaic astronomy. At that time there was no reason to accept the Copernican theory, except for its mathematical simplicity [by avoiding using the equant in determining planetary positions].”[87] Tycho Brahe’s system (“that the earth is stationary, the sun revolves about the earth, and the other planets revolve about the sun”)[87] also directly competed with Copernicus’s. It was only a half century later with the work of Kepler and Galileo that any substantial evidence defending Copernicanism appeared, starting “from the time when Galileo formulated the principle of inertia...[which] helped to explain why everything would not fall off the earth if it were in motion.”[87] It was not until “after Isaac Newton formulated the universal law of gravitation and the laws of mechanics [in his 1687 Principia], which unified terrestrial and celestial mechanics, was the heliocentric view generally accepted.”[87]

6. Exposition of the motions in latitude of the nonterrestrial planets

16.2.3

Successors

See also: Copernican Revolution

16.3 Controversy See also: Catholic Church and science

Only mild controversy was the immediate result of the 1543 publication of Copernicus’s book. At the Council of Trent (1545–63) neither Copernicus’s theory nor calendar reform (which would later use tables deduced from Copernicus’s calculations) were discussed.[88] It has been much debated why it was not until six decades after the publication of De revolutionibus that the Catholic Church took any official action against it, even the efforts of Despite the near universal acceptance later of the helio- Tolosani going unheeded. Catholic side opposition only centric idea (though not the epicycles or the circular or- commenced seventy-three years later, when it was occabits), Copernicus’s theory was originally slow to catch sioned by Galileo.[89] Georg Joachim Rheticus could have been Copernicus’s successor, but did not rise to the occasion.[61] Erasmus Reinhold could have been his successor, but died prematurely.[61] The first of the great successors was Tycho Brahe[61] (though he did not think the earth orbited the sun), followed by Johannes Kepler,[61] who had worked as Tycho’s assistant in Prague.


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16.3.1

CHAPTER 16. NICOLAUS COPERNICUS

Tolosani

The first notable to move against Copernicanism was the Magister of the Holy Palace (i.e., the Catholic Church’s chief censor), Dominican Bartolomeo Spina, who “expressed a desire to stamp out the Copernican doctrine”.[90] But with Spina’s death in 1546, his cause fell to his friend, the well known theologian-astronomer, the Dominican Giovanni Maria Tolosani of the Convent of St. Mark in Florence. Tolosani had written a treatise on reforming the calendar (in which astronomy would play a large role) and had attended the Fifth Lateran Council (1512–17) to discuss the matter. He had obtained a copy of De Revolutionibus in 1544. His denunciation of Copernicanism was written a year later, in 1545, in an appendix to his unpublished work, On the Truth of Sacred Scripture.[91]

idea of what caused them. In this, Tolosani was linking Copernicus’s mathematical equations with the practices of the Pythagoreans (whom Aristotle had made arguments against, which were later picked up by Thomas Aquinas). It was argued that mathematical numbers were a mere product of the intellect without any physical reality, and as such could not provide physical causes in the investigation of nature.[92] Some astronomical hypotheses at the time (such as epicycles and eccentrics) were seen as mere mathematical devices to adjust calculations of where the heavenly bodies would appear, rather than an explanation of the cause of those motions. (As Copernicus still maintained the idea of perfectly spherical orbits, he relied on epicycles.) This “saving the phenomena” was seen as proof that astronomy and mathematics could not be taken as serious means to determine physical causes. Tolosani invoked this view in his final critique of Copernicus, saying that his biggest error was that he had started with “inferior” fields of science to make pronouncements about “superior” fields. Copernicus had used mathematics and astronomy to postulate about physics and cosmology, rather than beginning with the accepted principles of physics and cosmology to determine things about astronomy and mathematics. Thus Copernicus seemed to be undermining the whole system of the philosophy of science at the time. Tolosani held that Copernicus had fallen into philosophical error because he had not been versed in physics and logic; anyone without such knowledge would make a poor astronomer and be unable to distinguish truth from falsehood. Because Copernicanism had not met the criteria for scientific truth set out by Thomas Aquinas, Tolosani held that it could only be viewed as a wild unproven theory.[93][94]

Copernicus

Emulating the rationalistic style of Thomas Aquinas, Tolosani sought to refute Copernicanism by philosophical argument. Copernicanism was absurd, according to Tolosani, because it was scientifically unproven and unfounded. First, Copernicus had assumed the motion of the Earth but offered no physical theory whereby one would deduce this motion. (No one realized that the investigation into Copernicanism would result in a rethinking of the entire field of physics.) Second, Tolosani charged that Copernicus’s thought process was backwards. He held that Copernicus had come up with his idea and then sought phenomena that would support it, rather than observing phenomena and deducing from them the

Ptolemy and Copernicus, ca. 1686, at King Jan Sobieski's library, Wilanów Palace: an early Copernicus depiction

Tolosani recognized that the Ad Lectorem preface to Copernicus’s book was not actually by him. Its thesis that astronomy as a whole would never be able to make


16.3. CONTROVERSY truth claims was rejected by Tolosani (though he still held that Copernicus’s attempt to describe physical reality had been faulty); he found it ridiculous that Ad Lectorem had been included in the book (unaware that Copernicus had not authorized its inclusion). Tolosani wrote: “By means of these words [of the Ad Lectorem], the foolishness of this book’s author is rebuked. For by a foolish effort he [Copernicus] tried to revive the weak Pythagorean opinion [that the element of fire was at the center of the Universe], long ago deservedly destroyed, since it is expressly contrary to human reason and also opposes holy writ. From this situation, there could easily arise disagreements between Catholic expositors of holy scripture and those who might wish to adhere obstinately to this false opinion.”[95] Tolosani declared: “Nicolaus Copernicus neither read nor understood the arguments of Aristotle the philosopher and Ptolemy the astronomer.”[91] Tolosani wrote that Copernicus “is expert indeed in the sciences of mathematics and astronomy, but he is very deficient in the sciences of physics and logic. Moreover, it appears that he is unskilled with regard to [the interpretation of] holy scripture, since he contradicts several of its principles, not without danger of infidelity to himself and the readers of his book. ...his arguments have no force and can very easily be taken apart. For it is stupid to contradict an opinion accepted by everyone over a very long time for the strongest reasons, unless the impugner uses more powerful and insoluble demonstrations and completely dissolves the opposed reasons. But he does not do this in the least.”[95] Tolosani declared that he had written against Copernicus “for the purpose of preserving the truth to the common advantage of the Holy Church.”[96] Despite this, his work remained unpublished and there is no evidence that it received serious consideration. Robert Westman describes it as becoming a “dormant” viewpoint with “no audience in the Catholic world” of the late sixteenth century, but also notes that there is some evidence that it did become known to Tommaso Caccini, who would criticize Galileo in a sermon in December 1613.[96]

16.3.2

Theology

Tolosani may have criticized the Copernican theory as scientifically unproven and unfounded, but the theory also conflicted with the theology of the time, as can be seen in a sample of the works of John Calvin. In his Commentary on Genesis he said that “We indeed are not ignorant that the circuit of the heavens is finite, and that the earth, like a little globe, is placed in the centre.”[97] In his commentary on Psalms 93:1 he states that “The heavens revolve daily, and, immense as is their fabric and inconceivable the rapidity of their revolutions, we experience no concussion.... How could the earth hang suspended in the air were it not upheld by God’s hand? By what means could it maintain itself unmoved, while the heavens above are in constant rapid motion, did not its

167 Divine Maker fix and establish it.”[98] One sharp point of conflict between Copernicus’s theory and the Bible concerned the story of the Battle of Gibeon in the Book of Joshua where the Hebrew forces were winning but whose opponents were likely to escape once night fell. This is averted by Joshua’s prayers causing the sun and the moon to stand still. Martin Luther once made a remark about Copernicus, although without mentioning his name. According to Anthony Lauterbach, while eating with Martin Luther the topic of Copernicus arose during dinner on 4 June 1539 (in the same year as professor George Joachim Rheticus of the local University had been granted leave to visit him). Luther is said to have remarked “So it goes now. Whoever wants to be clever must agree with nothing others esteem. He must do something of his own. This is what that fellow does who wishes to turn the whole of astronomy upside down. Even in these things that are thrown into disorder I believe the Holy Scriptures, for Joshua commanded the sun to stand still and not the earth.”[87] These remarks were made four years before the publication of On the Revolutions of the Heavenly Spheres and a year before Rheticus’ Narratio Prima. In John Aurifaber’s account of the conversation Luther calls Copernicus “that fool” rather than “that fellow”, this version is viewed by historians as less reliably sourced.[87] Luther’s collaborator Philipp Melanchthon also took issue with Copernicanism. After receiving the first pages of Narratio Prima from Rheticus himself, Melanchthon wrote to Mithobius (physician and mathematician Burkard Mithob of Feldkirch) on 16 October 1541 condemning the theory and calling for it to be repressed by governmental force, writing “certain people believe it is a marvelous achievement to extol so crazy a thing, like that Polish astronomer who makes the earth move and the sun stand still. Really, wise governments ought to repress impudence of mind.”[99] It had appeared to Rheticus that Melanchton would understand the theory and would be open to it. This was because Melanchton had taught Ptolemaic astronomy and had even recommended his friend Rheticus to an appointment to the Deanship of the Faculty of Arts & Sciences at the University of Wittenberg after he had returned from studying with Copernicus.[100] Rheticus’ hopes were dashed when six years after the publication of De Revolutionibus Melanchthon published his Initia Doctrinae Physicae presenting three grounds to reject Copernicanism. These were “the evidence of the senses, the thousand-year consensus of men of science, and the authority of the Bible”.[101] Blasting the new theory Melanchthon wrote “Out of love for novelty or in order to make a show of their cleverness, some people have argued that the earth moves. They maintain that neither the eighth sphere nor the sun moves, whereas they attribute motion to the other celestial spheres, and also place the earth among the heavenly bodies. Nor were these jokes invented recently. There is still extant Archimedes’ book on The sand-reckoner; in which he re-


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ports that Aristarchus of Samos propounded the paradox that the sun stands still and the earth revolves around the sun. Even though subtle experts institute many investigations for the sake of exercising their ingenuity, nevertheless public proclamation of absurd opinions is indecent and sets a harmful example.”[99] Melanchthon went on to cite Bible passages and then declare “Encouraged by this divine evidence, let us cherish the truth and let us not permit ourselves to be alienated from it by the tricks of those who deem it an intellectual honor to introduce confusion into the arts.”[99] In the first edition of Initia Doctrinae Physicae, Melanchthon even questioned Copernicus’s character claiming his motivation was “either from love of novelty or from desire to appear clever”, these more personal attacks were largely removed by the second edition in 1550.[101] Another Protestant theologian who took issue with Copernicus was John Owen who declared that “the late hypothesis, fixing the sun as in the centre of the world' was 'built on fallible phenomena, and advanced by many arbitrary presumptions against evident testimonies of Scripture.”[102] In Roman Catholic circles, German Jesuit Nicolaus Serarius was one of the first to write against Copernicus’s theory as heretical, citing the Joshua passage, in a work published in 1609–1610, and again in a book in 1612.[103] In his 12 April 1615 letter to a Catholic defender of Copernicus, Paolo Antonio Foscarini, Catholic Cardinal Robert Bellarmine condemned Copernican theory, writing "...not only the Holy Fathers, but also the modern commentaries on Genesis, the Psalms, Ecclesiastes, and Joshua, you will find all agreeing in the literal interpretation that the sun is in heaven and turns around the earth with great speed, and that the earth is very far from heaven and sits motionless at the center of the world...Nor can one answer that this is not a matter of faith, since if it is not a matter of faith 'as regards the topic,' it is a matter of faith 'as regards the speaker': and so it would be heretical to say that Abraham did not have two children and Jacob twelve, as well as to say that Christ was not born of a virgin, because both are said by the Holy Spirit through the mouth of prophets and apostles.”[104]

16.3.3

Ingoli

Perhaps the most influential opponent of the Copernican theory was Francesco Ingoli, a Catholic priest. Ingoli wrote a January 1616 essay to Galileo presenting more than twenty arguments against the Copernican theory.[105] Though “it is not certain, it is probable that he [Ingoli] was commissioned by the Inquisition to write an expert opinion on the controversy”,[106] (after the Congregation of the Index’s decree against Copernicanism on 5 March 1616, Ingoli was officially appointed its consultant).[106] Galileo himself was of the opinion that the essay played an important role in the rejection of the theory by church authorities, writing in a later let-

ter to Ingoli that he was concerned that people thought the theory was rejected because Ingoli was right.[105] Ingoli presented five physical arguments against the theory, thirteen mathematical arguments (plus a separate discussion of the sizes of stars), and four theological arguments. The physical and mathematical arguments were of uneven quality, but many of them came directly from the writings of Tycho Brahe, and Ingoli repeatedly cited Brahe, the leading astronomer of the era. These included arguments about the effect of a moving earth on the trajectory of projectiles, and about parallax and Brahe’s argument that the Copernican theory required that stars be absurdly large.[107] Two of Ingoli’s theological issues with the Copernican theory were “common Catholic beliefs not directly traceable to Scripture: the doctrine that hell is located at the center of Earth and is most distant from heaven; and the explicit assertion that Earth is motionless in a hymn sung on Tuesdays as part of the Liturgy of the Hours of the Divine Office prayers regularly recited by priests.”[108] Ingoli cited Robert Bellarmine in regards to both of these arguments, and may have been trying to convey to Galileo a sense of Bellarmine’s opinion.[109] Ingoli also cited Genesis 1:14 where God places “lights in the firmament of the heavens to divide the day from the night.” Ingoli did not think the central location of the sun in the Copernican theory was compatible with it being described as one of the lights placed in the firmament.[108] Like previous commentators Ingoli also pointed to the passages about the Battle of Gibeon. He dismissed arguments that they should be taken metaphorically, saying “Replies which assert that Scripture speaks according to our mode of understanding are not satisfactory: both because in explaining the Sacred Writings the rule is always to preserve the literal sense, when it is possible, as it is in this case; and also because all the [Church] Fathers unanimously take this passage to mean that the sun which was truly moving stopped at Joshua’s request. An interpretation which is contrary to the unanimous consent of the Fathers is condemned by the Council of Trent, Session IV, in the decree on the edition and use of the Sacred Books. Furthermore, although the Council speaks about matters of faith and morals, nevertheless it cannot be denied that the Holy Fathers would be displeased with an interpretation of Sacred Scriptures which is contrary to their common agreement.”[108] However, Ingoli closed the essay by suggesting Galileo respond primarily to the better of his physical and mathematical arguments rather than to his theological arguments, writing “Let it be your choice to respond to this either entirely of in part—clearly at least to the mathematical and physical arguments, and not to all even of these, but to the more weighty ones.”[110] When Galileo wrote a letter in reply to Ingoli years later, he in fact only addressed the mathematical and physical arguments.[110] In March 1616, in connection with the Galileo affair, the Roman Catholic Church’s Congregation of the Index issued a decree suspending De revolutionibus until it could be “corrected,” on the grounds of ensur-


16.4. NATIONALITY

169

ing that Copernicanism, which it described as a “false Pythagorean doctrine, altogether contrary to the Holy Scripture,” would not “creep any further to the prejudice of Catholic truth.”[111] The corrections consisted largely of removing or altering wording that the spoke of heliocentrism as a fact, rather than a hypothesis.[112] The corrections were made based largely on work by Ingoli.[106]

16.3.4

Galileo

Bust by Schadow, 1807, in the Walhalla memorial

On the orders of Pope Paul V, Cardinal Robert Bellarmine gave Galileo prior notice that the decree was about to be issued, and warned him that he could not “hold or defend” the Copernican doctrine.[lower-alpha 9] The corrections to De revolutionibus, which omitted or altered nine sentences, were issued four years later, in 1620.[113] In 1633 Galileo Galilei was convicted of grave suspicion of heresy for “following the position of Copernicus, which is contrary to the true sense and authority of Holy Scripture”,[114] and was placed under house arrest for the rest of his life.[115][116] At the instance of Roger Boscovich, the Catholic Church’s 1758 Index of Prohibited Books omitted the general prohibition of works defending heliocentrism,[117] but retained the specific prohibitions of the original uncensored versions of De revolutionibus and Galileo’s Dialogue Concerning the Two Chief World Systems. Those prohibitions were finally dropped from the 1835 Index.[118]

16.4 Nationality

There has been discussion of Copernicus’s nationality and of whether, in fact, it is meaningful to ascribe to him a nationality in the modern sense. But there are some facts that should be considered when talking about Copernicus’s nationality. Nicolaus Copernicus was born and raised in Royal Prussia, a semiautonomous and polyglot region under rule by the Kingdom of Poland.[119][120] Copernicus was the child of German-speaking parents and grew up with German as his mother tongue.[121][122][123][124] His alma mater was the University of Kraków in Poland. When he later studied in Italy, Copernicus joined the “German Nation”, the student organization for German speakers at the University of Bologna.[125][126] His family stood against the Teutonic Order and actively supported the city of Toruń during the Thirteen Years’ War. The father of Nicolaus Copernicus lent money to King Casimir IV Jagiellon of Poland to finance the war against the Teutonic Knights,[127] but the inhabitants of Royal Prussia also resisted the Polish crown’s efforts for greater control over the region.[119] Encyclopædia Britannica,[128] Encyclopedia Americana,[129] The Concise Columbia Encyclopedia,[130] The Oxford World Encyclopedia,[131] and World Book Encyclopedia[132] refer to Copernicus as a “Polish astronomer”. Sheila Rabin, writing in the Stanford Encyclopedia of Philosophy, describes Copernicus as a “child of a German family [who] was a subject of the Polish crown”,[8] while Martin Weissenbacher writes that Copernicus’s father was a Germanized Pole.[133] Historian Michael Burleigh describes the nationality debate as a “totally insignificant battle” between German and Polish scholars during the interwar period.[134] Polish astronomer Konrad Rudnicki calls the discussion a “fierce scholarly quarrel in ... times of nationalism” and describes Copernicus as an inhabitant of a Germanspeaking territory that belonged to Poland, himself being of mixed Polish-German extraction.[135]

Poet Czesław Miłosz describes the debate as an “absurd” Replica of Warsaw’s projection of a modern understanding of nationality onto Copernicus Monument, in Montreal, Canada


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Renaissance people, who identified with their home territories rather than with a nation.[136] Similarly, historian Norman Davies writes that Copernicus, as was common in his era, was “largely indifferent” to nationality, being a local patriot who considered himself "Prussian".[137] Miłosz and Davies both write that Copernicus had a German-language cultural background, while his working language was Latin in accord with the usage of the time.[136][137] Additionally, according to Davies, “there is ample evidence that he knew the Polish language”.[137] Davies concludes: “Taking everything into consideration, there is good reason to regard him both as a German and as a Pole: and yet, in the sense that modern nationalists understand it, he was neither.”[137]

16.5 Commemoration

U.S. postage stamp on 500th anniversary of Copernicus’s birth (1973)

chemical element 112 (temporarily named ununbium) proposed to the International Union of Pure and Applied Chemistry that its permanent name be "copernicium" (symbol Cn). “After we had named elements after our city and our state, we wanted to make a statement with a name that was known to everyone,” said Hofmann. “We didn't want to select someone who was a German. We were looking world-wide.”[138] On the 537th anniversary of his birthday the official naming was released to the public.[139]

16.5.2 55 Cancri A In July 2014 the International Astronomical Union launched a process for giving proper names to certain exoplanets and their host stars.[140] The process involved Enamel mosaic by Stefan Knapp, 1972, on building of Nicolaus public nomination and voting for the new names.[141] In Copernicus University, in Toruń, Poland. December 2015, the IAU announced the winning name for 55 Cancri A was Copernicus.[142]

16.5.1

Copernicium

Main article: Copernicium

16.5.3 Veneration

Copernicus is honored, together with Johannes Kepler, On 14 July 2009, the discoverers, from the Gesellschaft in the liturgical calendar of the Episcopal Church (USA), für Schwerionenforschung in Darmstadt, Germany, of with a feast day on 23 May.[143]


16.8. REFERENCES

16.5.4

Influence

Contemporary literary and artistic works inspired by Copernicus • Mover of the Earth, Stopper of the Sun for symphony orchestra (overture), written by composer Svitlana Azarova commissioned by ONDIF[144][145] • Doctor Copernicus, a 1975 novel by John Banville, sketches the life of Copernicus and the 16th-century world in which he lived.

16.6 See also • List of Roman Catholic scientist-clerics

16.7 Notes [1] Linton 2004, pp. 39, 119. Copernicus was not the first to propose a heliocentric system; the Greek mathematician and astronomer Aristarchus of Samos, for instance, proposed such a system during the third century BCE, but there is little evidence that his ideas were developed beyond a basic outline (Dreyer 1953, pp. 135–48). Copernicus was aware of Aristarchus’ heliocentric theory and cited him in an early (unpublished) manuscript of De Revolutionibus (which still survives), though he removed the reference from his final published manuscript.[4] [2] He used Latin and German, knew enough Greek to translate the 7th-century Byzantine poet Theophylact Simocatta's verses into Latin prose[28] and “there is ample evidence that he knew the Polish language".[29] During his several years’ studies in Italy, Copernicus presumably would also have learned some Italian. Professor Stefan Melkowski of Nicolaus Copernicus University in Toruń likewise asserts that Copernicus spoke both German and Polish.[30] [3] See the title page at The book [4] Dobrzycki and Hajdukiewicz (1969) describe Copernicus having attended school at Włocławek as unlikely.[9] [5] A reference to the “Commentariolus” is contained in a library catalogue, dated 1 May 1514, of a 16th-century historian, Matthew of Miechów, so it must have begun circulating before that date (Koyré, 1973, p. 85; Gingerich, 2004, p. 32). Thoren (1990 p. 99) gives the length of the manuscript as 40 pages. [6] Koyré (1973, pp. 27, 90) and Rosen (1995, pp. 64,184) take the view that Copernicus was indeed concerned about possible objections from theologians, while Lindberg and Numbers (1986) argue against it. Koestler (1963) also denies it. Indirect evidence that Copernicus was concerned about objections from theologians comes from a letter written to him by Andreas Osiander in 1541, in which Osiander advises Copernicus to adopt a proposal by which he

171

says “you will be able to appease the Peripatetics and theologians whose opposition you fear”. (Koyré, 1973, pp. 35, 90) [7] Particularly his use of the Tusi couple and his models for the motions of Mercury and the Moon (Linton 2004, pp. 124, 137–38) [8] Rosen (1995, pp. 187–92), originally published in 1967 in Saggi su Galileo Galilei . Rosen is particularly scathing about this and other statements in The Sleepwalkers, which he criticizes as inaccurate. [9] Fantoli (2005, pp. 118–19); Finocchiaro (1989, pp. 148, 153). On-line copies of Finocchiaro’s translations of the relevant documents, Inquisition Minutes of 25 February 1616 and Cardinal Bellarmine’s certificate of 26 May 1616, have been made available by Gagné (2005). This notice of the decree would not have prevented Galileo from discussing heliocentrism solely as a mathematical hypothesis, but a stronger formal injunction (Finocchiaro, 1989, p. 147-148) not to teach it “in any way whatever, either orally or in writing”, allegedly issued to him by the Commissary of the Holy Office, Father Michelangelo Segizzi, would certainly have done so (Fantoli, 2005, pp. 119–20, 137). There has been much controversy over whether the copy of this injunction in the Vatican archives is authentic; if so, whether it was ever issued; and if so, whether it was legally valid (Fantoli, 2005, pp. 120–43).

16.8 References [1] Jones, Daniel (2003) [1917], Peter Roach, James Hartmann and Jane Setter, eds., English Pronouncing Dictionary, Cambridge: Cambridge University Press, ISBN 312-539683-2 [2] “Copernicus”. House.

Dictionary.com Unabridged.

Random

[3] “Copernicus”. Merriam-Webster Dictionary. [4] Gingerich, O. “Did Copernicus Owe a Debt to Aristarchus?" Journal for the History of Astronomy, Vol.16, NO.1/FEB, P. 37, 1985 [5] Hagen, J. (1908). Nicolaus Copernicus. In The Catholic Encyclopedia. New York: Robert Appleton Company. Retrieved November 6, 2015 from New Advent: http: //www.newadvent.org/cathen/04352b.htm [6] “Copernicus seems to have drawn up some notes [on the displacement of good coin from circulation by debased coin] while he was at Olsztyn in 1519. He made them the basis of a report on the matter, written in German, which he presented to the Prussian Diet held in 1522 at Grudziądz... He later drew up a revised and enlarged version of his little treatise, this time in Latin, and setting forth a general theory of money, for presentation to the Diet of 1528.” Angus Armitage, The World of Copernicus, 1951, p. 91. [7] Iłowiecki, Maciej (1981). Dzieje nauki polskiej (in Polish). Warszawa: Wydawnictwo Interpress. p. 40. ISBN 83223-1876-6.


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[8] Sheila Rabin. “Nicolaus Copernicus”. Stanford Encyclopedia of Philosophy. Retrieved 22 April 2007. [9] Dobrzycki and Hajdukiewicz (1969), p. 4. [10] “The name of the village, not unlike that of the astronomer’s family, has been variously spelled. A large German atlas of Silesia, published by Wieland in Nuremberg in 1731, spells it Kopernik.” Mizwa, p. 36. [11] Dobrzycki and Hajdukiewicz (1969), p. 3. [12] Bieńkowska (1973), p. 15 [13] Rybka (1973), p. 23. [14] Sakolsky (2005), p. 8. [15] Biskup (1973), p. 16 [16] Mizwa, 1943, p. 38. [17] “In 1512, Bishop Watzenrode died suddenly after attending King Sigismund’s wedding feast in Kraków. Rumors abounded that the bishop had been poisoned by agents of his long-time foe, the Teutonic Knights.” Hirshfeld, p. 38. [18] “The Watzelrodes—or Watzenrodes—in spite of their rather Germanic name seemed to have been good Poles (enemies of the Teutonic Order).” Koyre, p. 38. [19] "[Watzenrode] was also firm, and the Teutonic Knights, who remained a constant menace, did not like him at all; the Grand Master of the order once described him as 'the devil incarnate'. [Watzenrode] was the trusted friend and advisor of three [Polish] kings in succession: John Albert, Alexander (not to be confused with the poisoning pope), and Sigismund; and his influence greatly strengthened the ties between Warmia and Poland proper.” Moore (1994), pp. 52, 62. [20] Wojciech Iwanczak (1998). “Watzenrode, Lucas”. In Bautz, Traugott. Biographisch-Bibliographisches Kirchenlexikon (BBKL) (in German). 13. Herzberg: Bautz. col. 389–393. ISBN 3-88309-072-7. [21] “Lucas was on more friendly terms with his successors, Johann Albert (Jan Olbracht) (from 1492 to 1501), and later Alexander (Aleksander) (from 1501 to 1506), and Sigismund (Zygmunt) I (from 1506).” Gassendi & Thill, p. 22.

CHAPTER 16. NICOLAUS COPERNICUS

[27] “He was a linguist with a command of Polish, German and Latin, and he possessed also a knowledge of Greek rare at that period in northeastern Europe and probably had some acquaintance with Italian and Hebrew.” Angus Armitage, Copernicus, the founder of modern astronomy, p. 62. [28] Angus Armitage, The World of Copernicus, pp. 75–77. [29] Davies, Norman (2005). God’s playground. A History of Poland in Two Volumes. II. Oxford University Press. p. 26. ISBN 0-19-925340-4. [30] Melkowski, Stefan (May 2003). "O historii i o współczesności (On History and the Present Day)" (in Polish). Retrieved 22 April 2007. [31] "Deutsch war für Kopernikus Muttersprache und Alltagssprache, wenn auch der schriftliche Umgang fast ausschließlich auf Lateinisch erfolgte." Carrier, p. 192. [32] Rosen (1995, p. 127). [33] “Although great importance has frequently been ascribed to this fact, it does not imply that Copernicus considered himself to be a German. The 'nationes’ of a medieval university had nothing in common with nations in the modern sense of the word. Students who were natives of Prussia and Silesia were automatically described as belonging to the Natio Germanorum. Furthmore, at Bologna, this was the 'privileged' nation; consequently, Copernicus had very good reason for inscribing himself on its register.” Koyre, p. 21 [34] “It is important to recognize, however, that the medieval Latin concept of natio, or “nation”, referred to the community of feudal lords both in Germany and elsewhere, not to 'the people' in the nineteenth-century democratic or nationalistic sense of the word.” Johnson, p. 23. [35] Koestler, 1968, p. 129. [36] Gassendi & Thill (2002), p. 37. [37] “Kopernik, Koperek, Kopr and Koprnik in Polish—also similarly in other Slavonic languages—means simply dill such as is used in dill pickling. Be it as it may, although the present writer is more inclined towards the occupational interpretation, it is interesting to note ...” Mizwa, p. 37. [38] Angus Armitage, The World of Copernicus, p. 51.

[22] Dobrzycki and Hajdukiewicz (1969), p. 5.

[39] Gingerich (2004), p. 143.

[23] “To obtain for his nephews [Nicolaus and Andreas] the necessary support [for their studies in Italy], the bishop [Lucas Watzenrode the Younger] procured their election as canons by the chapter of Frauenburg (1497–1498).” "Nicolaus Copernicus" , New Advent (online version of the 1913 Catholic Encyclopedia). Retrieved 9 June 2013.

[40] Biskup (1973), p. 32

[24] Ed Rosen points out that he used phonetic descriptions of Polish words which suggests he was not fluent. See Nicolas Copernicus Thorunensis

[43] Malagola (1878), p. 562–65

[25] “He spoke German, Polish and Latin with equal fluency as well as Italian.” Stone, p. 101. [26] “He spoke Polish, Latin, and Greek.” Somerville, p. 10.

[41] “In the [enrollment] documents still in existence we find the entry: Nicolaus Nicolai de Torunia.” Moore (1994), p. 50. [42] Biskup (1973), pp. 38, 82

[44] Maximilian Curtze, Ueber die Orthographie des Namens Coppernicus, 1879 [45] Czesław Miłosz, The History of Polish Literature, p. 38. [46] Angus Armitage, The World of Copernicus, p. 55.


16.8. REFERENCES

[47] Dobrzycki and Hajdukiewicz (1969), pp. 4–5. [48] Rosen, Ed (December 1960). “Copernicus was not a priest” (PDF). PROC AMER PHIL SOC. 104 (6). [49] Rosen, Edward (1995). “Chapter 6: Copernicus’ Alleged Priesthood”. In Hilfstein, Erna. Copernicus and his successors. U.K.: The Hambledon Press. pp. 47–56. ISBN 1-85285-071-X. Retrieved 17 December 2014. [50] Dobrzycki and Hajdukiewicz (1969), pp. 5–6. [51] Dobrzycki and Hajdukiewicz (1969), p. 6. [52] Rabin (2005). [53] Gingerich (2004, pp. 187–89, 201); Koyré (1973, p. 94); Kuhn (1957, p. 93); Rosen (2004, p. 123); Rabin (2005). Robbins (1964, p.x), however, includes Copernicus among a list of Renaissance astronomers who “either practiced astrology themselves or countenanced its practice”. [54] “Nicolaus Copernicus Gesamtausgabe Bd. VI: Urkunden, Akten und NachrichtenDocumenta Copernicana – Urkunden, Akten und Nachrichten, alle erhaltenen Urkunden und Akten zur Familiengeschichte, zur Biographie und Tätigkeitsfeldern von Copernicus, 1996, ISBN 978-3-05-003009-8 [5], pp. 62–63. [55] Sedlar (1994). [56] Dobrzycki and Hajdukiewicz (1969), p. 7. [57] Dobrzycki and Hajdukiewicz (1969), pp. 7–8. [58] Repcheck (2007), p. 66. [59] Dobrzycki and Hajdukiewicz (1969), p. 9. [60] Oliver Volckart (1997). “Early Beginnings of the Quantity Theory of Money and Their Context in Polish and Prussian Monetary Policies, c. 1520–1550”. The Economic History Review. New Series. 50 (3): 430–49. doi:10.1111/1468-0289.00063.

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[70] Koestler 1963, page 189, says the following about a letter from Canon Tiedemann Giese to Georg Joachim Rheticus. […] the end came only after several months, on 24 May. In a letter to Rheticus, written a few weeks later, Giese recorded the event in a single, tragic sentence: For many days he had been deprived of his memory and mental vigour; he only saw his completed book at the last moment, on the day he died. Koestler attributes this quotation to Leopold Prowe, Nicolaus Copernicus, Berlin 1883–1884, Volume 1, part 2, page 554. [71] Easton, Adam (21 November 2008). “Polish tests 'confirm Copernicus’". BBC News. Retrieved 18 January 2010. [72] “Copernicus’s grave found in Polish church”. USA Today. 3 November 2005. Retrieved 26 July 2012. [73] Bowcott, Owen (21 November 2008). “16th-century skeleton identified as astronomer Copernicus”. The Guardian. Retrieved 18 January 2010. [74] Bogdanowicz, W.; Allen, M.; Branicki, W.; Lembring, M.; Gajewska, M.; Kupiec, T. (2009). “Genetic identification of putative remains of the famous astronomer Nicolaus Copernicus”. PNAS. 106 (30): 12279–12282. Bibcode:2009PNAS..10612279B. doi:10.1073/pnas.0901848106. PMC 2718376 . PMID 19584252. [75] Gingerich, O. (2009). “The Copernicus grave mystery”. PNAS. 106 (30): 12215– 12216. Bibcode:2009PNAS..10612215G. doi:10.1073/pnas.0907491106. PMC 2718392 . PMID 19622737.

[61] Repcheck (2007), pp. 79, 78, 184, 186.

[76] “16th-century astronomer Copernicus reburied as hero in Poland”. Cleveland Plain Dealer/Associated Press. 25 May 2010.

[62] Dobrzycki and Hajdukiewicz (1969), p. 11.

[77] Dreyer (1953), pp. 40–52; Linton (2004, p. 20).

[63] Angus Armitage, The World of Copernicus, pp. 97–98.

[78] Dreyer (1953), pp. 123–35; Linton (2004, p. 24).

[64] Angus Armitage, The World of Copernicus, p. 98. [65] Kuhn, 1957, pp. 187–88. [66] Goddu (2010: 245–6) [67] “Schönberg, Nicholas, Letter to Nicolaus Copernicus, translated by Edward Rosen”.

[79] Dreyer (1953, pp. 135–48); Heath (1913), pp. 301–8) [80] Heath (1913), p. 302. [81] George Saliba, 'Revisiting the Astronomical Contacts Between the World of Islam and Renaissance Europe: The Byzantine Connection', 'The occult sciences in Byzantium', 2006, p.368

[68] Dreyer (1953, p. 319).

[82] Gingerich, Owen (1997). “Ptolemy, Copernicus, and Kepler”. The Eye of Heaven. Springer. pp. 3–51.

[69] According to Bell 1992, p. 111:

[83] Rosen (2004), pp. 58–59

[…] Copernicus, on his deathbed, received the printer’s proofs of his epoch-breaking Dē revolutionibus orbium coelestium.

[84] Danielson (2006) [85] Koestler (1959, p. 191).


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[86] Peter DeMarco (13 April 2004). “Book quest took him [115] Hilliam, Rachel (2005). Galileo Galilei: Father of Modern around the globe”. The Boston Globe. Retrieved 3 June Science. The Rosen Publishing Group. p. 96. 2013. [116] “Galileo is convicted of heresy”. history.com. Retrieved [87] Donald H. Kobe (1998). “Copernicus and Martin 13 December 2013. Luther: An Encounter Between Science and Religion”. American Journal of Physics. 66 (3): 190. [117] Heilbron (2005, p. 307); Coyne (2005, p. 347). Bibcode:1998AmJPh..66..190K. doi:10.1119/1.18844. [118] McMullin (2005, p. 6); Coyne (2005, pp. 346–47). [88] Westman (2011, p. 194) [119] Krystyna Poray Goddu: Copernicus and the Aristotelian [89] Hagen, John. “Nicolaus Copernicus.” The Catholic EncyTradition. BRILL, 2010, ISBN 978-9004181076, Part 1, clopedia. Vol. 4. New York: Robert Appleton Company, Chapter 1, p.7 1908. 19 Feb. 2014 [120] Jack Repcheck: Copernicus’ Secret: How the Scientific [90] Feldhay (1995, p. 205) Revolution Began Simon & Schuster, 2008, ISBN 9780743289528,p.32 [91] Westman (2011, p. 195) [92] Feldhay (1995, p. 205-207) [93] Feldhay (1995, p. 207) [94] Westman (2011, p. 195-196) [95] Westman (2011, p. 196) [96] Westman (2011, p. 197) [97] Rosen (1960, p. 437) [98] Rosen (1960, p. 438) [99] Rosen (1995, p. 198)

[121] Pierre Gassendi,Oliver Thill: The Life of Copernicus (1473-1543) Xulon Press, 2002, ISBN 9781591601937,p.19 [122] Manfred Weissenbacher : Sources of Power: How Energy Forges Human HistoryPraeger, 2009, ISBN 9780313356261,p.170 [123] Marvin Bolt,JoAnn Palmeri,Thomas Hockey: The Biographical Encyclopedia of Astronomers Springer, 2009, ISBN 978-0387351339,p.252 [124] Charles E. Hummel: The Galileo Connection InterVarsity Press, 1986, ISBN 978-0877845003,p.40

[125] Krystyna Poray Goddu: Copernicus and the Aristotelian Tradition. BRILL, 2010, ISBN 978-9004181076, Chap[101] I. Bernard Cohen (1985). Revolution in Science. Camter 6,p.173 bridge, MA: Belknap Press of Harvard University Press. p. 497. ISBN 0-674-767780. [126] John Freely: Celestial Revolutionary:Copernicus, the Man and His Universe I.B.Tauris, 2014, ISBN 978[102] Rosen (1995, p. 166-167) 0857734907,p.56-57 [100] Repcheck (2007, p. 160)

[103] Finocchiaro (2010, p. 71) [104] Finocchiaro (2010, p. 75) [105] Graney (2015, p. 68-69) [106] Finocchiaro (2010, p. 72) [107] Graney (2015, p. 69-75) [108] Finocchiaro (2010, p. 73) [109] Graney (2015, p. 74) [110] Graney (2015, p. 70)

[127] q=copernicus%20father%20lent%20money%20on%20war&f=false “Celestial Revolutionary: Copernicus, the Man and His Universe” by John Freely. [128] “Copernicus, Nicolaus”. Encyclopædia Britannica Online. Encyclopædia Britannica. 2007. Retrieved 21 September 2007. [129] “Copernicus, Nicolaus”, Encyclopedia Americana, 1986, vol. 7, pp. 755–56. [130] “Copernicus, Nicholas”, The Concise Columbia Encyclopedia, New York, Avon Books, 1983, ISBN 0-38063396-5, p. 198: “Polish astronomer”.

[111] Decree of the General Congregation of the Index, 5 March 1616, translated from the Latin by Finocchiaro (1989, pp. [131] “Copernicus, Nicolaus”, The Oxford World Encyclopedia, Oxford University Press, 1998. 148–149). An on-line copy of Finocchiaro’s translation has been made available by Gagné (2005). [132] Paula Findlen (2013). “Copernicus, Nicolaus”. World Book Advanced. Retrieved 31 May 2013. [112] Finocchiaro (1989, p. 30) [113] Catholic Encyclopedia.

[133] Weissenbacher (2009), p. 170.

[114] From the Inquisition’s sentence of 22 June 1633 (de San- [134] Burleigh, Michael (1988). Germany turns eastwards. A tillana, 1976, pp. 306–10; Finocchiaro 1989, pp. 287– study of Ostforschung in the Third Reich. CUP Archive. 91) pp. 60, 133, 280. ISBN 0-521-35120-0.


16.9. FURTHER READING

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[135] Rudnicki, Konrad (November–December 2006). “The Genuine Copernican Cosmological Principle”. Southern Cross Review: note 2. Retrieved 21 January 2010.

• Coyne, George V., S.J. (2005). The Church’s Most Recent Attempt to Dispel the Galileo Myth. In McMullin (2005, pp. 340–59).

[136] Miłosz, Czesław (1983). The history of Polish literature (2 ed.). University of California Press. p. 37. ISBN 0520-04477-0.

• Danielson, Dennis Richard (2006). The First Copernican: Georg Joachim Rheticus and the Rise of the Copernican Revolution. New York: Walker & Company. ISBN 0-8027-1530-3.

[137] Davies, Norman (2005). God’s playground. A History of Poland in Two Volumes. II. Oxford University Press. p. 20. ISBN 0-19-925340-4. [138] Fox, Stuart (14 July 2009). “Newly Discovered Element 112 Named 'Copernicum'". popsci.com. Retrieved 17 August 2012. [139] Renner, Terrence (20 February 2010). “Element 112 is Named Copernicium”. International Union of Pure and Applied Chemistry. Archived from the original on 22 February 2010. Retrieved 20 February 2010. [140] NameExoWorlds: An IAU Worldwide Contest to Name Exoplanets and their Host Stars. IAU.org. 9 July 2014 [141] NameExoWorlds The Process [142] Final Results of NameExoWorlds Public Vote Released, International Astronomical Union, 15 December 2015. [143] “Calendar of the Church Year according to the Episcopal Church”. Satucket.com. 12 June 2010. Retrieved 17 August 2012. [144] World premiere 23 January 2013 Salle Pleyel [145] Dutch premiere 1st of March 2014 at Concertgebouw, Amsterdam - Movers of the Earth

16.9 Further reading • Armitage, Angus (1951). The World of Copernicus. New York, NY: Mentor Books. • Armitage, Angus (1990). Copernicus, the founder of modern astronomy. Dorset Press. ISBN 978-088029-553-6. • Bell, Eric Temple (1992) [1940]. The development of mathematics. New York: Dover Publications. ISBN 978-0-486-27239-9. • Bieńkowska, Barbara (1973). The Scientific World of Copernicus: On the Occasion of the 500th Anniversary of His Birth, 1473–1973. Springer. ISBN 90-277-0353-1. • Marian Biskup (1973). Regesta Copernicana: (calendar of Copernicus’ papers). (in Polish). Ossolineum. • Martin Carrier (2001). Nikolaus Kopernikus. C.H.Beck. ISBN 978-3-406-47577-1.

• Davies, Norman, God’s Playground: A History of Poland, 2 vols., New York, Columbia University Press, 1982, ISBN 0-231-04327-9. • Dobrzycki, Jerzy, and Leszek Hajdukiewicz, “Kopernik, Mikołaj”, Polski słownik biograficzny (Polish Biographical Dictionary), vol. XIV, Wrocław, Polish Academy of Sciences, 1969, pp. 3–16. • Dreyer, John Louis Emil (1953) [1905]. A History of Astronomy from Thales to Kepler. New York, NY: Dover Publications. • Fantoli, Annibale (2005). The Disputed Injunction and its Role in Galileo’s Trial. In McMullin (2005, pp. 117–49). • Feldhay, Rivka (1995). Galileo and the Church: Political Inquisition Or Critical Dialogue?. Cambridge: Cambridge University Press. ISBN 9780521344685. • Maurice A. Finocchiaro (2010). Defending Copernicus and Galileo: Critical Reasoning in the Two Affairs. Springer Science & Business Media. • Finocchiaro, Maurice A. (1989). The Galileo Affair: A Documentary History. Berkeley, CA: University of California Press. ISBN 0-520-06662-6. • Gagné, Marc (2005). “Texts from The Galileo Affair: A Documentary History edited and translated by Maurice A. Finocchiaro”. West Chester University course ESS 362/562 in History of Astronomy. Archived from the original on 30 September 2007. Retrieved 15 January 2008. (Extracts from Finocchiaro (1989)) • Pierre Gassendi; Olivier Thill (September 2002). The Life of Copernicus 1473–1543. Xulon Press. ISBN 978-1-59160-193-7. • Gingerich, Owen (2004). The Book Nobody Read. London: William Heinemann. ISBN 0-434-013153. • Goddu, André (2010). Copernicus and the Aristotelian tradition. Leiden, Netherlands: Brill. ISBN 978-90-04-18107-6. • Graney, Christopher M. (2015). Setting Aside All Authority: Giovanni Battista Riccioli and the Science Against Copernicus in the Age of Galileo. Notre


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CHAPTER 16. NICOLAUS COPERNICUS Dame, Indiana: University of Notre Dame Press. ISBN 9780268029883.

• Goodman, David C.; Russell, Colin A. (1991). The Rise of Scientific Europe, 1500–1800. Hodder Arnold H&S. ISBN 0-340-55861-X. • Heath, Sir Thomas (1913). Aristarchus of Samos, the ancient Copernicus ; a history of Greek astronomy to Aristarchus, together with Aristarchus’s Treatise on the sizes and distances of the sun and moon : a new Greek text with translation and notes. London: Oxford University Press. • Alan W. Hirshfeld (1 May 2002). Parallax: The Race to Measure the Cosmos. Henry Holt and Company. ISBN 978-0-8050-7133-7. • Heilbron, John L. (2005). Censorship of Astronomy in Italy after Galileo. In McMullin (2005, pp. 279– 322). • Michael Hoskin (18 March 1999). The Cambridge Concise History of Astronomy. Cambridge University Press. ISBN 978-0-521-57600-0. • Lonnie Johnson (28 September 1996). Central Europe: Enemies, Neighbors, Friends. Oxford University Press, USA. ISBN 978-0-19-802607-5. • Koestler, Arthur (1963) [1959]. The Sleepwalkers: A History of Man’s Changing Vision of the Universe. New York, NY: Grosset & Dunlap. ISBN 0-44800159-4. Original edition published by Hutchinson (1959, London) • Arthur Koestler (1968). The Sleepwalkers. Macmillan. • Koeppen, Hans; et al. (1973). Nicolaus Copernicus zum 500. Geburtstag. Böhlau Verlag. ISBN 3-41283573-0. • Koyré, Alexandre (1973). The Astronomical Revolution: Copernicus – Kepler – Borelli. Ithaca, NY: Cornell University Press. ISBN 0-8014-0504-1. • Kuhn, Thomas (1957). The Copernican Revolution: Planetary Astronomy in the Development of Western Thought. Cambridge, MA: Harvard University Press. OCLC 535467. • Lindberg, David C.; Numbers, Ronald L. (1986). “Beyond War and Peace: A Reappraisal of the Encounter between Christianity and Science”. Church History. Cambridge University Press. 55 (3): 338– 354. doi:10.2307/3166822. JSTOR 3166822. • Linton, Christopher M. (2004). From Eudoxus to Einstein: A History of Mathematical Astronomy. Cambridge: Cambridge University Press. ISBN 978-0-521-82750-8.

• Carlo Malagola (1878). Della vita e delle opere di Antonio Urceo detto Codro: studi e ricerch. Fava e Garagnani. • Manetho; Ptolemy (1964) [1940]. Manetho Ptolemy Tetrabiblos. Loeb Classical Library edition, translated by W.G.Waddell and F.E.Robbins PhD. London: William Heinemann. • McMullin, Ernan, ed. (2005). The Church and Galileo. Notre Dame, IN: University of Notre Dame Press. ISBN 0-268-03483-4. • Miłosz, Czesław, The History of Polish Literature, second edition, Berkeley, University of California Press, 1969, ISBN 0-520-04477-0. • Mizwa, Stephen, Nicolaus Copernicus, 1543–1943, Kessinger Publishing, 1943. • Moore, Patrick (1994). The great astronomical revolution 1543–1687 and the Space Age epilogue. Albion. ISBN 978-1-898563-18-1. • Ptolemy, Claudius (1964) [1940]. Tetrabiblos. Loeb Classical Library edition, translated by F.E.Robbins PhD. London: William Heinemann. • Rabin, Sheila (2005). "Copernicus". The Stanford Encyclopedia of Philosophy (summer 2005 edition), Edward N. Zalta (ed.). Retrieved 26 May 2008. • Repcheck, Jack (2007). Copernicus’ Secret: How the Scientific Revolution Began. New York: Simon & Schuster. ISBN 0-7432-8951-X. • Rosen, Edward (1960). “Calvin’s Attitude toward Copernicus”. Journal of the History of Ideas. 21 (3): 431–41. doi:10.2307/2708147. • Rosen, Edward (1995). Copernicus and his Successors. London: Hambledon Press. ISBN 1-85285071-X. • Rosen, Edward (translator) (2004) [1939]. Three Copernican Treatises:The Commentariolus of Copernicus; The Letter against Werner; The Narratio Prima of Rheticus (Second Edition, revised ed.). New York, NY: Dover Publications. ISBN 0-48643605-5. • Russell, Jeffrey Burton (1997) [1991]. Inventing the Flat Earth—Columbus and Modern Historians. New York, NY: Praeger. ISBN 0-275-95904-X. • The Review of the Polish Academy of Sciences. “Ossolineum”, the Polish Academy of Sciences Press. 1973. • Josh Sakolsky (1 October 2004). Copernicus And Modern Astronomy. The Rosen Publishing Group. ISBN 978-1-4042-0305-1.


16.10. EXTERNAL LINKS

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• de Santillana, Giorgio (1976) [1955]. The Crime of Galileo (Midway reprint). Chicago, Ill: University of Chicago Press. ISBN 0-226-73481-1.

• O'Connor, John J.; Robertson, Edmund F., “Nicolaus Copernicus”, MacTutor History of Mathematics archive, University of St Andrews.

• Sedlar, Jean W. (1994). East Central Europe in the Middle Ages 1000–1500. University of Washington Press. ISBN 0-295-97290-4.

• Nicolaus Copernicus at the Mathematics Genealogy Project

• Dava Sobel, A More Perfect Heaven: How Copernicus Revolutionized the Cosmos, New York, Walker & Company, 2011, ISBN 978-0-8027-1793-1. Features a fictional play about Rheticus' visit to Copernicus, sandwiched between chapters about the visit’s pre-history and post-history. • Barbara A. Somervill (1 January 2005). Nicolaus Copernicus: Father Of Modern Astronomy. Capstone. ISBN 978-0-7565-0812-8.

• Copernicus in Torun • Nicolaus Copernicus Thorunensis Copernican Academic Portal

by

the

• Nicolaus Copernicus Museum in Frombork • Portraits of Copernicus: Copernicus’s face reconstructed; Portrait; Nicolaus Copernicus • Copernicus and Astrology • Stanford Encyclopedia of Philosophy entry

• Daniel Stone (2001). The Polish-Lithuanian State: 1386–1795. University of Washington Press. ISBN 978-0-295-98093-5.

• 'Body of Copernicus’ identified – BBC article including image of Copernicus using facial reconstruction based on located skull

• Thoren, Victor E. (1990). The Lord of Uraniborg. Cambridge: Cambridge University Press. ISBN 0521-35158-8. (A biography of Danish astronomer and alchemist Tycho Brahe.)

• Nicolaus Copernicus on the 1000 Polish Zloty banknote.

• Manfred Weissenbacher (September 2009). Sources of Power: How Energy Forges Human History. ABC-CLIO. ISBN 978-0-313-35626-1. • Westman, Robert S. (2011). The Copernican Question: Prognostication, Skepticism, and Celestial Order. Los Angeles: University of California Press. ISBN 9780520254817.

• Copernicus’s model for Mars • Retrograde Motion • Copernicus’s explanation for retrograde motion • Geometry of Maximum Elongation • Copernican Model • Portraits of Nicolaus Copernicus About De Revolutionibus

16.10 External links

• The Copernican Universe from the De Revolutionibus

Primary sources

• De Revolutionibus, 1543 first edition – Full digital facsimile, Lehigh University

• Works by Nicolaus Copernicus at Project Gutenberg

• The text of the De Revolutionibus • Works by or about Nicolaus Copernicus at Internet Archive Prizes • Works by Nicolaus Copernicus at LibriVox (public domain audiobooks)

• Nicolaus Copernicus Prize, founded by the City of Kraków, awarded since 1995

• De Revolutionibus, autograph manuscript – Full German-Polish cooperation digital facsimile, Jagiellonian University • (Polish) Polish translations of letters written by Copernicus in Latin or German • Online Galleries, History of Science Collections, University of Oklahoma Libraries High resolution images of works by and/or portraits of Nicolaus Copernicus in .jpg and .tiff format. General

• (English) (German) (Polish) German-Polish “Copernicus Prize” awarded to German and Polish scientists (DFG website) • (English) (German) (Polish) Büro Kopernikus – An initiative of German Federal Cultural Foundation • (German) (Polish) German-Polish school project on Copernicus


Chapter 17

Ptolemy For other uses, see Ptolemy (name). Claudius Ptolemy (/ˈtɒləmi/; Greek: Κλαύδιος Πτολεμαῖος, Klaúdios Ptolemaîos, [kláwdios ptolɛmɛ́ ːos]; Latin: Claudius Ptolemaeus; c. AD 100 – c. 170)[2] was a Greco-Egyptian writer, known as a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology.[3][4] He lived in the city of Alexandria in the Roman province of Egypt, wrote in Koine Greek, and held Roman citizenship.[5] Beyond that, few reliable details of his life are known. His birthplace has been given as Ptolemais Hermiou in the Thebaid in an uncorroborated statement by the 14th-century astronomer Theodore Meliteniotes.[6] This is a very late attestation, however, and there is no other reason to suppose that he ever lived anywhere else than Alexandria,[6] where he died around AD 168.[7] Ptolemy wrote several scientific treatises, three of which were of importance to later Byzantine, Islamic and European science. The first is the astronomical treatise now known as the Almagest, although it was originally entitled the “Mathematical Treatise” (Μαθηματικὴ Σύνταξις, Mathēmatikē Syntaxis) and then known as the “Great Treatise” (Ἡ Μεγάλη Σύνταξις, Ē Megálē Syntaxis). The second is the Geography, which is a thorough discussion of the geographic knowledge of the GrecoRoman world. This manuscript was used by Christopher Columbus as the map for his westward-bound path to Asia, in which he discovered the hitherto unknown lands of the Americas. The third is the astrological treatise in which he attempted to adapt horoscopic astrology to the Aristotelian natural philosophy of his day. This is sometimes known as the Apotelesmatika (Ἀποτελεσματικά) but more commonly known as the Tetrabiblos from the Greek (Τετράβιβλος) meaning “Four Books” or by the Latin Quadripartitum.

17.1 Background

Engraving of a crowned Ptolemy being guided by the muse Astronomy, from Margarita Philosophica by Gregor Reisch, 1508. Although Abu Ma’shar believed Ptolemy to be one of the Ptolemies who ruled Egypt after the conquest of Alexander the title ‘King Ptolemy’ is generally viewed as a mark of respect for Ptolemy’s elevated standing in science.

citizenship. It would have suited custom if the first of Ptolemy’s family to become a citizen (whether he or an ancestor) took the nomen from a Roman called Claudius who was responsible for granting citizenship. If, as was common, this was the emperor, citizenship would have been granted between AD 41 and 68 (when Claudius, and then Nero, were Roman emperors). The astronomer would also have had a praenomen, which remains unknown.

Ptolemaeus (Πτολεμαῖος – Ptolemaios) is a Greek name. The name Claudius is a Roman nomen; the fact that It occurs once in Greek mythology, and is of Homeric Ptolemy bore it indicates he lived under the Roman rule form.[8] It was common among the Macedonian upper of Egypt with the privileges and political rights of Roman class at the time of Alexander the Great, and there were 178


17.2. ASTRONOMY

179

several of this name among Alexander’s army, one of whom made himself King of Egypt in 323 BC: Ptolemy I Soter. All the kings after him, until Egypt became a Roman province in 30 BC, were also Ptolemies. Perhaps for no other reason than the association of name, the 9th-century Persian astronomer Abu Ma’shar assumed Ptolemy to be a member of Egypt’s royal lineage, stating that the ten kings of Egypt who followed Alexander were wise “and included Ptolemy the Wise, who composed the book of the Almagest". Abu Ma’shar recorded a belief that a different member of this royal line “composed the book on astrology and attributed it to Ptolemy”. We can evidence historical confusion on this point from Abu Ma’shar’s subsequent remark “It is sometimes said that the very learned man who wrote the book of astrology also wrote the book of the Almagest. The correct answer is not known”.[9] There is little evidence on the subject of Ptolemy’s ancestry, apart from what can be drawn from the details of his name (see above); however, modern scholars refer to Abu Ma’shar’s account as erroneous,[10] and it is no longer doubted that the astronomer who wrote the Almagest also wrote the Tetrabiblos as its astrological counterpart.[11] Ptolemy wrote in Greek and can be shown to have utilized Babylonian astronomical data.[12][13] He was a Roman citizen, but most scholars conclude that Ptolemy was ethnically Greek,[14][15][16] although some suggest he was Ptolemy with an armillary sphere model, by Joos van Ghent and a Hellenized Egyptian.[15][17][18] He was often known in Pedro Berruguete, 1476, Louvre, Paris later Arabic sources as “the Upper Egyptian",[19] suggesting he may have had origins in southern Egypt.[20] Later Arabic astronomers, geographers and physicists referred authoritative text on astronomy, with its author becomto him by his name in Arabic: ‫ بَطْلُم ْيوس‬Batlamyus.[21] ing an almost mythical figure, called Ptolemy, King of Alexandria.[24] The Almagest was preserved, like most of Classical Greek science, in Arabic manuscripts (hence its 17.2 Astronomy familiar name). Because of its reputation, it was widely sought and was translated twice into Latin in the 12th Further information: Almagest century, once in Sicily and again in Spain.[25] Ptolemy’s The Almagest is the only surviving comprehensive an- model, like those of his predecessors, was geocentric and cient treatise on astronomy. Babylonian astronomers was almost universally accepted until the appearance of had developed arithmetical techniques for calculating simpler heliocentric models during the scientific revoluastronomical phenomena; Greek astronomers such as tion. Hipparchus had produced geometric models for calculating celestial motions. Ptolemy, however, claimed to His Planetary Hypotheses went beyond the mathematical realization have derived his geometrical models from selected astro- model of the Almagest to present a physical [26] in which he of the universe as a set of nested spheres, nomical observations by his predecessors spanning more used the epicycles of his planetary model to compute the than 800 years, though astronomers have for centuries dimensions of the universe. He estimated the Sun was at suspected that his models’ parameters were adopted inan average distance of 1,210 Earth radii, while the radius [22] Ptolemy presented his dependently of observations. of the fixed stars was 20,000 times the radius astronomical models in convenient tables, which could of the sphere [27] of the Earth. be used to compute the future or past position of the planets.[23] The Almagest also contains a star catalogue, Ptolemy presented a useful tool for astronomical calcuwhich is a version of a catalogue created by Hipparchus. lations in his Handy Tables, which tabulated all the data Its list of forty-eight constellations is ancestral to the needed to compute the positions of the Sun, Moon and modern system of constellations, but unlike the mod- planets, the rising and setting of the stars, and eclipses of ern system they did not cover the whole sky (only the the Sun and Moon. Ptolemy’s Handy Tables provided the sky Hipparchus could see). Across Europe, the Middle model for later astronomical tables or zījes. In the Phaseis East and North Africa in the Medieval period, it was the (Risings of the Fixed Stars), Ptolemy gave a parapegma, a


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star calendar or almanac, based on the hands and disap- lands near the left extreme of the blue sea of Ptolemy’s pearances of stars over the course of the solar year. map here reproduced.

17.3 The Geography Main article: Geography (Ptolemy) Ptolemy’s other main work is his Geography (also called

A 15th-century manuscript copy of the Ptolemy world map, reconstituted from Ptolemy’s Geography (circa 150), indicating the countries of "Serica" and "Sinae" (China) at the extreme east, beyond the island of “Taprobane” (Sri Lanka, oversized) and the "Aurea Chersonesus" (Malay Peninsula).

Geography by Ptolemy, Latin manuscript of the early 15th century Prima Europe tabula. A C15th copy of Ptolemy’s map of Britain

the Geographia), a compilation of geographical coordinates of the part of the world known to the Roman Empire during his time. He relied somewhat on the work of an earlier geographer, Marinos of Tyre, and on gazetteers of the Roman and ancient Persian Empire. He also acknowledged ancient astronomer Hipparchus for having provided the elevation of the north pole for a few cities.[28] The first part of the Geography is a discussion of the data and of the methods he used. As with the model of the solar system in the Almagest, Ptolemy put all this information into a grand scheme. Following Marinos, he assigned coordinates to all the places and geographic features he knew, in a grid that spanned the globe. Latitude was measured from the equator, as it is today, but Ptolemy preferred [29] to express it as climata, the length of the longest day rather than degrees of arc: the length of the midsummer day increases from 12h to 24h as one goes from the equator to the polar circle. In books 2 through 7, he used degrees and put the meridian of 0 longitude at the most western land he knew, the "Blessed Islands", often identified as the Canary Islands, as suggested by the location of the six dots labelled the “FORTUNATA” is-

Ptolemy also devised and provided instructions on how to create maps both of the whole inhabited world (oikoumenè) and of the Roman provinces. In the second part of the Geography, he provided the necessary topographic lists, and captions for the maps. His oikoumenè spanned 180 degrees of longitude from the Blessed Islands in the Atlantic Ocean to the middle of China, and about 80 degrees of latitude from Shetland to anti-Meroe (east coast of Africa); Ptolemy was well aware that he knew about only a quarter of the globe, and an erroneous extension of China southward suggests his sources did not reach all the way to the Pacific Ocean. The maps in surviving manuscripts of Ptolemy’s Geography, however, only date from about 1300, after the text was rediscovered by Maximus Planudes. It seems likely that the topographical tables in books 2–7 are cumulative texts – texts which were altered and added to as new knowledge became available in the centuries after Ptolemy.[30] This means that information contained in different parts of the Geography is likely to be of different dates.


17.4. ASTROLOGY

181 added that his original topographic list cannot be reconstructed: the long tables with numbers were transmitted to posterity through copies containing many scribal errors, and people have always been adding or improving the topographic data: this is a testimony to the persistent popularity of this influential work in the history of cartography.

17.4 Astrology Main article: Tetrabiblos Ptolemy has been referred to as “a pro-astrological auA printed map from the 15th century depicting Ptolemy’s description of the Ecumene, (1482, Johannes Schnitzer, engraver).

Maps based on scientific principles had been made since the time of Eratosthenes, in the 3rd century BC, but Ptolemy improved map projections. It is known from a speech by Eumenius that a world map, an orbis pictus, doubtless based on the Geography, was on display in a school in Augustodunum, Gaul in the third century.[31] In the 15th century, Ptolemy’s Geography began to be printed with engraved maps; the earliest printed edition with engraved maps was produced in Bologna in 1477, followed quickly by a Roman edition in 1478 (Campbell, 1987). An edition printed at Ulm in 1482, including woodcut maps, was the first one printed north of the Alps. The maps look distorted when compared to modern maps, because Ptolemy’s data were inaccurate. One reason is that Ptolemy estimated the size of the Earth as too small: while Eratosthenes found 700 stadia for a great circle degree on the globe, Ptolemy uses 500 stadia in the Geography. It is highly probable that these were the same stadion, since Ptolemy switched from the former scale to the latter between the Syntaxis and the Geography, and severely readjusted longitude degrees accordingly. See also Ancient Greek units of measurement and History of geodesy. Because Ptolemy derived many of his key latitudes from crude longest day values, his latitudes are erroneous on average by roughly a degree (2 degrees for Byzantium, 4 degrees for Carthage), though capable ancient astronomers knew their latitudes to more like a minute. (Ptolemy’s own latitude was in error by 14'.) He agreed (Geography 1.4) that longitude was best determined by simultaneous observation of lunar eclipses, yet he was so out of touch with the scientists of his day that he knew of no such data more recent than 500 years before (Arbela eclipse). When switching from 700 stadia per degree to 500, he (or Marinos) expanded longitude differences between cities accordingly (a point first realized by P.Gosselin in 1790), resulting in serious over-stretching of the Earth’s east-west scale in degrees, though not distance. Achieving highly precise longitude remained a problem in geography until the application of Galileo's Jovian moon method in the 18th century. It must be

The mathematician Claudius Ptolemy 'the Alexandrian' as imagined by a 16th-century artist

thority of the highest magnitude”.[32] His astrological treatise, a work in four parts, is known by the Greek term Tetrabiblos, or the Latin equivalent Quadripartitum: ‘Four Books’. Ptolemy’s own title is unknown, but may have been the term found in some Greek manuscripts: Apotelesmatika, roughly meaning 'Astrological Outcomes,' 'Effects’ or ‘Prognostics’.[33][34] As a source of reference, the Tetrabiblos is said to have “enjoyed almost the authority of a Bible among the astrological writers of a thousand years or more”.[35] It was first translated from Arabic into Latin by Plato of Tivoli (Tiburtinus) in 1138, while he was in Spain.[36] The Tetrabiblos is an extensive and continually reprinted treatise on the ancient principles of horoscopic astrology. That it did not quite attain the unrivaled status of the Almagest was, perhaps, because it did not cover some popular areas of the subject, particularly electional astrology (interpreting astrological charts for a particular moment to determine the outcome of a course of action to be initiated at that time), and medical astrology, which were later adoptions.


182 The great popularity that the Tetrabiblos did possess might be attributed to its nature as an exposition of the art of astrology, and as a compendium of astrological lore, rather than as a manual. It speaks in general terms, avoiding illustrations and details of practice. Ptolemy was concerned to defend astrology by defining its limits, compiling astronomical data that he believed was reliable and dismissing practices (such as considering the numerological significance of names) that he believed to be without sound basis. Much of the content of the Tetrabiblos was collected from earlier sources; Ptolemy’s achievement was to order his material in a systematic way, showing how the subject could, in his view, be rationalized. It is, indeed, presented as the second part of the study of astronomy of which the Almagest was the first, concerned with the influences of the celestial bodies in the sublunar sphere. Thus explanations of a sort are provided for the astrological effects of the planets, based upon their combined effects of heating, cooling, moistening, and drying.

CHAPTER 17. PTOLEMY it should just generally involve tetrachords and octaves. He presented his own divisions of the tetrachord and the octave, which he derived with the help of a monochord. His Harmonics never had the influence of his Almagest or Planetary Hypotheses, but a part of it (Book III) did encourage Kepler in his own musings on the harmony of the world (Kepler, Harmonice Mundi, Appendix to Book V).[37] Ptolemy’s astronomical interests also appeared in a discussion of the "music of the spheres". See: Ptolemy’s intense diatonic scale.

17.6 Optics His Optics is a work that survives only in a poor Arabic translation and in about twenty manuscripts of a Latin version of the Arabic, which was translated by Eugene of Palermo (c. 1154). In it Ptolemy writes about properties of light, including reflection, refraction, and colour. The work is a significant part of the early history of optics[38] and influenced the more famous 11th-century Book of Optics by Alhazen (Ibn al-Haytham). It contains the earliest surviving table of refraction from air to water, for which the values (with the exception of the 60° angle of incidence), although historically praised as experimentally derived, appear to have been obtained from an arithmetic progression.[39]

Ptolemy’s astrological outlook was quite practical: he thought that astrology was like medicine, that is conjectural, because of the many variable factors to be taken into account: the race, country, and upbringing of a person affects an individual’s personality as much as, if not more than, the positions of the Sun, Moon, and planets at the precise moment of their birth, so Ptolemy saw astrology as something to be used in life but in no way relied The work is also important for the early history of percepon entirely. tion. Ptolemy combined the mathematical, philosophical A collection of one hundred aphorisms about astrology and physiological traditions. He held an extramissioncalled the Centiloquium, ascribed to Ptolemy, was widely intromission theory of vision: the rays (or flux) from the reproduced and commented on by Arabic, Latin and eye formed a cone, the vertex being within the eye, and Hebrew scholars, and often bound together in medieval the base defining the visual field. The rays were sensitive, manuscripts after the Tetrabiblos as a kind of summation. and conveyed information back to the observer’s intellect It is now believed to be a much later pseudepigraphical about the distance and orientation of surfaces. Size and composition. The identity and date of the actual author shape were determined by the visual angle subtended at of the work, referred to now as Pseudo-Ptolemy, remains the eye combined with perceived distance and orientation. This was one of the early statements of size-distance the subject of conjecture. invariance as a cause of perceptual size and shape constancy, a view supported by the Stoics.[40] Ptolemy offered explanations for many phenomena concerning illumination and colour, size, shape, movement and binocu17.5 Music lar vision. He also divided illusions into those caused by physical or optical factors and those caused by judgemenPtolemy also wrote an influential work, Harmonics, on tal factors. He offered an obscure explanation of the sun music theory and the mathematics of music. After critor moon illusion (the enlarged apparent size on the horiicizing the approaches of his predecessors, Ptolemy arzon) based on the difficulty of looking upwards.[41][42] gued for basing musical intervals on mathematical ratios (in contrast to the followers of Aristoxenus and in agreement with the followers of Pythagoras), backed up by empirical observation (in contrast to the overly the- 17.7 Named after Ptolemy oretical approach of the Pythagoreans). Ptolemy wrote about how musical notes could be translated into math- There are several characters or items named after ematical equations and vice versa in Harmonics. This Ptolemy, including: is called Pythagorean tuning because it was first discovered by Pythagoras. However, Pythagoras believed that • The crater Ptolemaeus on the Moon; the mathematics of music should be based on the spe• The crater Ptolemaeus[43] on Mars; cific ratio of 3:2, whereas Ptolemy merely believed that


17.9. FOOTNOTES • The asteroid 4001 Ptolemaeus; • The Ptolemy Stone used in the mathematics courses at both St. John’s College campuses. • Ptolemy’s theorem on distances in a cyclic quadrilateral, and its generalization, Ptolemy’s inequality, to non-cyclic quadrilaterals • Ptolemaic graphs, the graphs whose distances obey Ptolemy’s inequality

17.8 See also • Pei Xiu • Messier 7 – Ptolemy Cluster, star cluster described by Ptolemaeus • Ptolemy’s Canon – a dated list of kings used by ancient astronomers. • Ptolemy’s table of chords • Zhang Heng

183

[13] Alexander Jones, “The Adaptation of Babylonian Methods in Greek Numerical Astronomy,” in The Scientific Enterprise in Antiquity and the Middle Ages, p. 99. [14] Britannica.com Encyclopaedia “Claudius Ptolemaeus”

Britannica

2007,

[15] Victor J. Katz (1998). A History of Mathematics: An Introduction, p. 184. Addison Wesley, ISBN 0-321-016181. [16] “Ptolemy.” Britannica Concise Encyclopedia. Encyclopædia Britannica, Inc., 2006. Answers.com 20 Jul. 2008. [17] George Sarton (1936). “The Unity and Diversity of the Mediterranean World”, Osiris 2, p. 406–463 [429]. [18] John Horace Parry (1981). The Age of Reconnaissance, p. 10. University of California Press. ISBN 0-520-04235-2. [19] J. F. Weidler (1741). Historia astronomiae, p. 177. Wittenberg: Gottlieb. (cf. Martin Bernal (1992). “Animadversions on the Origins of Western Science”, Isis 83 (4), p. 596–607 [606].) [20] Martin Bernal (1992). “Animadversions on the Origins of Western Science”, Isis 83 (4), p. 596–607 [602, 606].

[2] “Ptolemy | Accomplishments, Biography, & Facts”. Encyclopedia Britannica. Retrieved 2016-03-06.

[21] Shahid Rahman; Tony Street; Hassan Tahiri, eds. (2008). “The Birth of Scientific Controversies, The Dynamics of the Arabic Tradition and Its Impact on the Development of Science: Ibn al-Haytham’s Challenge of Ptolemy’s Almagest”. The Unity of Science in the Arabic Tradition. 11. Springer Netherlandsdoi=10.1007/978-1-40208405-8. pp. 183–225 [183]. doi:10.1007/978-1-40208405-8. ISBN 978-1-4020-8404-1.

[3] Select Epigrams from the Greek Anthology By John William Mackail Page 246 ISBN 1406922943, 2007

[22] “Dennis Rawlins”. The International Journal of Scientific History. Retrieved 2009-10-07.

17.9 Footnotes [1] http://www.britannica.com/biography/Ptolemy

[4] Mortal am I, the creature of a day.. [5] See 'Background' section on his status as a Roman citizen [6] G. J. Toomer, “Ptolemy (or Claudius Ptolemaeus). " Complete Dictionary of Scientific Biography. 2008. Retrieved from Encyclopedia.com. 21 Jan, 2013. [7] Jean Claude Pecker (2001), Understanding the Heavens: Thirty Centuries of Astronomical Ideas from Ancient Thinking to Modern Cosmology, p. 311, Springer, ISBN 3-540-63198-4. [8] Πτολεμαῖος, Georg Autenrieth, A Homeric Dictionary, on Perseus [9] Abu Ma’shar, De magnis coniunctionibus, ed.-transl. K. Yamamoto, Ch. Burnett, Leiden, 2000, 2 vols. (Arabic & Latin text); 4.1.4. [10] Jones (2010) ‘Ptolemy’s Doctrine of the Terms and Its Reception’ by Stephan Heilen, p. 68.

[23] Bernard R. Goldstein, “Saving the Phenomena: The Background to Ptolemy’s Planetary Theory”, Journal for the History of Astronomy, 28 (1997): 1–12 [24] S. C. McCluskey, Astronomies and Cultures in Early Medieval Europe, Cambridge: Cambridge Univ. Pr. 1998, pp. 20–21. [25] Charles Homer Haskins, Studies in the History of Mediaeval Science, New York: Frederick Ungar Publishing, 1967, reprint of the Cambridge, Mass., 1927 edition [26] Dennis Duke, Ptolemy’s Cosmology [27] Bernard R. Goldstein, ed., The Arabic Version of Ptolemy’s Planetary Hypotheses, Transactions of the American Philosophical Society 57, no. 4 (1967), pp. 9– 12. [28] Shcheglov D.A. (2002–2007): “Hipparchus’ Table of Climata and Ptolemy’s Geography”, Orbis Terrarum 9 (2003–2007), 177–180.

[11] Robbins, Ptolemy Tetrabiblos ‘Introduction’; p. x. [12] Asger Aaboe, Episodes from the Early History of Astronomy, New York: Springer, 2001, pp. 62–65.

[29] Book 8 [30] Bagrow 1945.


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[31] Richard J.A. Talbert, “Urbs Roma to Orbis Romanus”, in Talbert, Ancient Perspectives: Maps and Their Places in Mesopotamia, Egypt, Greece and Rome (Chicago) 2012, pp 170–72. [32] Jones (2010) ‘The Use and Abuse of Ptolemy’s Tetrabiblos in Renaissance and Early Modern Europe’ by H. Darrel Rutkin, p. 135. [33] Robbins, Ptolemy Tetrabiblos, 'Introduction' p. x. [34] Jones (2010) p. xii. [35] Robbins, Ptolemy Tetrabiblos, 'Introduction' p. xii. [36] FA Robbins, 1940; Thorndike 1923 [37] Hetherington, Norriss S. Encyclopedia of Cosmology (Routledge Revivals): Historical, Philosophical, and Scientific Foundations of Modern Cosmology Routledge, 8 apr. 2014 ISBN 978-1317677666 p 527 [38] Smith, A. Mark (1996). Ptolemy’s Theory of Visual Perception– An English translation of the Optics. The American Philosophical Society. ISBN 0-87169-862-5. Retrieved 27 June 2009. [39] Carl Benjamin Boyer, The Rainbow: From Myth to Mathematics (1959) [40] H. W. Ross and C. Plug, “The History of Size Constancy and Size Illusions”, in V. Walsh & J. Kulikowski (eds.) Perceptual Constancy: Why Things Look as They Do. Cambridge: Cambridge University Press, 1998, pp. 499–528. [41] H. E. Ross and G. M. Ross, “Did Ptolemy Understand the Moon Illusion?", Perception 5 (1976): 377–395. [42] A. I. Sabra, “Psychology Versus Mathematics: Ptolemy and Alhazen on the Moon Illusion”, in E. Grant & J. E. Murdoch (eds.) Mathematics and Its Application to Science and Natural Philosophy in the Middle Ages. Cambridge: Cambridge University Press, 1987, pp. 217–247. [43] Mars Labs. Google Maps.

17.10 References 17.10.1

Texts and translations

• Bagrow, L. (January 1, 1945). “The Origin of Ptolemy’s Geographia”. Geografiska Annaler. Geografiska Annaler, Vol. 27. 27: 318–387. doi:10.2307/520071. ISSN 1651-3215. JSTOR 520071. • Berggren, J. Lennart, and Alexander Jones. 2000. Ptolemy’s Geography: An Annotated Translation of the Theoretical Chapters. Princeton and Oxford: Princeton University Press. ISBN 0-691-01042-0. • Campbell, T. (1987). The Earliest Printed Maps. British Museum Press.

• Hübner, Wolfgang, ed. 1998. Claudius Ptolemaeus, Opera quae exstant omnia Vol III/Fasc 1: ΑΠΟΤΕΛΕΣΜΑΤΙΚΑ (= Tetrabiblos). De Gruyter. ISBN 978-3-598-71746-8 (Bibliotheca scriptorum Graecorum et Romanorum Teubneriana). (The most recent edition of the Greek text of Ptolemy’s astrological work, based on earlier editions by F. Boll and E. Boer.) • Lejeune, A. (1989) L'Optique de Claude Ptolémée dans la version latine d'après l'arabe de l'émir Eugène de Sicile. [Latin text with French translation]. Collection de travaux de l'Académie International d'Histoire des Sciences, No. 31. Leiden: E.J.Brill. • Neugebauer, Otto (1975). A History of Ancient Mathematical Astronomy. I-III. Berlin and New York: Sprnger Verlag. • Nobbe, C. F. A., ed. 1843. Claudii Ptolemaei Geographia. 3 vols. Leipzig: Carolus Tauchnitus. (The most recent edition of the complete Greek text) • Ptolemy. 1930. Die Harmonielehre des Klaudios Ptolemaios, edited by Ingemar Düring. Göteborgs högskolas årsskrift 36, 1930:1. Göteborg: Elanders boktr. aktiebolag. Reprint, New York: Garland Publishing, 1980. • Ptolemy. 2000. Harmonics, translated and commentary by Jon Solomon. Mnemosyne, Bibliotheca Classica Batava, Supplementum, 0169-8958, 203. Leiden and Boston: Brill Publishers. ISBN 90-0411591-9 • Robbins, Frank E. (ed.) 1940. Ptolemy Tetrabiblos. Cambridge, Massachusetts: Harvard University Press (Loeb Classical Library). ISBN 0-67499479-5. • Smith, A.M. (1996) Ptolemy’s theory of visual perception: An English translation of the Optics with introduction and commentary. Transactions of the American Philosophical Society, Vol. 86, Part 2. Philadelphia: The American Philosophical Society. • Stevenson, Edward Luther (trans. and ed.). 1932. Claudius Ptolemy: The Geography. New York: New York Public Library. Reprint, New York: Dover, 1991. (This is the only complete English translation of Ptolemy’s most famous work. Unfortunately, it is marred by numerous mistakes and the placenames are given in Latinised forms, rather than in the original Greek). • Stückelberger, Alfred, and Gerd Graßhoff (eds). 2006. Ptolemaios, Handbuch der Geographie, Griechisch-Deutsch. 2 vols. Basel: Schwabe Verlag. ISBN 978-3-7965-2148-5. (Massive 1018 pp. scholarly edition by a team of a dozen scholars that takes account of all known manuscripts, with facing Greek and German text, footnotes on manuscript


17.11. EXTERNAL LINKS

185

variations, color maps, and a CD with the geograph- 17.11.2 Secondary material ical data) • Arnett, Bill (2008). “Ptolemy, the Man”. obs.nineplanets.org. Retrieved 2008-11-24. • Taub, Liba Chia (1993). Ptolemy’s Universe: The Natural Philosophical and Ethical Foundations of • Danzer, Gerald (1988). “Cartographic Images of Ptolemy’s Astronomy. Chicago: Open Court Press. the World on the Eve of the Discoveries”. The NewISBN 0-8126-9229-2. berry Library. Retrieved 26 November 2008. • Ptolemy’s Almagest, Translated and annotated by G. J. Toomer. Princeton University Press, 1998

17.11 External links • Online Galleries, History of Science Collections, University of Oklahoma Libraries High resolution images of works by Ptolemy in .jpg and .tiff format.

17.11.1

Primary sources

• Ptolemy’s Tetrabiblos at LacusCurtius (Transcription of the Loeb Classical Library's English translation) • Entire Tetrabiblos of J.M. Ashmand’s 1822 translation. • Ptolemy’s Geography at LacusCurtius (English translation, incomplete) • Extracts of Ptolemy on the country of the Seres (China) (English translation) • Geography (the Balkan Provinces, with old maps) at Sorin Olteanu’s LTDM Project (soltdm.com) • Almagest books 1–13 The complete text of Heiberg’s edition (PDF) Greek. • Almagest books 1–6 (Greek) with preface (Latin) at archive.org • Geography, digitized codex made in Italy between 1460 and 1477, translated to Latin by Jacobus Angelus at Somni. Also known as codex valentinus, it is the oldest manuscript of the codices with maps of Ptolemy with the donis projections. • Hieronymi Cardani ... In Cl. Ptolemaei ... IIII De astrorum judiciis From the Rare Book and Special Collection Division at the Library of Congress • Almagestū Cl. Ptolemei From the Rare Book and Special Collection Division at the Library of Congress

• Haselein, Frank (2007). "Κλαυδιου Πτολεμιου: Γεωγραφικῆς Ύφηγήσεως (Geographie)" (in German and English). Frank Haselein. Retrieved 200811-24. • Houlding, Deborah (2003). “The Life & Work of Ptolemy”. Skyscript.co. Retrieved 2008-11-24. • Jones, Alexander (ed.) 2010. Ptolemy in Perspective: Use and Criticism of his Work from Antiquity to the Nineteenth Century. New York: Series: Archimedes, Vol. 23., ISBN 978-90-481-2787-0 • Toomer, Gerald J. (1970). “Ptolemy (Claudius Ptolemæus)" (PDF). In Gillispie, Charles. Dictionary of Scientific Biography. 11. New York: Scribner & American Council of Learned Societies. pp. 186–206. ISBN 978-0-684-10114-9. • Sprague, Ben (2001–2007). “Claudius Ptolemaeus (Ptolemy): Representation, Understanding, and Mathematical Labeling of the Spherical Earth”. Center for Spatially Integrated Social Science. Retrieved 26 November 2008. Animated illustrations • Java simulation of the Ptolemaic System – at Paul Stoddard’s Animated Virtual Planetarium, Northern Illinois University • Animation of Ptolemy’s Two Solar Hypotheses on YouTube • Epicycle and Deferent Demo – at Rosemary Kennett’s website at the University of Syracuse • Flash animation of Ptolemy’s universe. (best in Internet Explorer)


Chapter 18

Galileo Galilei “Galileo” redirects here. For other uses of “Galileo”, 18.1 Early life and family see Galileo (disambiguation). For other uses of “Galileo Galilei”, see Galileo Galilei (disambiguation). Galileo was born in Pisa (then part of the Duchy of Florence), Italy, in 1564,[17] the first of six children of Galileo Galilei (Italian pronunciation: [ɡaliˈlɛːo ɡal- Vincenzo Galilei, a famous lutenist, composer, and music iˈlɛi]; 15 February 1564[3] – 8 January 1642) was an theorist, and Giulia Ammannati. Galileo became an acItalian astronomer, physicist, engineer, philosopher, and complished lutenist himself and would have learned early mathematician who played a major role in the scientific from his father a scepticism for established authority,[18] the value of well-measured or quantified experimentarevolution of the seventeenth century. tion, an appreciation for a periodic or musical measure He has been called the “father of observational astronof time or rhythm, as well as the results expected from a omy",[4] the “father of modern physics",[5][6] the “father combination of mathematics and experiment. of scientific method",[7] and the “father of science".[8][9] Three of Galileo’s five siblings survived infancy. The His contributions to observational astronomy include the youngest, Michelangelo (or Michelagnolo), also became telescopic confirmation of the phases of Venus, the disa noted lutenist and composer although he contributed covery of the four largest satellites of Jupiter (named to financial burdens during Galileo’s young adulthood. the Galilean moons in his honour), and the observation Michelangelo was unable to contribute his fair share of and analysis of sunspots. Galileo also worked in applied their father’s promised dowries to their brothers-in-law, science and technology, inventing an improved military who would later attempt to seek legal remedies for paycompass and other instruments. ments due. Michelangelo would also occasionally have to Galileo’s championing of heliocentrism and borrow funds from Galileo to support his musical endeavCopernicanism was controversial during his life- ours and excursions. These financial burdens may have time, when most subscribed to either geocentrism or contributed to Galileo’s early fire to develop inventions the Tychonic system.[10] He met with opposition from that would bring him additional income. astronomers, who doubted heliocentrism because of the When Galileo Galilei was eight, his family moved to absence of an observed stellar parallax.[10] The matter Florence, but he was left with Jacopo Borghini for was investigated by the Roman Inquisition in 1615, two years.[17] He then was educated in the Camalwhich concluded that heliocentrism was “foolish and dolese Monastery at Vallombrosa, 35 km southeast of absurd in philosophy, and formally heretical since it Florence.[17] explicitly contradicts in many places the sense of Holy Scripture.”[10][11][12] Galileo later defended his views in Dialogue Concerning the Two Chief World Systems, 18.1.1 Name which appeared to attack Pope Urban VIII and thus alienated him and the Jesuits, who had both supported The surname Galilei derives from the given name of an Galileo up until this point.[10] He was tried by the ancestor, Galileo Bonaiuti, a physician, university teacher Inquisition, found “vehemently suspect of heresy”, and and politician who lived in Florence from 1370 to 1450; forced to recant. He spent the rest of his life under house his descendents had changed their family name from [13][14] While under house arrest, he wrote one of arrest. Bonaiuti (or Buonaiuti) to Galilei in his honor in the late his best-known works, Two New Sciences, in which he 14th century.[19] Galileo Bonaiuti was buried in the same summarized work he had done some forty years earlier church, the Basilica of Santa Croce in Florence, where on the two sciences now called kinematics and strength about 200 years later his more famous descendant Galileo [15][16] of materials. Galilei was also buried. It was common for mid-sixteenth century Tuscan families to name the eldest son after the parents’ surname[20] 186


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there for the rest of their lives.[28] Virginia took the name Maria Celeste upon entering the convent. She died on 2 April 1634, and is buried with Galileo at the Basilica of Santa Croce, Florence. Livia took the name Sister Arcangela and was ill for most of her life. Vincenzo was the legal heir of Galileo and married The biblical roots of Galileo’s name and surname were to later legitimised as [29] Sestilia Bocchineri. [23] In 1614, durbecome the subject of a famous pun. ing the Galileo affair, one of Galileo’s opponents, the Dominican priest Tommaso Caccini, delivered against Galileo a controversial and influential sermon. In it he 18.2 Career as a scientist made a point of quoting Acts 1:11, “Ye Men of Galilee, why stand you gazing up in heaven?".[24] Although Galileo seriously considered the priesthood as a young man, at his father’s urging he instead enrolled at the University of Pisa for a medical degree.[30] In 1581, 18.1.2 Children when he was studying medicine, he noticed a swinging chandelier, which air currents shifted about to swing in larger and smaller arcs. To him it seemed, by comparison with his heartbeat, that the chandelier took the same amount of time to swing back and forth, no matter how far it was swinging. When he returned home, he set up two pendulums of equal length and swung one with a large sweep and the other with a small sweep and found that they kept time together. It was not until the work of Christiaan Huygens, almost one hundred years later, that the tautochrone nature of a swinging pendulum was used to create an accurate timepiece.[31] Up to this point, Galileo had deliberately been kept away from mathematics, since a physician earned a higher income than a mathematician. However, after accidentally attending a lecture on geometry, he talked his reluctant father into letting him study mathematics and natural philosophy instead of medicine.[31] He created a thermoscope, a forerunner of the thermometer, and in 1586 published a small book on the design of a hydrostatic balance he had invented (which first brought him to the attention of the scholarly world). Galileo also studied disegno, a term encompassing fine art, and in 1588 obtained the position of instructor in the Accademia delle Arti del Disegno in Florence, teaching perspective and chiaroscuro. Being inspired by the artistic tradition of the city and the works of the Renaissance artists, Galileo acquired an aesthetic Galileo’s beloved elder daughter, Virginia (Sister Maria Celeste), mentality. While a young teacher at the Accademia, he was particularly devoted to her father. She is buried with him in began a lifelong friendship with the Florentine painter his tomb in the Basilica of Santa Croce, Florence. Cigoli, who included Galileo’s lunar observations in one of his paintings.[32][33] [25] Despite being a genuinely pious Roman Catholic, In 1589, he was appointed to the chair of mathematics in Galileo fathered three children out of wedlock with Pisa. In 1591, his father died, and he was entrusted with Marina Gamba. They had two daughters, Virginia (born the care of his younger brother Michelagnolo. In 1592, in 1600) and Livia (born in 1601), and a son, Vincenzo he moved to the University of Padua where he taught ge(born in 1606).[26] ometry, mechanics, and astronomy until 1610.[34] Durhence, Galileo Galilei was not necessarily named after his ancestor Galileo Bonaiuti. The Italian male given name “Galileo” (and thence the surname “Galilei”) derives from the Latin “Galilaeus”, meaning “of Galilee", a biblically significant region in Northern Israel.[21][22]

Because of their illegitimate birth, their father considered the girls unmarriageable, if not posing problems of prohibitively expensive support or dowries, which would have been similar to Galileo’s previous extensive financial problems with two of his sisters.[27] Their only worthy alternative was the religious life. Both girls were accepted by the convent of San Matteo in Arcetri and remained

ing this period, Galileo made significant discoveries in both pure fundamental science (for example, kinematics of motion and astronomy) as well as practical applied science (for example, strength of materials and pioneering the telescope). His multiple interests included the study of astrology, which at the time was a discipline tied to the studies of mathematics and astronomy.[35]


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Galileo, Kepler and theories of tides and other factors.[39] Against the assertion that Galileo was deceptive in making these arguments, Albert Einstein expressed the opinion that Galileo developed his “fascinating arguments” and accepted them uncritically out of a desire for physical proof of the motion of the Earth.[40] Galileo dismissed the idea, held by his contemporary Johannes Kepler, that the moon caused the tides.[41] (Galileo also took no interest in Kepler’s elliptical orbits of the planets.)[42][43]

18.2.2 Controversy over comets and The Assayer Main article: The Assayer In 1619, Galileo became embroiled in a controversy with Father Orazio Grassi, professor of mathematics at the Jesuit Collegio Romano. It began as a dispute over the nature of comets, but by the time Galileo had published The Assayer (Il Saggiatore) in 1623, his last salvo in the dispute, it had become a much wider controversy over the very nature of science itself. The title page of the book describes Galileo as philosopher and “Matematico Primario” of the Grand Duke of Tuscany.

Galileo Galilei. Portrait by Leoni

Because The Assayer contains such a wealth of Galileo’s ideas on how science should be practised, it has been referred to as his scientific manifesto.[44] Early in 1619, Father Grassi had anonymously published a pamphlet, An Astronomical Disputation on the Three Comets of the Year 1618,[45] which discussed the nature of a comet that had appeared late in November of the previous year. Grassi concluded that the comet was a fiery body which had moved along a segment of a great circle at a constant distance from the earth,[46] and since it moved in the sky more slowly than the moon, it must be farther away than the moon.

Cardinal Bellarmine had written in 1615 that the Copernican system could not be defended without “a true physical demonstration that the sun does not circle the earth but the earth circles the sun”.[36] Galileo considered his theory of the tides to provide the required physical proof of the motion of the earth. This theory was so important to him that he originally intended to entitle his Dialogue on the Two Chief World Systems the Dialogue Grassi’s arguments and conclusions were criticised in a on the Ebb and Flow of the Sea.[37] The reference to tides subsequent article, Discourse on the Comets,[47] published was removed from the title by order of the Inquisition. under the name of one of Galileo’s disciples, a FloFor Galileo, the tides were caused by the sloshing back rentine lawyer named Mario Guiducci, although it had and forth of water in the seas as a point on the Earth’s been largely written by Galileo himself.[48] Galileo and surface sped up and slowed down because of the Earth’s Guiducci offered no definitive theory of their own on the rotation on its axis and revolution around the Sun. He cir- nature of comets[49] although they did present some tentaculated his first account of the tides in 1616, addressed to tive conjectures that are now known to be mistaken. In its Cardinal Orsini.[38] His theory gave the first insight into opening passage, Galileo and Guiducci’s Discourse grathe importance of the shapes of ocean basins in the size tuitously insulted the Jesuit Christopher Scheiner,[50] and and timing of tides; he correctly accounted, for instance, various uncomplimentary remarks about the professors for the negligible tides halfway along the Adriatic Sea of the Collegio Romano were scattered throughout the compared to those at the ends. As a general account of work.[51] The Jesuits were offended,[52] and Grassi soon the cause of tides, however, his theory was a failure. replied with a polemical tract of his own, The Astronom[53] under the pseudonym If this theory were correct, there would be only one ical and Philosophical Balance, [54] Lothario Sarsio Sigensano, purporting to be one of his high tide per day. Galileo and his contemporaries were own pupils. aware of this inadequacy because there are two daily high tides at Venice instead of one, about twelve hours apart. The Assayer was Galileo’s devastating reply to the AstroGalileo dismissed this anomaly as the result of several nomical Balance.[55] It has been widely recognized as a secondary causes including the shape of the sea, its depth, masterpiece of polemical literature,[56] in which “Sarsi’s”


18.2. CAREER AS A SCIENTIST arguments are subjected to withering scorn.[57] It was greeted with wide acclaim, and particularly pleased the new pope, Urban VIII, to whom it had been dedicated.[58] In Rome, in the previous decade, Barberini, the future Urban VIII, had come down on the side of Galileo and the Lincean Academy.[59]

189 than Saturn, and the Sun and stars were comparable in size.[66] Religious opposition to heliocentrism arose from Biblical references such as Psalm 93:1, 96:10, and 1 Chronicles 16:30 which include text stating that “the world is firmly established, it cannot be moved.” In the same manner, Psalm 104:5 says, “the Lord set the earth on its foundations; it can never be moved.” Further, Ecclesiastes 1:5 states that “And the sun rises and sets and returns to its place.”[67]

Galileo’s dispute with Grassi permanently alienated many of the Jesuits who had previously been sympathetic to his ideas,[60] and Galileo and his friends were convinced that these Jesuits were responsible for bringing about his later condemnation.[61] The evidence for this is at best equiv- Galileo defended heliocentrism based on his astronomocal, however.[62] ical observations of 1609 (Sidereus Nuncius 1610). In December 1613 the Grand Duchess Christina of Florence confronted one of Galileo’s friends and followers, 18.2.3 Controversy over heliocentrism Benedetto Castelli, with biblical objections to the motion of the earth. According to Maurice Finocchiaro this was Main article: Galileo affair done in a friendly and gracious manner, out of curiosIn the Christian world prior to Galileo’s conflict with ity. Prompted by this incident, Galileo wrote a letter to Castelli in which he argued that heliocentrism was actually not contrary to biblical texts, and that the bible was an authority on faith and morals, not on science. This letter was not published, but circulated widely.[68]

Cristiano Banti's 1857 painting Galileo facing the Roman Inquisition

the Church, the majority of educated people subscribed either to the Aristotelian geocentric view that the earth was the center of the universe and that all heavenly bodies revolved around the Earth,[63] or the Tychonic system that blended geocentrism with heliocentrism.[64] Nevertheless, following the death of Copernicus and before Galileo, heliocentrism was relatively uncontroversial;[64] Copernicus’s work was used by Pope Gregory XIII to reform the calendar in 1582.[65] Opposition to heliocentrism and Galileo’s writings combined religious and scientific objections and were fueled by political events. Scientific opposition came from Tycho Brahe and others, and arose from the fact that, if heliocentrism were true, an annual stellar parallax should be observed, though none was. Copernicus had correctly postulated that parallax was negligible because the stars were so distant. However, Brahe had countered that, since stars appeared to have measurable size, if the stars were that distant, they would be gigantic, and in fact far larger than the Sun or any other celestial body. In Brahe’s system, by contrast, the stars were a little more distant

By 1615 Galileo’s writings on heliocentrism had been submitted to the Roman Inquisition by Father Niccolo Lorini, who claimed that Galileo and his followers were attempting to reinterpret the Bible, which was seen as a violation of the Council of Trent and looked dangerously like Protestantism.[69] Lorini specifically cited Galileo’s letter to Castelli.[70] Galileo went to Rome to defend himself and his Copernican and biblical ideas. At the start of 1616, Monsignor Francesco Ingoli initiated a debate with Galileo, sending him an essay disputing the Copernican system. Galileo later stated that he believed this essay to have been instrumental in the action against Copernicanism that followed.[71] According to Maurice Finocchiaro, Ingoli had probably been commissioned by the Inquisition to write an expert opinion on the controversy, and the essay provided the “chief direct basis” for the Inquisition’s actions.[72] The essay focused on eighteen physical and mathematical arguments against heliocentrism. It borrowed primarily from the arguments of Tycho Brahe, and it notedly mentioned Brahe’s argument that heliocentrism required the stars to be much larger than the Sun. Ingoli wrote that the great distance to the stars in the heliocentric theory “clearly proves ... the fixed stars to be of such size, as they may surpass or equal the size of the orbit circle of the Earth itself.”[73] The essay also included four theological arguments, but Ingoli suggested Galileo focus on the physical and mathematical arguments, and he did not mention Galileo’s biblical ideas.[74] In February 1616, an Inquisitorial commission declared heliocentrism to be “foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places the sense of Holy Scripture.” The Inquisition found that the idea of the Earth’s movement “receives the same judgement in philosophy and... in regard to theological truth it is at least erroneous in faith”.[75] (The original document from


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the Inquisitorial commission was made widely available defend his writings[82] in September 1632. He finally arin 2014.[76] ) rived in February 1633 and was brought before inquisiPope Paul V instructed Cardinal Bellarmine to deliver tor Vincenzo Maculani to be charged. Throughout his this finding to Galileo, and to order him to abandon the trial Galileo steadfastly maintained that since 1616 he had opinion that heliocentrism was physically true. On 26 faithfully kept his promise not to hold any of the conFebruary, Galileo was called to Bellarmine’s residence demned opinions, and initially he denied even defending them. However, he was eventually persuaded to admit and ordered: that, contrary to his true intention, a reader of his Dialogue could well have obtained the impression that it was ... to abandon completely... the opinion intended to be a defence of Copernicanism. In view of that the sun stands still at the center of the Galileo’s rather implausible denial that he had ever held world and the earth moves, and henceforth not Copernican ideas after 1616 or ever intended to defend to hold, teach, or defend it in any way whatever, them in the Dialogue, his final interrogation, in July 1633, either orally or in writing.[77] concluded with his being threatened with torture if he did not tell the truth, but he maintained his denial despite the threat.[83] The decree of the Congregation of the Index banned Copernicus’s De Revolutionibus and other heliocentric The sentence of the Inquisition was delivered on 22 June. works until correction.[77] Bellarmine’s instructions did It was in three essential parts: not prohibit Galileo from discussing heliocentrism as a mathematical and philosophic idea, so long as he did not • Galileo was found “vehemently suspect of heresy”, advocate for its physical truth.[10][78] namely of having held the opinions that the Sun lies motionless at the centre of the universe, that the For the next decade, Galileo stayed well away from the Earth is not at its centre and moves, and that one controversy. He revived his project of writing a book may hold and defend an opinion as probable afon the subject, encouraged by the election of Cardinal ter it has been declared contrary to Holy Scripture. Maffeo Barberini as Pope Urban VIII in 1623. Barberini He was required to “abjure, curse and detest” those was a friend and admirer of Galileo, and had opposed opinions.[84] the condemnation of Galileo in 1616. Galileo’s resulting book, Dialogue Concerning the Two Chief World Systems, was published in 1632, with formal authorization from the Inquisition and papal permission.[79] Earlier, Pope Urban VIII had personally asked Galileo to give arguments for and against heliocentrism in the book, and to be careful not to advocate heliocentrism. He made another request, that his own views on the matter be included in Galileo’s book. Only the latter of those requests was fulfilled by Galileo. Whether unknowingly or deliberately, Simplicio, the defender of the Aristotelian geocentric view in Dialogue Concerning the Two Chief World Systems, was often caught in his own errors and sometimes came across as a fool. Indeed, although Galileo states in the preface of his book that the character is named after a famous Aristotelian philosopher (Simplicius in Latin, “Simplicio” in Italian), the name “Simplicio” in Italian also has the connotation of “simpleton”.[80] This portrayal of Simplicio made Dialogue Concerning the Two Chief World Systems appear as an advocacy book: an attack on Aristotelian geocentrism and defence of the Copernican theory. Unfortunately for his relationship with the Pope, Galileo put the words of Urban VIII into the mouth of Simplicio. Most historians agree Galileo did not act out of malice and felt blindsided by the reaction to his book.[81] However, the Pope did not take the suspected public ridicule lightly, nor the Copernican advocacy. Galileo had alienated one of his biggest and most powerful supporters, the Pope, and was called to Rome to

• He was sentenced to formal imprisonment at the pleasure of the Inquisition.[85] On the following day this was commuted to house arrest, which he remained under for the rest of his life. • His offending Dialogue was banned; and in an action not announced at the trial, publication of any of his works was forbidden, including any he might write in the future.[86] According to popular legend, after recanting his theory that the Earth moved around the Sun, Galileo allegedly muttered the rebellious phrase And yet it moves. A 1640s painting by the Spanish painter Bartolomé Esteban Murillo or an artist of his school, in which the words were hidden until restoration work in 1911, depicts an imprisoned Galileo apparently gazing at the words “E pur si muove” written on the wall of his dungeon. The earliest known written account of the legend dates to a century after his death, but Stillman Drake writes “there is no doubt now that the famous words were already attributed to Galileo before his death”.[87] After a period with the friendly Ascanio Piccolomini (the Archbishop of Siena), Galileo was allowed to return to his villa at Arcetri near Florence in 1634, where he spent the remainder of his life under house arrest. Galileo was ordered to read the seven penitential psalms once a week for the next three years. However, his daughter Maria Celeste relieved him of the burden after securing ecclesiastical permission to take it upon herself.[88]


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191

Tomb of Galileo Galilei, Santa Croce

Portrait, attributed to Murillo, of Galileo gazing at the words “E pur si muove” (And yet it moves) (not legible in this image) scratched on the wall of his prison cell

These plans were dropped, however, after Pope Urban VIII and his nephew, Cardinal Francesco Barberini, protested,[93] because Galileo had been condemned by the Catholic Church for “vehement suspicion of heresy”.[94] He was instead buried in a small room next to the novices’ chapel at the end of a corridor from the southern transept of the basilica to the sacristy.[95] He was reburied in the main body of the basilica in 1737 after a monument had been erected there in his honour;[96] during this move, three fingers and a tooth were removed from his remains.[97] One of these fingers, the middle finger from Galileo’s right hand, is currently on exhibition at the Museo Galileo in Florence, Italy.[98]

It was while Galileo was under house arrest that he dedicated his time to one of his finest works, Two New Sciences. Here he summarised work he had done some forty years earlier, on the two sciences now called kinematics and strength of materials, published in Holland to avoid the censor. This book has received high praise from Albert Einstein.[89] As a result of this work, Galileo is 18.4 Scientific methods often called the “father of modern physics”. He went completely blind in 1638 and was suffering from a painful hernia and insomnia, so he was permitted to travel to Flo- Galileo made original contributions to the science of motion through an innovative combination of experiment rence for medical advice.[15][16] and mathematics.[99] More typical of science at the time Dava Sobel argues that prior to Galileo’s 1633 trial and were the qualitative studies of William Gilbert, on magjudgement for heresy, Pope Urban VIII had become prenetism and electricity. Galileo’s father, Vincenzo Galilei, occupied with court intrigue and problems of state, and a lutenist and music theorist, had performed experiments began to fear persecution or threats to his own life. In establishing perhaps the oldest known non-linear relathis context, Sobel argues that the problem of Galileo was tion in physics: for a stretched string, the pitch varies as presented to the pope by court insiders and enemies of the square root of the tension.[100] These observations lay Galileo. Having been accused of weakness in defending within the framework of the Pythagorean tradition of muthe church, Urban reacted against Galileo out of anger sic, well-known to instrument makers, which included the [90] and fear. fact that subdividing a string by a whole number produces a harmonious scale. Thus, a limited amount of mathematics had long related music and physical science, and young Galileo could see his own father’s observations ex18.3 Death pand on that tradition.[101] Galileo continued to receive visitors until 1642, when, after suffering fever and heart palpitations, he died on 8 January 1642, aged 77.[15][91] The Grand Duke of Tuscany, Ferdinando II, wished to bury him in the main body of the Basilica of Santa Croce, next to the tombs of his father and other ancestors, and to erect a marble mausoleum in his honour.[92]

Galileo was one of the first modern thinkers to clearly state that the laws of nature are mathematical. In The Assayer he wrote “Philosophy is written in this grand book, the universe ... It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures;....”[102] His mathematical analyses are a further development of a tradition employed by late


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scholastic natural philosophers, which Galileo learned when he studied philosophy.[103] His work marked another step towards the eventual separation of science from both philosophy and religion; a major development in human thought. He was often willing to change his views in accordance with observation. In order to perform his experiments, Galileo had to set up standards of length and time, so that measurements made on different days and in different laboratories could be compared in a reproducible fashion. This provided a reliable foundation on which to confirm mathematical laws using inductive reasoning. Galileo showed a modern appreciation for the proper relationship between mathematics, theoretical physics, and experimental physics. He understood the parabola, both in terms of conic sections and in terms of the ordinate (y) varying as the square of the abscissa (x). Galilei further asserted that the parabola was the theoretically ideal trajectory of a uniformly accelerated projectile in the absence of air resistance or other disturbances. He conceded that there are limits to the validity of this theory, noting on theoretical grounds that a projectile trajectory of a size comparable to that of the Earth could not possibly be a parabola,[104] but he nevertheless maintained that for distances up to the range of the artillery of his day, the deviation of a projectile’s trajectory from a parabola It was on this page that Galileo first noted an observation of the would be only very slight.[105]

18.5 Astronomy

moons of Jupiter. This observation upset the notion that all celestial bodies must revolve around the Earth. Galileo published a full description in Sidereus Nuncius in March 1610

EARTH

The phases of Venus, observed by Galileo in 1610

ing year, made a telescope with about 3x magnification. He later made improved versions with up to about 30x magnification.[107] With a Galilean telescope, the observer could see magnified, upright images on the earth— it was what is commonly known as a terrestrial telescope Galileo showed the Doge of Venice how to use the telescope or a spyglass. He could also use it to observe the sky; for a time he was one of those who could construct telescopes (Fresco by Giuseppe Bertini) good enough for that purpose. On 25 August 1609, he Based only on uncertain descriptions of the first prac- demonstrated one of his early telescopes, with a magnifitical telescope which Hans Lippershey tried to patent cation of about 8 or 9, to Venetian lawmakers. His telein the Netherlands in 1608,[106] Galileo, in the follow- scopes were also a profitable sideline for Galileo, who


18.5. ASTRONOMY sold them to merchants who found them useful both at sea and as items of trade. He published his initial telescopic astronomical observations in March 1610 in a brief treatise entitled Sidereus Nuncius (Starry Messenger).[108]

18.5.1

Kepler’s supernova

Tycho and others had observed the supernova of 1572. Ottavio Brenzoni’s letter of 15 January 1605 to Galileo brought the 1572 supernova and the less bright nova of 1601 to Galileo’s notice. Galileo observed and discussed Kepler’s supernova in 1604. Since these new stars displayed no detectable diurnal parallax, Galileo concluded that they were distant stars, and therefore disproved the Aristotelian belief in the immutability of the heavens.[109]

18.5.2

Jupiter’s moons

On 7 January 1610, Galileo observed with his telescope what he described at the time as “three fixed stars, totally invisible[110] by their smallness”, all close to Jupiter, and lying on a straight line through it.[111] Observations on subsequent nights showed that the positions of these “stars” relative to Jupiter were changing in a way that would have been inexplicable if they had really been fixed stars. On 10 January, Galileo noted that one of them had disappeared, an observation which he attributed to its being hidden behind Jupiter. Within a few days, he concluded that they were orbiting Jupiter:[112] he had discovered three of Jupiter’s four largest moons. He discovered the fourth on 13 January. Galileo named the group of four the Medicean stars, in honour of his future patron, Cosimo II de' Medici, Grand Duke of Tuscany, and Cosimo’s three brothers.[113] Later astronomers, however, renamed them Galilean satellites in honour of their discoverer. These satellites are now called Io, Europa, Ganymede, and Callisto.

193 The heliocentric model of the solar system developed by Nicolaus Copernicus predicted that all phases would be visible since the orbit of Venus around the Sun would cause its illuminated hemisphere to face the Earth when it was on the opposite side of the Sun and to face away from the Earth when it was on the Earth-side of the Sun. On the other hand, in Ptolemy’s geocentric model it was impossible for any of the planets’ orbits to intersect the spherical shell carrying the Sun. Traditionally the orbit of Venus was placed entirely on the near side of the Sun, where it could exhibit only crescent and new phases. It was, however, also possible to place it entirely on the far side of the Sun, where it could exhibit only gibbous and full phases. After Galileo’s telescopic observations of the crescent, gibbous and full phases of Venus, therefore, this Ptolemaic model became untenable. Thus in the early 17th century as a result of his discovery the great majority of astronomers converted to one of the various geo-heliocentric planetary models,[118] such as the Tychonic, Capellan and Extended Capellan models,[119] each either with or without a daily rotating Earth. These all had the virtue of explaining the phases of Venus without the vice of the 'refutation' of full heliocentrism’s prediction of stellar parallax. Galileo’s discovery of the phases of Venus was thus arguably his most empirically practically influential contribution to the two-stage transition from full geocentrism to full heliocentrism via geo-heliocentrism. Galileo observed the planet Saturn, and at first mistook its rings for planets, thinking it was a three-bodied system. When he observed the planet later, Saturn’s rings were directly oriented at Earth, causing him to think that two of the bodies had disappeared. The rings reappeared when he observed the planet in 1616, further confusing him.[120]

Galileo also observed the planet Neptune in 1612. It appears in his notebooks as one of many unremarkable dim stars. He did not realise that it was a planet, but he did note its motion relative to the stars before losing track of His observations of the satellites of Jupiter caused a rev- it.[121] olution in astronomy: a planet with smaller planets orbiting it did not conform to the principles of Aristotelian cosmology, which held that all heavenly bodies should 18.5.4 Sunspots circle the Earth,[114] and many astronomers and philosophers initially refused to believe that Galileo could have Galileo was one of the first Europeans to observe discovered such a thing.[115] His observations were con- sunspots, although Kepler had unwittingly observed one firmed by the observatory of Christopher Clavius and in 1607, but mistook it for a transit of Mercury. He he received a hero’s welcome when he visited Rome in also reinterpreted a sunspot observation from the time of 1611.[116] Galileo continued to observe the satellites over Charlemagne, which formerly had been attributed (imthe next eighteen months, and by mid-1611, he had ob- possibly) to a transit of Mercury. The very existence of tained remarkably accurate estimates for their periods—a sunspots showed another difficulty with the unchanging feat which Kepler had believed impossible.[117] perfection of the heavens as posited in orthodox Aristotelian celestial physics. And the annual variations in sunspots’ motions, discovered by Francesco Sizzi and 18.5.3 Venus, Saturn, and Neptune others in 1612–1613,[122] provided a powerful argument against both the Ptolemaic system and the geoheliocenFrom September 1610, Galileo observed that Venus ex- tric system of Tycho Brahe.[123] A dispute over priority in hibited a full set of phases similar to that of the Moon. the discovery of sunspots, and in their interpretation, led


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Galileo to a long and bitter feud with the Jesuit Christoph ported that he had found the apparent diameter of a star Scheiner. of first magnitude to be no more than 5 arcseconds, and 5 In fact, there is little doubt that both of them were that of one of sixth magnitude to be about /6 arcseconds. beaten by David Fabricius and his son Johannes. Scheiner Like most astronomers of his day, Galileo did not recogquickly adopted Kepler’s 1615 proposal of the modern nise that the apparent sizes of stars that he measured were telescope design, which gave larger magnification at the spurious, caused by diffraction and atmospheric distorcost of inverted images; Galileo apparently never changed tion (see seeing disk or Airy disk), and did not represent the true sizes of stars. However, Galileo’s values were to Kepler’s design. much smaller than previous estimates of the apparent sizes of the brightest stars, such as those made by Tycho Brahe (see Magnitude) and enabled Galileo to counter 18.5.5 Moon anti-Copernican arguments such as those made by TyPrior to Galileo’s construction of his version of a tele- cho that these stars would have to be absurdly large for [127] Other asscope, Thomas Harriot, an English mathematician and their annual parallaxes to be undetectable. Simon Marius, Giovanni Battista Rictronomers such as explorer, had already used what he dubbed a “perspective and Martinus Hortensius made similar measurecioli, tube” to observe the moon. Reporting his observations, Harriot noted only “strange spottednesse” in the waning ments of stars, and Marius and Riccioli concluded the of the crescent, but was ignorant to the cause. Galileo, smaller sizes were not small enough to answer Tycho’s [128] due in part to his artistic training[33] and the knowledge of argument. chiaroscuro,[32] had understood the patterns of light and shadow were in fact topographical markers. While not being the only one to observe the moon through a telescope, Galileo was the first to deduce the cause of the uneven waning as light occlusion from lunar mountains and craters. In his study he also made topographical charts, estimating the heights of the mountains. The moon was not what was long thought to have been a translucent and perfect sphere, as Aristotle claimed, and hardly the first “planet”, an “eternal pearl to magnificently ascend into the heavenly empyrian”, as put forth by Dante.

18.5.6

18.6 Engineering

Milky Way and stars

Galileo observed the Milky Way, previously believed to be nebulous, and found it to be a multitude of stars packed so densely that they appeared from Earth to be clouds. He located many other stars too distant to be visible with the naked eye. He observed the double star Mizar in Ursa Major in 1617.[124]

Galileo’s geometrical and military compass, thought to have been made c. 1604 by his personal instrument-maker Marc'Antonio Mazzoleni

Galileo made a number of contributions to what is now known as engineering, as distinct from pure physics. Between 1595 and 1598, Galileo devised and improved a Geometric and Military Compass suitable for use by gunners and surveyors. This expanded on earlier instruments designed by Niccolò Tartaglia and Guidobaldo del Monte. For gunners, it offered, in addition to a new and safer way of elevating cannons accurately, a way of quickly computing the charge of gunpowder for cannonballs of different sizes and materials. As a geometric instrument, it enabled the construction of any regular polygon, computation of the area of any polygon or circular sector, and a variety of other calculations. Under Galileo’s direction, instrument maker Marc'Antonio Mazzoleni produced more than 100 of these compasses, which Galileo sold (along with an instruction manual he wrote) for 50 lire and offered a course of instruction in the use of the compasses for 120 lire.[129]

In the Starry Messenger, Galileo reported that stars appeared as mere blazes of light, essentially unaltered in appearance by the telescope, and contrasted them to planets, which the telescope revealed to be discs. But shortly thereafter, in his letters on sunspots, he reported that the telescope revealed the shapes of both stars and planets to be “quite round”. From that point forward, he continued to report that telescopes showed the roundness of stars, and that stars seen through the telescope measured a few seconds of arc in diameter.[125] He also devised a method for measuring the apparent size of a star without a telescope. As described in his Dialogue Concerning the two Chief World Systems, his method was to hang a thin rope in his line of sight to the star and measure the maximum distance from which it would wholly obscure the star. From his measurements of this distance and of the width of the rope, he could calculate the angle subtended by the star at his viewing point.[126] In his Dialogue, he re- In about 1593, Galileo constructed a thermometer, using


18.7. PHYSICS

195

the expansion and contraction of air in a bulb to move portable marine chronometer, such as that of John Harwater in an attached tube. rison.[139] Late in his life, when totally blind, Galileo designed an escapement mechanism for a pendulum clock (called Galileo’s escapement), although no clock using this was built until after the first fully operational pendulum clock was made by Christiaan Huygens in the 1650s.

18.7 Physics

A replica of the earliest surviving telescope attributed to Galileo Galilei, on display at the Griffith Observatory.

In 1609, Galileo was, along with Englishman Thomas Harriot and others, among the first to use a refracting telescope as an instrument to observe stars, planets or moons. The name “telescope” was coined for Galileo’s instrument by a Greek mathematician, Giovanni Demisiani,[130] at a banquet held in 1611 by Prince Federico Cesi to make Galileo a member of his Accademia dei Lincei.[131] The name was derived from the Greek tele = 'far' and skopein = 'to look or see'. In 1610, he used a telescope at close range to magnify the parts of insects.[132] By 1624 Galileo had used[133] a compound microscope. He gave one of these instruments to Cardinal Zollern in May of that year for presentation to the Duke of Bavaria,[134] and in September he sent another to Prince Cesi.[135] The Linceans played a role again in naming the “microscope” a year later when fellow academy member Giovanni Faber coined the word for Galileo’s invention from the Greek words μικρόν (micron) meaning “small”, and σκοπεῖν (skopein) meaning “to look at”. The word was meant to be analogous with “telescope”.[136][137] Illustrations of insects made using one of Galileo’s microscopes, and published in 1625, appear to have been the first clear documentation of the use of a compound microscope.[138] In 1612, having determined the orbital periods of Jupiter’s satellites, Galileo proposed that with sufficiently accurate knowledge of their orbits, one could use their positions as a universal clock, and this would make possible the determination of longitude. He worked on this problem from time to time during the remainder of his life; but the practical problems were severe. The method was first successfully applied by Giovanni Domenico Cassini in 1681 and was later used extensively for large land surveys; this method, for example, was used to survey France, and later by Zebulon Pike of the midwestern United States in 1806. For sea navigation, where delicate telescopic observations were more difficult, the longitude problem eventually required development of a practical

Galileo e Viviani, 1892, Tito Lessi

Galileo’s theoretical and experimental work on the motions of bodies, along with the largely independent work of Kepler and René Descartes, was a precursor of the classical mechanics developed by Sir Isaac Newton. Galileo conducted several experiments with pendulums. It is popularly believed (thanks to the biography by Vincenzo Viviani) that these began by watching the swings of the bronze chandelier in the cathedral of Pisa, using his pulse as a timer. Later experiments are described in his Two New Sciences. Galileo claimed that a simple pendulum is isochronous, i.e. that its swings always take the same amount of time, independently of the amplitude. In fact, this is only approximately true,[140] as was discovered by Christiaan Huygens. Galileo also found that the square of the period varies directly with the length of the pendulum. Galileo’s son, Vincenzo, sketched a clock based on his father’s theories in 1642. The clock was never built and, because of the large swings required by its verge escapement, would have been a poor timekeeper. (See Engineering above.) Galileo is lesser known for, yet still credited with, being one of the first to understand sound frequency. By scraping a chisel at different speeds, he linked the pitch of the sound produced to the spacing of the chisel’s skips, a measure of frequency. In 1638, Galileo described an experimental method to measure the speed of light by arranging that two observers, each having lanterns equipped with shutters, observe each other’s lanterns at some distance. The first observer opens the shutter of his lamp, and, the second, upon seeing the light, immediately opens


196 the shutter of his own lantern. The time between the first observer’s opening his shutter and seeing the light from the second observer’s lamp indicates the time it takes light to travel back and forth between the two observers. Galileo reported that when he tried this at a distance of less than a mile, he was unable to determine whether or not the light appeared instantaneously.[141] Sometime between Galileo’s death and 1667, the members of the Florentine Accademia del Cimento repeated the experiment over a distance of about a mile and obtained a similarly inconclusive result.[142] We now know that the speed of light is far too fast to be measured by such methods (with human shutter-openers on Earth).

CHAPTER 18. GALILEO GALILEI experiment described was actually performed by Simon Stevin (commonly known as Stevinus) and Jan Cornets de Groot,[31] although the building used was actually the church tower in Delft in 1586.[148] However most of his experiments with falling bodies were carried out using inclined planes where both the issues of timing and wind resistance were much reduced.

In his 1638 Discorsi, Galileo’s character Salviati, widely regarded as Galileo’s spokesman, held that all unequal weights would fall with the same finite speed in a vacuum. But this had previously been proposed by Lucretius[149] and Simon Stevin.[150] Cristiano Banti's Salviati also held it could be experimentally demonstrated by the comparGalileo put forward the basic principle of relativity, that ison of pendulum motions in air with bobs of lead and the laws of physics are the same in any system that is mov- of cork which had different weight but which were othing at a constant speed in a straight line, regardless of its erwise similar. particular speed or direction. Hence, there is no absolute Galileo proposed that a falling body would fall with a unimotion or absolute rest. This principle provided the basic form acceleration, as long as the resistance of the medium framework for Newton’s laws of motion and is central to through which it was falling remained negligible, or in the Einstein’s special theory of relativity. limiting case of its falling through a vacuum.[151] He also derived the correct kinematical law for the distance travelled during a uniform acceleration starting from rest— 18.7.1 Falling bodies namely, that it is proportional to the square of the elapsed time ( d ∝ t 2 ).[152] Prior to Galileo, Nicole Oresme, See also: Equations for a falling body in the 14th century, had derived the times-squared law A biography by Galileo’s pupil Vincenzo Viviani stated for uniformly accelerated change,[153] and Domingo de Soto had suggested in the 16th century that bodies falling through a homogeneous medium would be uniformly accelerated.[154] Galileo expressed the time-squared law using geometrical constructions and mathematically precise words, adhering to the standards of the day. (It remained for others to re-express the law in algebraic terms). He also concluded that objects retain their velocity in the absence of any impediments to their motion, thereby contradicting the generally accepted Aristotelian hypothesis that a body could only remain in so-called “violent”, “unnatural”, or “forced” motion so long as an agent of change (the “mover”) continued to act on it.[155] Philosophical ideas relating to inertia had been proposed by John Philoponus and Jean Buridan. Galileo stated: “Imagine any During the Apollo 15 mission in 1971, astronaut David Scott showed that Galileo was right: acceleration is the same for all particle projected along a horizontal plane without fricbodies subject to gravity on the Moon, even for a hammer and a tion; then we know, from what has been more fully explained in the preceding pages, that this particle will move feather. along this same plane with a motion which is uniform and [156] This was that Galileo had dropped balls of the same material, but perpetual, provided the plane has no limits” Newton’s laws of motion (first law). incorporated into different masses, from the Leaning Tower of Pisa to demonstrate that their time of descent was independent of their mass.[143] This was contrary to what Aristotle had taught: that heavy objects fall faster than lighter ones, in direct proportion to weight.[144] While this story has 18.8 Mathematics been retold in popular accounts, there is no account by Galileo himself of such an experiment, and it is gener- While Galileo’s application of mathematics to experially accepted by historians that it was at most a thought mental physics was innovative, his mathematical methexperiment which did not actually take place.[145][146] An ods were the standard ones of the day, including dozens exception is Drake,[147] who argues that the experiment of examples of an inverse proportion square root method did take place, more or less as Viviani described it. The passed down from Fibonacci and Archimedes. The anal-


18.9. WRITINGS

197

Dome of the Cathedral of Pisa with the “lamp of Galileo”

ysis and proofs relied heavily on the Eudoxian theory of proportion, as set forth in the fifth book of Euclid’s Elements. This theory had become available only a century before, thanks to accurate translations by Tartaglia and others; but by the end of Galileo’s life, it was being superseded by the algebraic methods of Descartes. The concept now named Galileo’s paradox was not original with him. His proposed solution, that infinite numbers cannot be compared, is no longer considered useful. Statue outside the Uffizi, Florence

18.9 Writings Galileo’s early works describing scientific instruments include the 1586 tract entitled The Little Balance (La Billancetta) describing an accurate balance to weigh objects in air or water[157] and the 1606 printed manual Le Operazioni del Compasso Geometrico et Militare on the operation of a geometrical and military compass.[158] His early works in dynamics, the science of motion and mechanics were his 1590 Pisan De Motu (On Motion) and his circa 1600 Paduan Le Meccaniche (Mechanics). The former was based on Aristotelian–Archimedean fluid dynamics and held that the speed of gravitational fall in a fluid medium was proportional to the excess of a body’s specific weight over that of the medium, whereby in a vacuum, bodies would fall with speeds in proportion to their specific weights. It also subscribed to the Philoponan impetus dynamics in which impetus is self-dissipating and free-fall in a vacuum would have an essential terminal speed according to specific weight after an initial period of acceleration.

observations made through a telescope. It reported his discoveries of: • the Galilean moons • the roughness of the Moon’s surface • the existence of a large number of stars invisible to the naked eye, particularly those responsible for the appearance of the Milky Way • differences between the appearances of the planets and those of the fixed stars—the former appearing as small discs, while the latter appeared as unmagnified points of light

Galileo published a description of sunspots in 1613 entitled Letters on Sunspots[159] suggesting the Sun and heavens are corruptible. The Letters on Sunspots also reported his 1610 telescopic observations of the full set of phases of Venus, and his discovery of the puzzling “appendages” of Saturn and their even more puzzling subsequent disapGalileo’s 1610 The Starry Messenger (Sidereus Nuncius) pearance. In 1615 Galileo prepared a manuscript known was the first scientific treatise to be published based on as the Letter to the Grand Duchess Christina which was


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not published in printed form until 1636. This letter was a revised version of the Letter to Castelli, which was denounced by the Inquisition as an incursion upon theology by advocating Copernicanism both as physically true and as consistent with Scripture.[160] In 1616, after the order by the inquisition for Galileo not to hold or defend the Copernican position, Galileo wrote the Discourse on the Tides (Discorso sul flusso e il reflusso del mare) based on the Copernican earth, in the form of a private letter to Cardinal Orsini.[161] In 1619, Mario Guiducci, a pupil of Galileo’s, published a lecture written largely by Galileo under the title Discourse on the Comets (Discorso Delle Comete), arguing against the Jesuit interpretation of comets.[162] In 1623, Galileo published The Assayer—Il Saggiatore, which attacked theories based on Aristotle’s authority and promoted experimentation and the mathematical formulation of scientific ideas. The book was highly successful and even found support among the higher echelons of the Christian church.[163] Following the success of The Assayer, Galileo published the Dialogue Concerning the Two Chief World Systems (Dialogo sopra i due massimi sistemi del mondo) in 1632. Despite taking care to adhere to the Inquisition’s 1616 instructions, the claims in the book favouring Copernican theory and a non Geocentric model of the solar system led to Galileo being tried and banned on publication. Despite the publication ban, Galileo published his Discourses and Mathematical Demonstrations Relating to Two New Sciences (Discorsi e Dimostrazioni Matematiche, intorno a due nuove scienze) in 1638 in Holland, outside the jurisdiction of the Inquisition.

18.9.1

Published written works

Galileo’s main written works are as follows: • The Little Balance (1586; in Italian: La Billancetta)

• Letter to the Grand Duchess Christina (1615; published in 1636) • Discourse on the Tides (1616; in Italian: Discorso del flusso e reflusso del mare) • Discourse on the Comets (1619; in Italian: Discorso delle Comete) • The Assayer (1623; in Italian: Il Saggiatore) • Dialogue Concerning the Two Chief World Systems (1632; in Italian: Dialogo sopra i due massimi sistemi del mondo) • Discourses and Mathematical Demonstrations Relating to Two New Sciences (1638; in Italian: Discorsi e Dimostrazioni Matematiche, intorno a due nuove scienze)

18.10 Legacy 18.10.1 Later Church reassessments The Galileo affair was largely forgotten after Galileo’s death, and the controversy subsided. The Inquisition’s ban on reprinting Galileo’s works was lifted in 1718 when permission was granted to publish an edition of his works (excluding the condemned Dialogue) in Florence.[165] In 1741 Pope Benedict XIV authorised the publication of an edition of Galileo’s complete scientific works[166] which included a mildly censored version of the Dialogue.[167] In 1758 the general prohibition against works advocating heliocentrism was removed from the Index of prohibited books, although the specific ban on uncensored versions of the Dialogue and Copernicus’s De Revolutionibus remained.[168] All traces of official opposition to heliocentrism by the church disappeared in 1835 when these works were finally dropped from the Index.[169]

Interest in the Galileo affair was revived in the early 1590; in Latin: De Motu An- 19th century, when Protestant polemicists used it (and other events such as the Spanish Inquisition and the Flat Earth Myth) to attack Roman Catholicism.[10] Interest Mechanics (c. 1600; in Italian: Le mecaniche) in it has waxed and waned ever since. In 1939 Pope The Operations of Geometrical and Military Com- Pius XII, in his first speech to the Pontifical Academy pass (1606; in Italian: Le operazioni del compasso of Sciences, within a few months of his election to the geometrico et militare) papacy, described Galileo as being among the “most auThe Starry Messenger (1610; in Latin: Sidereus Nun- dacious heroes of research... not afraid of the stumbling blocks and the risks on the way, nor fearful of the funecius) real monuments”.[170] His close advisor of 40 years, ProDiscourse on Floating Bodies (1612; in Italian: Dis- fessor Robert Leiber, wrote: “Pius XII was very careful corso intorno alle cose che stanno in su l'acqua, o che not to close any doors (to science) prematurely. He was in quella si muovono, “Discourse on Bodies that Stay energetic on this point and regretted that in the case of Atop Water, or Move in It”) Galileo.”[171]

• On Motion (c. tiquiora)[164] • •

• •

• History and Demonstration Concerning Sunspots (1613; in Italian: Istoria e dimostrazioni intorno alle macchie solari; work based on the Three Letters on Sunspots, Tre lettere sulle macchie solari, 1612)

On 15 February 1990, in a speech delivered at the Sapienza University of Rome,[172] Cardinal Ratzinger (later to become Pope Benedict XVI) cited some current views on the Galileo affair as forming what he called “a


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symptomatic case that permits us to see how deep the self-doubt of the modern age, of science and technology goes today”.[173] Some of the views he cited were those of the philosopher Paul Feyerabend, whom he quoted as saying “The Church at the time of Galileo kept much more closely to reason than did Galileo himself, and she took into consideration the ethical and social consequences of Galileo’s teaching too. Her verdict against Galileo was rational and just and the revision of this verdict can be justified only on the grounds of what is politically opportune.”[173] The Cardinal did not clearly indicate whether he agreed or disagreed with Feyerabend’s assertions. He did, however, say “It would be foolish to construct an impulsive apologetic on the basis of such views.”[173] On 31 October 1992, Pope John Paul II expressed regret for how the Galileo affair was handled, and issued a declaration acknowledging the errors committed by the Catholic Church tribunal that judged the scientific positions of Galileo Galilei, as the result of a study conducted by the Pontifical Council for Culture.[174][175] In March 2008 the head of the Pontifical Academy of Sciences, Nicola Cabibbo, announced a plan to honour Galileo by erecting a statue of him inside the Vatican walls.[176] In December of the same year, during events to mark the 400th anniversary of Galileo’s earliest telescopic observations, Pope Benedict XVI praised his contributions to astronomy.[177] A month later, however, the head of the Pontifical Council for Culture, Gianfranco Ravasi, revealed that the plan to erect a statue of Galileo in the grounds of the Vatican had been suspended.[178]

International Year of Astronomy commemorative coin

sponsible for educational, scientific and cultural matters. The International Year of Astronomy 2009 was intended to be a global celebration of astronomy and its contributions to society and culture, stimulating worldwide interest not only in astronomy but science in general, with a particular slant towards young people. Asteroid 697 Galilea is named in his honour.

18.10.3 In artistic and popular media

Galileo is mentioned several times in the “opera” section of the Queen song, "Bohemian Rhapsody".[184] He fea18.10.2 Impact on modern science tures prominently in the song "Galileo" performed by the According to Stephen Hawking, Galileo probably bears Indigo Girls and Amy Grant's Galileo on her Heart in Momore of the responsibility for the birth of modern science tion album. than anybody else,[179] and Albert Einstein called him the Twentieth-century plays have been written on Galileo’s father of modern science.[180][181] life, including Life of Galileo (1943) by the German playof it, Galileo’s astronomical discoveries and investigations into wright Bertolt Brecht, with a film adaptation (1975) and Lamp At Midnight (1947) by Barrie Stavis,[185] as well the Copernican theory have led to a lasting legacy which [186] includes the categorisation of the four large moons of as the 2008 play “Galileo Galilei”. Jupiter discovered by Galileo (Io, Europa, Ganymede and Callisto) as the Galilean moons. Other scientific endeavours and principles are named after Galileo including the Galileo spacecraft,[182] the first spacecraft to enter orbit around Jupiter, the proposed Galileo global satellite navigation system, the transformation between inertial systems in classical mechanics denoted Galilean transformation and the Gal (unit), sometimes known as the Galileo, which is a non-SI unit of acceleration. Partly because 2009 was the fourth centenary of Galileo’s first recorded astronomical observations with the telescope, the United Nations scheduled it to be the International Year of Astronomy.[183] A global scheme was laid out by the International Astronomical Union (IAU), also endorsed by UNESCO—the UN body re-

Kim Stanley Robinson wrote a science fiction novel entitled Galileo’s Dream (2009), in which Galileo is brought into the future to help resolve a crisis of scientific philosophy; the story moves back and forth between Galileo’s own time and a hypothetical distant future, and contains a great deal of biographical information.[187] Galileo Galilei was recently selected as a main motif for a high value collectors’ coin: the €25 International Year of Astronomy commemorative coin, minted in 2009. This coin also commemorates the 400th anniversary of the invention of Galileo’s telescope. The obverse shows a portion of his portrait and his telescope. The background shows one of his first drawings of the surface of the moon. In the silver ring other telescopes are depicted: the Isaac Newton Telescope, the observatory in


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Kremsmünster Abbey, a modern telescope, a radio telescope and a space telescope. In 2009, the Galileoscope was also released. This is a mass-produced, low-cost educational 2-inch (51 mm) telescope with relatively high quality.

• 1591 – Death of his father, Vicenzo Galilei

18.11 Timeline

• ~1595 – Invents improved ballistics calculation geometric and military compass, which he later improves for surveying and general calculations and earns income from tutoring on its use

• 1543 – Nicolaus Copernicus publishes De revolutionibus orbium coelestium as an alternative world system to the Ptolemy's geocentric model causing subsequent questions to be raised about Aristotelian physics following Copernicus’ death

• 1592 – Appointed professor of mathematics at University of Padua, remains 18 years • ~1593 – Invents early thermometer that unfortunately depended on both temperature and pressure

• 1597 – Letter to Kepler indicates his belief in the Copernican System

• 1563 – Parents Vincenzo Galilei and Giulia Ammannati marry

• 1600 – First child, Virginia is born; ~1600 Le Meccaniche (Mechanics)

• 1564 – Birth in Pisa, Italy

• 1600 – William Gilbert publishes On the Magnet and Magnetic Bodies, and on That Great Magnet the Earth with arguments supporting the Copernican system

• ~1570 – Thomas Digges publishes Pantometria describing a telescope built between 1540–1559 by his father Leonard Digges • 1573 – Tycho Brahe publishes De nova stella (On the new star) refuting Aristotelian belief in immutable celestial spheres and an eternal, unchanging, more perfect heavenly realm of celestial aether above the moon • 1576 – Giuseppe Moletti, Galileo’s predecessor in the mathematics chair at Padua, reports falling bodies of the same shape fall at the same speed, regardless of material[188] • 1581 – His father, Vincenzo Galilei publishes Dialogo della musica antica et moderna formulating musical theories[189] • 1581 – Enrols as medical student at University of Pisa • 1582 – Attends mathematics lecture by Ostilio Ricci and decides to study math and science • 1585 – Leaves University of Pisa without degree and works as tutor • 1586 – Invents hydrostatic balance; wrote La Balancitta (The little balance) • 1586 – Simon Stevin publishes results for dropping lead weights from 10 meters • 1588 – Tycho Brahe publishes work on comets containing a description of the Tychonic system of the world[190] • 1589 – Appointed to Mathematics Chair, University of Pisa • 1590 – Partially completes De Motu (On Motion), which is never published

• 1600 – Roman Inquisition finds Giordano Bruno, Copernican system supporter, guilty of heresy for opinions on pantheism and the eternal plurality of worlds, and for denial of the Trinity, divinity of Christ, virginity of Mary, and Transubstantiation; burned at the stake by civil authorities • 1601 – Daughter Livia is born • 1604 – Measures supernova position indicating no parallax for the new star • 1605 – Sued by brothers-in-law for nonpayment of sisters’ dowries • 1606 – Son Vincenzo born • 1606 – Publishes manual for his calculating compass • 1607 – Rotilio Orlandini attempts to assassinate Galileo’s friend, Friar Paolo Sarpi • 1608 – Hans Lippershey invents a refracting telescope • 1609 – Independently invents and improves telescopes based on description of invention by Hans Lippershey • 1609 – Kepler publishes Astronomia nova containing his first two laws and for the first time demonstrates the Copernican model is more accurate than the Ptolemaic for uses such as navigation and prediction • 1609 – Thomas Harriot sketches the Moon from telescopic observations made four months before Galileo’s


18.12. SEE ALSO • 1610 – Publishes Sidereus Nuncius (Starry Messenger); views our moon’s mountains and craters and brightest 4 of Jupiter’s moons • 1610 – Martin Horky publishes Brevissima Peregrinatio Contra Nuncium Sidereum, opposing Galileo • 1610 – Kepler requests one of Galileo’s telescopes or lenses, but Galileo replies he is too busy to build one and has no extras[191] • 1610 – Lifetime appointment to mathematics position at University of Padua, and as mathematician and philosopher for Cosimo II, Grand Duke of Tuscany • 1611 – Discovers phases of Venus; granted audience with Pope; made member of Lincean Academy • 1611 – Awarded an honorary degree by the Jesuit College in Rome[192] • 1611 – David Fabricius publishes Narration on Spots Observed on the Sun and their Apparent Rotation with the Sun prior to Christoph Scheiner and Galileo’s published works on the subject

201 • 1619 – Kepler publishes Harmonices Mundi which introduces his third law • 1619 – Discourse on the Comets • 1623 – Maffeo Barberini becomes Pope Urban VIII • 1623 – Publishes The Assayer • 1624 – Visits Pope who praises and honours him, leaving with assumed permission to publish work on the Copernican vs. Ptolemaic Systems; used a compound microscope • 1625 – Illustrations of insects made using one of Galileo’s microscopes published • 1630 – Completes Dialogue Concerning the Two Chief World Systems and subsequently receives approval of Church censor • 1632 – Publishes Dialogue Concerning the Two Chief World Systems • 1633 – sentenced by the Inquisition to imprisonment, commuted to house arrest, for vehement suspicion of heresy in violating the 1616 injunction

• 1612 – Proposed Jupiter’s moons could be used as a universal clock for possible determination of longitude

• 1633 – Catholic Church places Dialogue Concerning the Two Chief World Systems on the List of Prohibited Books

• ~1612 or 1613 – Francesco Sizzi discovers annual variations in sunspots’ motions

• 1638 – Publishes Dialogues Concerning Two New Sciences

• 1613 – Letters on Sunspots

• 1642 – Death in Arcetri, Italy

• 1613 – Letter to Benedetto Castelli discussing the rotation of the sun and Galileo’s support of the Copernican system. Using Biblical inerrancy as a basis, Galileo writes that Joshua's command for the sun to stand still in Joshua 10:13 proves the “impossibility of the Aristotelian and Ptolemaic world system, and on the other hand agrees very well with the Copernican one.”[193] He went on to write that “the sun gives not only light (as it obviously does) but also motion to all the planets that revolve around it” by its rotation.[193]

• 1668 – Isaac Newton builds his reflecting telescope

• 1615 – Letter to Grand Duchess Christina (not published until 1636) • 1616 – Officially warned by the Church not to hold or defend the Copernican System

• 1687 – Isaac Newton publishes Philosophiæ Naturalis Principia Mathematica deriving Kepler’s laws from the Universal Law of Gravitation and the Laws of Motion • 2016 – The American Juno spacecraft, carring a plaque and a Lego minifigure dedicated at Galileo arrives at Jupiter’s orbit

18.12 See also • Aristarchus of Samos • Catholic Church and science

• 1616 – The Catholic Church places De revolutionibus orbium coelestium on the List of Prohibited Books, pending correction

• Dialogo de Cecco di Ronchitti da Bruzene in perpuosito de la stella Nuova

• 1616 – Private letter Discourse on the Tides

• Letter to the Grand Duchess Christina

• 1617 – Moves into Bellosguardo, west of Florence, near his daughters’ convent; observes double star Mizar in Ursa Major

• Philolaus

• Galileo affair

• Seleucus of Seleucia


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• Tribune of Galileo (Memorial in the Florence Sci- [20] Sobel (1999, p. 13) ence Museum) • Villa Il Gioiello (Galileo’s main home in Florence)

18.13 Notes [1] F. Vinci, Ostilio Ricci da Fermo, Maestro di Galileo Galilei, Fermo, 1929. [2] “The Mathematics Genealogy Project - Galileo Galilei”. nodak.edu. [3] Drake (1978, p. 1). The date of Galileo’s birth is given according to the Julian calendar, which was then in force throughout Christendom. In 1582 it was replaced in Italy and several other Catholic countries with the Gregorian calendar. Unless otherwise indicated, dates in this article are given according to the Gregorian calendar. [4] Singer, Charles (1941). “A Short History of Science to the Nineteenth Century”. Clarendon Press: 217. [5] Whitehouse, David (2009). Renaissance Genius: Galileo Galilei & His Legacy to Modern Science. Sterling Publishing. p. 219. ISBN 1-4027-6977-6. [6] Weidhorn, Manfred (2005). The Person of the Millennium: The Unique Impact of Galileo on World History. iUniverse. p. 155. ISBN 0-595-36877-8. [7] Thomas Hobbes: Critical Assessments, Volume 1. Preston King. 1993. Page 59 [8] Finocchiaro (2007). [9] Disraeli, Isaac (1835). Curiosities of Literature. W. Pearson & Company. p. 371. [10] Hannam, James (2011). The Genesis of Science. pp. 329– 344. [11] Sharratt (1994, pp. 127–131), McMullin (2005a). [12] Finocchiaro, Maurice (2010). Defending Copernicus and Galileo: Critical Reasoning in the Two Affairs. Springer. p. 74. Retrieved 21 May 2016. [13] Finocchiaro (1997), p. 47. [14] Hilliam (2005), p. 96.

[21] “Galilean”. The Century Dictionary and Encyclopedia. III. New York: The Century Co. 1903 [1889]. p. 2436. [22] Sobel (1999, p. 16) “The meaning of the name Galileo, or Galilei, harks back to the land of Galilee, although, as Galileo explained on this score, he was not at all a Jew.” [23] Maurice Finnochiaro, The Galileo Affair: A Documentary History 300, 330 n. 13 (Univ. Cal. Press 1998) [24] Naess, Atle (2006). Galileo Galilei - When the World Stood Still. Springer Science & Business Media. pp. 89– 91. Retrieved 11 March 2015. [25] Sharratt (1994, pp. 17, 213) [26] Rosen, Joe; Gothard, Lisa Quinn (2009). Encyclopedia of Physical Science. Infobase Publishing. p. 268. ISBN 978-0-8160-7011-4. [27] Gribbin. John (2008). The Fellowship: Gilbert, Bacon, Harvey, Wren, Newton and the Story of the Scientific Revolution. Overlook Press. p. 42 [28] Sobel (2000, p. 5) Chapter 1. Retrieved on 26 August 2007. “But because he never married Virginia’s mother, he deemed the girl herself unmarriageable. Soon after her 13th birthday, he placed her at the Convent of San Matteo in Arcetri.” [29] Pedersen, Olaf (1985). “Galileo’s Religion”. In Coyne, George V.; Heller, Michał; Życiński, Józef. The Galileo Affair: A Meeting of Faith and Science, Proceedings of the Cracow Conference, May 24-27, 1984. Vatican City: Specola Vaticana. pp. 75–102. Bibcode:1985gamf.conf...75P. OCLC 16831024. [30] Reston (2000, pp. 3–14). [31] Asimov, Isaac (1964). Asimov’s Biographical Encyclopedia of Science and Technology. ISBN 978-0385177719 [32] Edgerton, Samuel Y. The Mirror, the Window, and the Telescope, 2009 [33] Panofsky, Erwin (1956). “Galileo as a Critic of the Arts: Aesthetic Attitude and Scientific Thought”. Isis. 47 (1): 3–15. doi:10.1086/348450. JSTOR 227542. [34] Sharratt (1994, pp. 45–66).

[15] Carney, Jo Eldridge (2000). Renaissance and Reformation, 1500–1620: a. Greenwood Publishing. ISBN 0313-30574-9.

[35] Rutkin, H. Darrel. “Galileo, Astrology, and the Scientific Revolution: Another Look”. Program in History & Philosophy of Science & Technology, Stanford University. Retrieved 2007-04-15.

[16] Allan-Olney (1870)

[36] Finocchiaro (1989), pp. 67–9.

[17] O'Connor, J. J.; Robertson, E.F. “Galileo Galilei”. The MacTutor History of Mathematics archive. University of St Andrews, Scotland. Retrieved 2007-07-24.

[37] Finocchiaro (1989), p. 354, n. 52

[18] John Gribbin. The Fellowship: Gilbert, Bacon, Harvey, Wren, Newton and the Story of the Scientific Revolution. The Overlook Press, 2008. p. 26 [19] Sobel (1999, p. 16)

[38] Finocchiaro (1989), pp. 119–133 [39] Finocchiaro (1989), pp. 127–131 and Galilei, (1953), pp. 432–6 [40] Einstein (1953) p. xvii [41] Galilei, (1953), p. 462.


18.13. NOTES

[42] James Robert Voelkel. The Composition of Kepler’s Astronomia Nova. Princeton University Press, 2001. p. 74 [43] Stillman Drake. Essays on Galileo and the History and Philosophy of Science, Volume 1. University of Toronto Press, 1999. p. 343 [44] Drake (1960, pp.vii, xxiii–xxiv), Sharratt (1994, pp. 139– 140). [45] Grassi (1960a).

203

[68] Finocchiaro (1989), pp. 27-28. [69] Langford (1992), pp. 56–57 [70] Finocchiaro (1989), pp. 28 & 134. [71] Graney (2015, pp. 68-69) Ingoli’s essay was published in English translation for the first time in 2015. [72] Finocchiaro (2010, pp. 72) [73] Graney (2015, pp. 71)

[46] Drake (1978, p. 268), Grassi (1960a, p. 16). [74] Graney (2015, pp. 66-76, 164-175, 187-195) [47] Galilei & Guiducci (1960). [48] Drake (1960, p.xvi). [49] Drake (1957, p. 222), Drake (1960, p.xvii). [50] Sharratt (1994, p. 135), Drake (1960, p.xii), Galilei & Guiducci (1960, p. 24).

[75] Finocchiaro, Maurice. “West Chester University— History of Astronomy; Lecture notes: Texts from The Galileo Affair: A Documentary History”. West Chester University. ESS 362 / 562. Archived from the original on 30 September 2007. Retrieved 18 February 2014.

[51] Sharratt (1994, p. 135).

[76] “Una errata reproducida durante siglos cambia la censura de la Iglesia a Galileo”. Materia.

[52] Sharratt (1994, p. 135), Drake (1960, p.xvii).

[77] Heilbron (2010), p. 218

[53] Grassi (1960b).

[78] Sharratt (1994, pp. 126–31).

[54] Drake (1978, p. 494), Favaro(1896, 6:111). The pseudonym was a slightly imperfect anagram of Oratio Grasio Savonensis, a Latinised version of his name and home town.

[79] “Pope Urban VIII Biography”. Galileo Project.

[55] Galilei (1960). [56] Sharratt (1994, p. 137), Drake (1957, p. 227). [57] Sharratt (1994, p. 138–142). [58] Drake (1960, p.xix). [59] Alexander, Amir (2014). Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World. Scientific American / Farrar, Straus and Giroux. p. 131. ISBN 978-0374176815. [60] Drake (1960, p.vii).

[80] Finocchiaro (1997), p. 82; Moss & Wallace (2003), p. 11 [81] See Langford (1966, pp. 133–34), and Seeger (1966, p. 30), for example. Drake (1978, p. 355) asserts that Simplicio’s character is modelled on the Aristotelian philosophers Lodovico delle Colombe and Cesare Cremonini, rather than Urban. He also considers that the demand for Galileo to include the Pope’s argument in the Dialogue left him with no option but to put it in the mouth of Simplicio (Drake, 1953, p. 491). Even Arthur Koestler, who is generally quite harsh on Galileo in The Sleepwalkers (1959), after noting that Urban suspected Galileo of having intended Simplicio to be a caricature of him, says “this of course is untrue” (1959, p. 483). [82] Lindberg, David. “Beyond War and Peace: A Reappraisal of the Encounter between Christianity and Science”.

[61] Sharratt (1994, p. 175). [62] Sharratt (1994, pp. 175–78), Blackwell (2006, p. 30). [63] Blackwell, Richard (1991). Galileo, Bellarmine, and the Bible. Notre Dame: University of Notre Dame Press. p. 25. ISBN 0-268-01024-2. [64] Hannam, James. “The Genesis of Science”. 2011. p303316. [65] “The Gregorian calendar, first adopted in 1582, was based on computations that made use of Copernicus’ work” (Kuhn, Thomas (1957), The Copernican Revolution, Harvard University Press, p. 125). [66] Graney and Danielson (2014). [67] Brodrick (1965, c1964, p. 95) quoting Cardinal Bellarmine’s letter to Foscarini, dated 12 April 1615. Translated from Favaro (1902, 12:171–72) (Italian).

[83] Sharratt (1994, pp. 171–75); Heilbron (2010, pp. 308– 17); Gingerich (1992, pp. 117–18). [84] Fantoli (2005, p. 139), Finocchiaro (1989, pp. 288–93). Finocchiaro’s translation of the Inquisition’s judgement against Galileo is available on-line at the Wayback Machine (archived 30 September 2007). “Vehemently suspect of heresy” was a technical term of canon law and did not necessarily imply that the Inquisition considered the opinions giving rise to the verdict to be heretical. The same verdict would have been possible even if the opinions had been subject to only the less serious censure of “erroneous in faith” (Fantoli, 2005, p. 140; Heilbron, 2005, pp. 282–84). [85] Finocchiaro (1989, pp. 38, 291, 306). Finocchiaro’s translation of the Inquisition’s judgement against Galileo is available on-line at the Wayback Machine (archived 30 September 2007).


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[86] Drake (1978, p. 367), Sharratt (1994, p. 184), [110] i.e., invisible to the naked eye. Favaro(1905, 16:209, 230) (Italian). See Galileo affair [111] Drake (1978, p. 146). for further details. [112] In Sidereus Nuncius (Favaro,1892, 3:81 (Latin)) Galileo stated that he had reached this conclusion on 11 January. [88] Shea, William (January 2006). “The Galileo Affair” (unDrake (1978, p. 152), however, after studying unpubpublished work). Grupo de Investigación sobre Ciencia, lished manuscript records of Galileo’s observations, conRazón y Fe (CRYF). Retrieved 12 September 2010. cluded that he did not do so until 15 January. [87] Drake (1978, p. 356-7).

[89] Stephen Hawking, ed. p. 398, On the Shoulders of Gi- [113] Sharratt (1994, p. 17). ants: “Galileo... is the father of modern physics—indeed [114] Linton (2004, pp. 98,205), Drake (1978, p. 157). of modern science”—Albert Einstein. [90] Sobel (2000, pp. 232–4).

[115] Drake (1978, pp. 158–68), Sharratt (1994, pp. 18–19).

[91] Herbermann, Charles, ed. (1913). "Galileo Galilei". [116] God’s Philosophers ju James Hannam Orion 2009 p313 Catholic Encyclopedia. New York: Robert Appleton [117] Drake (1978, p. 168), Sharratt (1994, p. 93). Company. by John Gerard. Retrieved 11 August 2007 [92] Shea & Artigas (2003, p. 199); Sobel (2000, p. 378). [93] Shea & Artigas (2003, p. 199); Sobel (2000, p. 378); Sharratt (1994, p. 207); Favaro(1906,18:378–80) (Italian).

[118] Thoren (1989), p. 8; Hoskin (1999) p. 117. [119] In the Capellan model only Mercury and Venus orbit the Sun, whilst in its extended version such as expounded by Riccioli, Mars also orbits the Sun, but the orbits of Jupiter and Saturn are centred on the Earth

[94] Monumental tomb of Galileo. Institute and Museum of [120] Baalke, Ron. Historical Background of Saturn’s Rings. the History of Science, Florence, Italy. Retrieved 2010Jet Propulsion Laboratory, California Institute of Tech02-15. nology, NASA. Retrieved on 2007-03-11 [95] Shea & Artigas (2003, p. 199); Sobel (2000, p. 380). [121] Drake & Kowal (1980) [96] Shea & Artigas (2003, p. 200); Sobel (2000, pp. 380– [122] Drake (1978, p. 209). Sizzi reported the observations 384). he and his companions had made over the course of a year to Orazio Morandi in a letter dated 10 April 1613 [97] Section of Room VII Galilean iconography and relics, (Favaro,1901, 11:491) (Italian). Morandi subsequently Museo Galileo. Accessed on line 27 May 2011. forwarded a copy to Galileo. [98] Middle finger of Galileo’s right hand, Museo Galileo. Ac[123] In geostatic systems the apparent annual variation in the cessed on line 27 May 2011. motion of sunspots could only be explained as the result [99] Sharratt (1994, pp. 204–05) of an implausibly complicated precession of the Sun’s axis of rotation (Linton, 2004, p. 212; Sharratt, 1994, p. 166; [100] Cohen, H. F. (1984). Quantifying Music: The Science of Drake, 1970, pp. 191–196). This did not apply, however, Music at. Springer. pp. 78–84. ISBN 90-277-1637-4. to the modified version of Tycho’s system introduced by his protegé, Longomontanus, in which the Earth was as[101] Field, Judith Veronica (2005). Piero Della Francesca: A sumed to rotate. Longomontanus’s system could account Mathematician’s Art. Yale University Press. pp. 317–320. for the apparent motions of sunspots just as well as the ISBN 0-300-10342-5. Copernican. [102] In Drake (1957, pp. 237–238) [124] Ondra (2004), p. 72–73 [103] Wallace, (1984). [125] Graney (2010, p. 455); Graney & Grayson (2011, p. 353). [104] Sharratt (1994, pp. 202–04), Galilei (1954, pp. 250–52), Favaro (1898), 8:274–75 (Italian) [126] Van Helden, (1985, p. 75); Chalmers, (1999, p. 25); Galilei (1953, pp. 361–62). [105] Sharratt (1994, pp. 202–04), Galilei (1954, pp. 252), Favaro (1898), 8:275 (Italian) [127] Finocchiaro (1989, pp. 167–76), Galilei (1953, pp. 359– 60), Ondra (2004, pp. 74–5). [106] King (2003, pp.30–32). The Netherlands States-General would not grant Lippershey his requested patent (King, [128] Graney (2010, p. 454-462); Graney & Grayson (2011, p. 2003, p.32). 352-355). [107] Drake (1990, pp. 133–34). [129] Reston (2000, p. 56). [108] Sharratt (1994, pp. 1–2) [130] Sobel (2000, p. 43), Drake (1978, p. 196). In the Starry [109] See Nicholas Kollerstrom, http://www.dioi.org/kn/ Messenger, written in Latin, Galileo had used the term NewStar.pdf “perspicillum”.


18.13. NOTES

205

[131] Rosen, Edward, The Naming of the Telescope (1947) [132] Drake (1978, pp. 164)(Latin)

[149] Lucretius, De rerum natura II, 225–229; Relevant passage appears in: Lane Cooper, Aristotle, Galileo, and the Tower 163–164), Favaro(1892, 3:163– of Pisa (Ithaca, N.Y.: Cornell University Press, 1935), p. 49.

[133] Probably in 1623, according to Drake (1978, p. 286). [134] Drake (1978, p. 289), Favaro(1903, 13:177) (Italian). [135] Drake (1978, p. 286), Favaro(1903, 13:208) (Italian). The actual inventors of the telescope and microscope remain debatable. A general view on this can be found in the article Hans Lippershey (last updated 2003-08-01), © 1995–2007 by Davidson, Michael W. and the Florida State University. Retrieved 2007-08-28 [136] “brunelleschi.imss.fi.it “Il microscopio di Galileo"" (PDF).

[150] Simon Stevin, De Beghinselen des Waterwichts, Anvang der Waterwichtdaet, en de Anhang komen na de Beghinselen der Weeghconst en de Weeghdaet [The Elements of Hydrostatics, Preamble to the Practice of Hydrostatics, and Appendix to The Elements of the Statics and The Practice of Weighing] (Leiden, Netherlands: Christoffel Plantijn, 1586) reports an experiment by Stevin and Jan Cornets de Groot in which they dropped lead balls from a church tower in Delft; relevant passage is translated in: E. J. Dijksterhuis, ed., The Principal Works of Simon Stevin Amsterdam, Netherlands: C. V. Swets & Zeitlinger, 1955 vol. 1, pp. 509, 511.

[151] [137] Van Helden, Al. Galileo Timeline (last updated 1995), The Galileo Project. Retrieved 2007-08-28. See also [152] Timeline of microscope technology. [153] [138] Drake (1978, p. 286). [139] Longitude: the true story of a lone genius who solved the greatest scientific problem of his time, Dava Sobel Penguin, 1996 ISBN 0-14-025879-5, ISBN 978-0-14-025879-0

Sharratt (1994, p. 203), Galilei (1954, pp. 251–54). Sharratt (1994, p. 198), Galilei (1954, p. 174). Clagett (1968, p. 561). Oresme, however, regarded this discovery as a purely intellectual exercise having no relevance to the description of any natural phenomena, and consequently failed to recognise any connection with the motion of falling bodies (Grant, 1996, p.103).

[154] Sharratt (1994, p. 198), Wallace (2004, pp.II 384, II 400, III 272) Soto, however, did not anticipate many of the qualifications and refinements contained in Galileo’s theory of falling bodies. He did not, for instance, recognise, as Galileo did, that a body would fall with a strictly uni[141] Galileo Galilei, Two New Sciences, (Madison: Univ. of form acceleration only in a vacuum, and that it would othWisconsin Pr., 1974) p. 50. erwise eventually reach a uniform terminal velocity. [140] Newton, R. G. (2004). Galileo’s Pendulum: From the Rhythm of Time to the Making of Matter. Harvard University Press. p. 51. ISBN 0-674-01331-X.

[142] I. Bernard Cohen, “Roemer and the First Determination [155] Jung (2011, p.504). This aspect of Aristotle’s theory of of the Velocity of Light (1676)", Isis, 31 (1940): 327– motion is covered in Books VII and VIII of his Physics. 379, see pp. 332–333 [156] http://oll.libertyfund.org/titles/753#Galileo_0416_799 [143] Drake (1978, pp. 19,20). At the time when Viviani asor Inertia#Classical inertia serts that the experiment took place, Galileo had not yet formulated the final version of his law of free fall. He [157] “Hydrostatic balance”. The Galileo Project. Retrieved 2008-07-17. had, however, formulated an earlier version which predicted that bodies of the same material falling through the same medium would fall at the same speed (Drake, 1978, [158] “The Works of Galileo”. The University of Oklahoma, College of Arts and Sciences. Retrieved 2008-07-17. p. 20). [159] “Sunspots and Floating Bodies”. The University of Oklahoma, College of Arts and Sciences. Archived from the original on 24 October 2008. Retrieved 2008-07-17. [145] Groleau, Rick. “Galileo’s Battle for the Heavens. July 2002”. Ball, Phil (2005-06-30). “Science history: setting [160] “Galileo, Letter to the Grand Duchess Christina”. The the record straight. 30 June 2005”. The Hindu. Chennai, University of Oklahoma, College of Arts and Sciences. India. Retrieved 2008-07-17. [144] Drake (1978, p. 9); Sharratt (1994, p. 31).

[146] Heilbron, John L. (2015), “That Galileo publicly refuted [161] “Galileo’s Theory of the Tides”. The Galileo Project. ReAristotle’s conclusions about motion by repeated expertrieved 2008-07-17. iments made from the campanile of Pisa”, in Numbers, Ronald L.; Kampourakis, Kostas, Newton’s Apple and [162] “Galileo Timeline”. The Galileo Project. Retrieved 2008Other Myths about Science, Harvard University Press, pp. 07-17. 40–47 [163] “Galileo Galilei”. Tel-Aviv University, Science and Tech[147] Drake (1978, pp. 19–21, 414–416) nology Education Center. Retrieved 2008-07-17. [148] Galileo Galilei: The Falling Bodies Experiment. Last ac- [164] “Collection of Galileo Galilei’s Manuscripts and Related cessed 26 Dec 2011. Translations”. Retrieved 2009-12-04.


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[165] Heilbron (2005, p. 299).

[181] Stephen Hawking, Galileo and the Birth of Modern Science, American Heritage’s Invention & Technology, [166] Two of his non-scientific works, the letters to Castelli and Spring 2009, Vol. 24, No. 1, p. 36 the Grand Duchess Christina, were explicitly not allowed [182] Fischer, Daniel (2001). Mission Jupiter: The Spectacular to be included (Coyne 2005, p. 347). Journey of the Galileo Spacecraft. Springer. pp. v. ISBN 0-387-98764-9. [167] Heilbron (2005, pp. 303–04); Coyne (2005, p. 347). The uncensored version of the Dialogue remained on the Index [183] United Nations Educational, Scientific and Cultural Orof prohibited books, however (Heilbron 2005, p. 279). ganization (11 August 2005). “Proclamation of 2009 as International year of Astronomy” (PDF). UNESCO. Re[168] Heilbron (2005, p. 307); Coyne (2005, p. 347) The trieved 2008-06-10. practical effect of the ban in its later years seems to have been that clergy could publish discussions of heliocentric [184] “Bohemian Rhapsody”. everything2. Retrieved 2010-08physics with a formal disclaimer assuring its hypotheti20. cal character and their obedience to the church decrees against motion of the earth: see for example the com- [185] Stavis, Barrie. Lamp at Midnight. South Brunswick, New mented edition (1742) of Newton’s 'Principia' by Fathers Jersey: A.S. Barnes, 1966. Le Seur and Jacquier, which contains such a disclaimer ('Declaratio') before the third book (Propositions 25 on- [186] Lalonde, Robert. Galileo Galilei/Vesalius and Servetus. February 2008. ISBN 978-0-9783909-1-4. wards) dealing with the lunar theory. [187] Robinson, Kim Stanley (2009). Galileo’s Dream. New [169] McMullin (2005, p. 6); Coyne (2005, p. 346). In fact, the York: Ballantine Books. ISBN 978-0-553-80659-5. Church’s opposition had effectively ended in 1820 when a Catholic canon, Giuseppe Settele, was given permission to [188] Giuseppe Moleti, Walter Roy Laird. The unfinished mepublish a work which treated heliocentrism as a physical chanics of Giuseppe Moletti. University of Toronto Press, fact rather than a mathematical fiction. The 1835 edition 1999. p. 5 of the Index was the first to be issued after that year. [189] Robert Henry Herman, Vincenzo Galilei. Dialogo della musica antica et della moderna of Vincenzo Galilei: trans[170] Discourse of His Holiness Pope Pius XII given on 3 Delation and commentary, Part 1. North Texas State Univercember 1939 at the Solemn Audience granted to the Plesity, 1973. p. 17 nary Session of the Academy, Discourses of the Popes from Pius XI to John Paul II to the Pontifical Academy [190] Adam, Mosley. “Tycho Brahe”. Starry Messenger. Hisof the Sciences 1939–1986, Vatican City, p. 34 tory & Philosophy of Science Dept, University of Cambridge. Retrieved 13 January 2012. [171] Robert Leiber, Pius XII Stimmen der Zeit, November 1958 in Pius XII. Sagt, Frankfurt 1959, p. 411

[191] Timothy Ferris. Coming of Age in the Milky Way. William Morrow & Company, Inc. 1988. p. 95

[172] An earlier version had been delivered on 16 December 1989, in Rieti, and a later version in Madrid on 24 Febru- [192] Shea, William; Artigas, Mariano. “The Galileo Affair”. ary 1990 (Ratzinger, 1994, p. 81). According to Feyerabend himself, Ratzinger had also mentioned him “in [193] Galileo Galilei, “Letter to Benedetto Castelli (1613)", Religion and Science. (Source of the English translation.) support of” his own views in a speech in Parma around the same time (Feyerabend, 1995, p. 178). [173] Ratzinger (1994, p. 98). [174] “Vatican admits Galileo was right”. New Scientist (1846). 1992-11-07. Retrieved 2007-08-09.. [175] “Papal visit scuppered by scholars”. BBC News. 200801-15. Retrieved 2008-01-16. [176] Owen & Delaney (2008). [177] “Pope praises Galileo’s astronomy”. BBC News. 200812-21. Retrieved 2008-12-22. [178] Owen (2009). [179] Hawking (1988, p. 179). [180] Einstein (1954, p. 271). “Propositions arrived at by purely logical means are completely empty as regards reality. Because Galileo realised this, and particularly because he drummed it into the scientific world, he is the father of modern physics—indeed, of modern science altogether.”

18.14 References • Allan-Olney, Mary (1870). The Private Life of Galileo: Compiled primarily from his correspondence and that of his eldest daughter, Sister Maria Celeste. Boston: Nichols and Noyes. • Biagi, Altieri; Luisa, Maria (1965). Galileo e la terminologia tecnico-scientifica. FloLCCN 71019084. rence: L. S. Olschki. IT\ICCU\SBL\0272939. • Biagioli, Mario (1993). Galileo, Courtier: The Practice of Science in the Culture of Absolutism. Chicago, IL: University of Chicago Press. ISBN 0-22604559-5. • Blackwell, Richard J. (2006). Behind the Scenes at Galileo’s Trial. Notre Dame, IN: University of Notre Dame Press. ISBN 0-268-02201-1.


18.14. REFERENCES • Brodrick, James, S. J. (1965). Galileo: the man, his work, his misfortunes. London: G. Chapman. • Chalmers, Alan Francis (1999) [1976]. What is this thing called Science? (third ed.). University of Chicago Press. ISBN 978-0-7022-3093-6. • Clagett, Marshall (editor & translator) (196). Nicole Oresme and the Medieval Geometry of Qualities and Motions; a treatise on the uniformity and difformity of intensities known as Tractatus de configurationibus qualitatum et motuum. Madison, WI: University of Wisconsin Press. ISBN 0-299-04880-2. • Clavelin, Maurice (1974). The Natural Philosophy of Galileo. MIT Press. • Coffa, J. (1968). “Galileo’s Concept of Inertia”. Physis Riv. Internaz. Storia Sci. 10: 261–281. • Consolmagno, Guy; Schaefer, Marta (1994). Worlds Apart, A Textbook in Planetary Science. Englewood, New Jersey: Prentice-Hall. ISBN 0-13964131-9. • Cooper, Lane (1935). Aristotle, Galileo, and the Tower of Pisa. Ithaca, NY: Cornell University Press. ISBN 1-4067-5263-0. • Coyne, George V. (2005). The Church’s Most Recent Attempt to Dispel the Galileo Myth. In McMullin. pp. 340–359. • Domínguez, Nuño (28 February 2014). “Una errata reproducida durante siglos cambia la censura de la Iglesia a Galileo”. EsMateria.com. • Drabkin, Israel; Drake, Stillman, eds. (1960). On Motion and On Mechanics. University of Wisconsin Press. ISBN 0-299-02030-4. • Drake, Stillman (1953). Notes to English translation of Galileo’s Dialogue. In Galilei. pp. 467–91. • Drake, Stillman (1957). Discoveries and Opinions of Galileo. New York: Doubleday & Company. ISBN 0-385-09239-3. • Drake, Stillman (1960). “Introduction”. Controversy on the Comets of 1618. In Drake & O'Malley. pp. vii–xxv. • Drake, Stillman (1970). Galileo Studies. Ann Arbor: University of Michigan Press. ISBN 0-47208283-3. • Drake, Stillman (1973). “Galileo’s Discovery of the Law of Free Fall”. Scientific American. 228 (5): 84– 92. doi:10.1038/scientificamerican0573-84. • Drake, Stillman (1978). Galileo At Work. Chicago: University of Chicago Press. ISBN 0-226-16226-5.

207 • Drake, Stillman (1990). Galileo: Pioneer Scientist. Toronto: The University of Toronto Press. ISBN 0-8020-2725-3. • Drake, Stillman; Kowal, C. T. (1980). “Galileo’s Sighting of Neptune”. Scientific American. 243 (6): 74–81. doi:10.1038/scientificamerican1280-74. • Dugas, René (1988) [1955]. A History of Mechanics. Dover Publications. ISBN 0-486-65632-2. • Duhem, Pierre (1906–1913). Études sur Leonard de Vinci. • Duhem, Pierre (1913). Le Système du Monde. • Duhem, Pierre. “History of Physics”. Catholic Encyclopedia. • Einstein, Albert (1953). “Foreword”. In Drake, Stillman. Dialogue Concerning the Two Chief World Systems. Berkeley, CA: University of California Press. ISBN 0-375-75766-X. • Einstein, Albert (1954). Ideas and Opinions. Translated by Bargmann, Sonja. London: Crown Publishers. ISBN 0-285-64724-5. • Fantoli, Annibale (2003). Galileo: For Copernicanism and the Church (third English ed.). Vatican Observatory Publications. ISBN 88-209-7427-4. • Fantoli, Annibale (2005). The Disputed Injunction and its Role in Galileo’s Trial. In McMullin. pp. 117–149. • Favaro, Antonio, ed. (1890–1909). Le Opere di Galileo Galilei, Edizione Nazionale [The Works of Galileo Galilei, National Edition] (in Italian). Florence: Barbera. ISBN 88-09-20881-1. Reprinted 1929–1939 and 1964–1966. A searchable online copy is available on the Institute and Museum of the History of Science, Florence, and a brief overview of Le Opere is available here at the Wayback Machine (archived 3 January 2011). • Feyerabend, Paul (1975). Againat Method. Verso. • Feyerabend, Paul (1995). Killing Time: The Autobiography of Paul Feyerabend. Chicago, MI: University of Chicago Press. ISBN 0-226-24531-4. • Fillmore, Charles (July 2004) [1931]. Metaphysical Bible Dictionary (17th ed.). Unity Village, Missouri: Unity House. ISBN 0-87159-067-0. • Finocchiaro, Maurice (2010). Defending Copernicus and Galileo: Critical Reasoning in the two Affairs. Springer. ISBN 978-9048132003. • Finocchiaro, Maurice A. (1997). Galileo on the world systems: a new abridged translation and guide. Berkeley and Los Angeles, CA: University of California Press. ISBN 0-520-20548-0.


208 • Finocchiaro, Maurice A. (1989). The Galileo Affair: A Documentary History. Berkeley, CA: University of California Press. ISBN 0-520-06662-6. • Finocchiaro, Maurice A. (Fall 2007). “Book Review—The Person of the Millennium: The Unique Impact of Galileo on World History”. The Historian. 69 (3): 601–602. doi:10.1111/j.15406563.2007.00189_68.x. • Galilei, Galileo (1960) [1623]. “The Assayer”. The Controversy on the Comets of 1618. Translated by Drake, Stillman. In Drake & O'Malley. pp. 151– 336. ISBN 1-158-34578-X. • Galilei, Galileo (1953) [1632]. Dialogue Concerning the Two Chief World System. Translated by Drake, Stillman. Berkeley, CA: University of California Press. ISBN 0-520-00449-3. • Galilei, Galileo (1954) [1638, 1914]. Crew, Henry; de Salvio, Alfonso, eds. Dialogues Concerning Two New Sciences. New York, NY: Dover Publications Inc. ISBN 0-486-60099-8. • Galilei, Galileo (1974). “Galileo’s 1638 Discourses and mathematical demonstrations concerning two new sciences". Galileo: Two New Sciences. Translated by Drake, Stillman. University of Wisconsin Press. ISBN 0-299-06400-X. • Galilei, Galileo & Guiducci, Mario (1960) [1619]. “Discourse on the Comets”. The Controversy on the Comets of 1618. Translated by Drake, Stillman. In Drake & O'Malley. pp. 21–65. • Galilei, Galileo; Scheiner, Christoph (2010). On Sunspots. Translated by Reeves, Eileen; Helden, Albert Van. Chicago: University of Chicago Press. ISBN 978-0-226-70715-0. • Gebler, Karl von (1879). Galileo Galilei and the Roman Curia. London: C.K. Paul & Co. ISBN 0915172-11-9. • Geymonat, Ludovico (1965). Galileo Galilei, A biography and inquiry into his philosophy and science. Translated by Drake, Stillman. McGraw-Hill. • Gingerich, Owen (1992). The Great Copernican Chase and other adventures in astronomical history. Cambridge, MA: Cambridge University Press. ISBN 0-521-32688-5. • Graney, Christopher (2015). Setting Aside All Authority: Giovanni Battista Riccioli and the Science against Copernicus in the Age of Galileo. Notre Dame, IN: University of Notre Dame Press. ISBN 978-0-268-02988-3. • Graney, Christopher M. (2010). “The Telescope Against Copernicus: Star Observations by Riccioli Supporting a Geocentric Universe”. Journal

CHAPTER 18. GALILEO GALILEI for the History of Astronomy. 41 (4): 453–467. Bibcode:2010JHA....41..453G. • Graney, Christopher M.; Danielson, Dennis (2014), “The Case Against Copernicus”, Scientific American, 310 (1): 72–77 • Graney, Christopher M.; Grayson, Timothy P. (2011). “On the Telescopic Disks of Stars: A Review and Analysis of Stellar Observations from the Early Seventeenth through the Middle Nineteenth Centuries”. Annals of Science. 68 (3): 351–373. doi:10.1080/00033790.2010.507472. • Grant, Edward (1996). The Foundations of Modern Science in the Middle Ages: Their Religious, Institutional, and Intellectual Contexts. Cambridge, UK: Cambridge University Press. ISBN 0-521-56762-9. • Grant, Edward (1965–1967). “Aristotle, Philoponus, Avempace, and Galileo’s Pisan Dynamics”. Centaurus. 11. • Grassi, Horatio (1960a) [1619]. “On the Three Comets of the Year MDCXIII”. Introduction to the Controversy on the Comets of 1618. Translated by O'Malley, C.D.. In Drake & O'Malley. pp. 3–19. • Grassi, Horatio (1960b) [1619]. “The Astronomical and Philosophical Balance”. Introduction to the Controversy on the Comets of 1618. Translated by O'Malley, C.D.. In Drake & O'Malley. pp. 67–132. • Grassi H, Guiducci M, Galilei G (1960) [1619, 1623]. The Controversy on the Comets of 1618. Translated by Drake S, O'Malley C. Philadelphia, PA: University of Pennsylvania Press. • Grisar, Hartmann (Professor of Church history at the University of Innsbruck) (1882). Historisch theologische Untersuchungen über die Urtheile römischen Congregationen im Galileiprocess (Historicotheological Discussions concerning the Decisions of the Roman Congregations in the case of Galileo). Regensburg: Pustet,. pp. 211–213. ISBN 0-79056229-4. • Hall, A. R. (1963). 'From Galileo to Newton. • Hall, A. R. (1964–1965). “Galileo and the Science of Motion”. British Journal for the History of Science. 2. • Hilliam, R. (2005). “Galileo Galilei: Father of modern science”. The Rosen Publishing Group: 96. ISBN 1-4042-0314-1. • Hoskin, Michael, ed. (1999). The Cambridge concise history of astronomy Cambridge University Press. • Hawking, Stephen (1988). A Brief History of Time. New York, NY: Bantam Books. ISBN 0-55334614-8.


18.14. REFERENCES • Heilbron, John L. (2005). Censorship of Astronomy in Italy after Galileo. In McMullin. pp. 279–322. Hellman, Hal (1988). Great Feuds in Science. Ten of the Liveliest Disputes Ever. New York: Wiley. • Heilbron, John L. (2010). Galileo. New York, NY: Oxford University Press. ISBN 978-0-19-9583522. • Humphreys, W. C. (1967). “Galileo, Falling Bodies and Inclined Planes. An Attempt at Reconstructing Galileo’s Discovery of the Law of Squares”. British Journal for the History of Science. • Jarrel, Richard A. (1989). The contemporaries of Tycho Brahe. In Taton and Wilson. pp. 22–32. • Jung, Elzbieta (2011). "Impetus". In Lagerlund, Henrik. Encyclopedia of Medieval Philosophy: Philosophy Between 500 and 1500. Volume 1. pp. 540–542. ISBN 978-1-4020-9728-7. • Kelter, Irving A. (2005) [1955]. The Refusal to Accommodate. Jesuit Exegetes and the Copernican System. In McMullin. pp. 38–53. • King, Charles C. (2003). The History of the Telescope (Dover reprint ed.). Dover Publications. ISBN 0-486-43265-3. • Koestler, Arthur (1990) [1959]. The Sleepwalkers: A History of Man’s Changing Vision of the Universe. Penguin. ISBN 0-14-019246-8. Original edition published by Hutchinson (1959, London). • Koyré, Alexandre (1955). “A Documentary History of the Problem of Fall from Kepler to Newton”. Transactions of the American Philosophical Society. • Koyré, Alexandre (1978). Galilean Studies. Harvester Press. • Kuhn, Thomas (1957). The Copernican Revolution. • Kuhn, Thomas (1962). The Structure of Scientific Revolutions. • Lattis, James M. (1994). Between Copernicus and Galileo: Christopher Clavius and the Collapse of Ptolemaic Cosmology. Chicago: University of Chicago Press. • Langford, Jerome K. (1998) [1966]. Galileo, Science and the Church (third ed.). St. Augustine’s Press. ISBN 1-890318-25-6.. Original edition by Desclee (New York, NY, 1966) • Lessl, Thomas (June 2000). “The Galileo Legend”. New Oxford Review: 27–33.

209 • Linton, Christopher M. (2004). From Eudoxus to Einstein—A History of Mathematical Astronomy. Cambridge: Cambridge University Press. ISBN 978-0-521-82750-8. • Losee, J. (1966). “Drake, Galileo, and the Law of Inertia”. American Journal of Physics. 34: 430–432. Bibcode:1966AmJPh..34..430L. doi:10.1119/1.1973014. • McMullin, Ernan, ed. (2005). The Church and Galileo. Notre Dame, IN: University of Notre Dame Press. ISBN 0-268-03483-4. • McMullin, Ernan (2005a). The Church’s Ban on Copernicanism, 1616. In McMullin. pp. 150–190. • Mach, Ernst (1893). The Science of Mechanics. • Machamer, Peter, ed. (1998). The Cambridge Companion to Galileo. Cambridge University Press. • Moss, Jean Dietz; Wallace, William (2003). Rhetoric & dialectic in the time of Galileo. Washington D.C.: CUA Press. ISBN 0-8132-1331-2. • Naylor, Ronald H. (1990). “Galileo’s Method of Analysis and Synthesis”. Isis. 81: 695–707. doi:10.1086/355546. • Newall, Paul (2004). “The Galileo Affair”. • Ondra, Leos (July 2004). “A New View of Mizar”. Sky & Telescope. 108: 72–75. Bibcode:2004S&T...108a..72O. • Owen, Richard (29 January 2009). “Catholic Church abandons plan to erect statue of Galileo”. London: TimesOnline News. Retrieved 2011-0422. • Owen, Richard; Delaney, Sarah (2008-03-04). “Vatican recants with a statue of Galileo”. TimesOnline News. London. Retrieved 2009-03-02. • Remmert, Volker R. (2005). “Galileo, God, and Mathematics”. In Koetsier, Teun; Bergmans, Luc. Mathematics and the Divine. A Historical Study. Amsterdam: Elsevier. pp. 347–360. • Ratzinger, Joseph Cardinal (1994). Turning point for Europe? The Church in the Modern World— Assessment and Forecast. Translated by McNeil, Brian. San Francisco, CA: Ignatius Press. ISBN 0-89870-461-8. OCLC 60292876. translated from the 1991 German edition • Reston, Jr., James (2000). Galileo: A Life. Beard Books. ISBN 1-893122-62-X. • Seeger, Raymond J. (1966). Galileo Galilei, his life and his works. Oxford: Pergamon Press. ISBN 008-012025-3.


210 • Settle, Thomas B. (1961). “An Experiment in the History of Science”. Science. 133 (3445): 19–23. Bibcode:1961Sci...133...19S. doi:10.1126/science.133.3445.19. PMID 17759858. • Sharratt, Michael (1994). Galileo: Decisive Innovator. Cambridge: Cambridge University Press. ISBN 0-521-56671-1. • Shapere, Dudley (1974). Galileo, a Philosophical Study. University of Chicago Press. • Shea, William R. & Artigas, Mario (2003). Galileo in Rome: The Rise and Fall of a Troublesome Genius. Oxford: Oxford University Press. ISBN 0-19516598-5.

CHAPTER 18. GALILEO GALILEI • White, Michael (2007). Galileo: Antichrist: A Biography. London: Weidenfeld & Nicolson. ISBN 978-0-297-84868-4. • Wisan, Winifred Lovell (1984). “Galileo and the Process of Scientific Creation”. Isis. 75 (2): 269– 286. doi:10.1086/353480. • Zik, Yaakov (2001). “Science and Instruments: The telescope as a scientific instrument at the beginning of the seventeenth century”. Perspectives on Science. 9 (3): 259–284. doi:10.1162/10636140160176143.

18.15 External links

• Sobel, Dava (2000) [1999]. Galileo’s Daughter. 18.15.1 London: Fourth Estate. ISBN 1-85702-712-4.

By Galileo

• Taton, René, ed. (1964) [1958]. The Beginnings of Modern Science from 1450 to 1800. London: Thames and Hudson.

• Works by Galileo Galilei at Project Gutenberg

• Taton, René; Wilson, Curtis, eds. (1989). Planetary astronomy from the Renaissance to the rise of astrophysics Part A: Tycho Brahe to Newton. Cambridge: Cambridge University Press. ISBN 0-521-24254-1.

• Works by Galilei Galileo at LibriVox (public domain audiobooks)

• Thoren, Victor E. (1989). “Tycho Brahe”. In Taton, René; Wilson, Curtis. Planetary astronomy from the Renaissance to the rise of astrophysics Part A: Tycho Brahe to Newton. In Taton and Wilson. pp. 3–21. ISBN 0-521-35158-8. • Van Helden, Albert (1989). “Galileo, telescopic astronomy, and the Copernican system”. In Taton, René; Wilson, Curtis. Planetary astronomy from the Renaissance to the rise of astrophysics Part A: Tycho Brahe to Newton. In Taton and Wilson. pp. 81–105. • Van Helden, Albert (1985). Measuring the Universe: Cosmic Dimensions from Aristarchus to Halley. University of Chicago Press. ISBN 0-226-84881-7. • Wallace, William A. (1984). Galileo and His Sources: The Heritage of the Collegio Romano in Galileo’s Science. Princeton, NJ: Princeton Univ. ISBN 0-691-08355-X.

• Works by or about Galileo at Internet Archive

• Electronic representation of Galilei’s notes on motion (MS. 72) • Galileo’s 1590 De Motu translation • Works by Galileo Galilei: text with concordances and frequencies. • Galilei, Galileo. Le Operazioni del Compasso Geometrico et Militare, Rome, 1610. From the Rare Book and Special Collections Division at the Library of Congress • Galilei, Galileo. Istoria e Dimostrazioni Intorno Alle Macchie Solar, Rome, 1613. From the Rare Book and Special Collections Division at the Library of Congress • Linda Hall Library features a first edition of Sidereus Nuncius Magna as well as a pirated edition from the same year, both fully digitised. • Sidereus Nuncius from the Collections at the Library of Congress

• Wallace, William A. (2004). Domingo de Soto and the Early Galileo. Aldershot: Ashgate Publishing. ISBN 0-86078-964-0. 18.15.2 • Walusinsky, G. (1964) [1958]. “The Golden age of Observational Astronomy”. In Taton, René. The Beginnings of Modern Science from 1450 to 1800. In Taton. pp. 268–286. • White, Andrew Dickson (1898). A History of the Warfare of Science with Theology in Christendom. New York: D. Appleton and Company. ISBN 07905-8168-X.

On Galileo

• Starry Messenger: Observing the Heavens in the Age of Galileo—an exhibition at the Beinecke Rare Book and Manuscript Library at Yale University • Museo Galileo—Florence, Italy • Galileo’s math genealogy • Portraits of Galileo


18.15. EXTERNAL LINKS

211

• The Galileo Project at Rice University • PBS documentary: 400 Years of the Telescope • Feather & Hammer Drop on Moon on YouTube • article by UK journalist on proposed disinterment to determine Galileo’s eyesight problems • “Galileo, The Starry Messenger” (NYT, 18 January 2013). Biography • Full text of Galileo. by Walter Bryant (public domain biography) • PBS Nova Online: Galileo’s Battle for the Heavens • Stanford Encyclopedia of Philosophy entry on Galileo • Animated Hero Classics: Galileo (1997) Internet Movie Database

at the

• O'Connor, John J.; Robertson, Edmund F., “Galileo Galilei”, MacTutor History of Mathematics archive, University of St Andrews. Galileo and the Church • Galileo Galilei, Scriptural Exegete, and the Church of Rome, Advocate of Science lecture (audio here) by Thomas Aquinas College tutor Dr. Christopher Decaen • "The End of the Myth of Galileo Galilei" by Atila Sinke Guimarães • Galileo and the Church, article by John Heilbron. • Galileo Affair catholic.net at the Wayback Machine (archived 9 December 2007)


Chapter 19

Heliocentrism “Heliocentric” redirects here. For the albums, see Heliocentric (Paul Weller album) and Heliocentric (The Ocean Collective album). For heliocentric orbit, see Heliocentric orbit. Heliocentrism, or heliocentricism,[1] is the

Bessel, and others, astronomers realized that the sun, although the center of Earth’s solar system, was not the center of the universe. And even more recent thinking is that there is no specific location that is the center of the universe, per Albert Einstein's principle of relativity.

19.1 Early developments Geocentric model

Earth Moon Mercury Venus Sun Mars Jupiter Saturn

Heliocentrism

Andreas Cellarius’s illustration of the Copernican system, from the Harmonia Macrocosmica (1708).

astronomical model in which the Earth and planets revolve around the Sun at the center of the Solar System. The word comes from the Greek (ἥλιος helios “sun” and κέντρον kentron “center”). Historically, Heliocentrism was opposed to geocentrism, which placed the Earth at the center. The notion that the Earth revolves around the Sun had been proposed as early as the 3rd century BC by Aristarchus of Samos,[2] but at least in the medieval world, Aristarchus’s Heliocentrism attracted little attention—possibly because of the loss of scientific works of the Hellenistic Era.[3]

A hypothetical geocentric model of the solar system (upper panel) in comparison to the heliocentric model (lower panel).

To anyone who stands and looks up at the sky, it seems that the Earth stays in one place, while everything in the sky rises in the east and sets in the west once a day. However, with more scrutiny one will observe more complicated movements. The positions at which the Sun and moon rise change over the course of a year, some planIt was not until the 16th century that a geometric ets and stars do not appear at all for many months, and mathematical model of a heliocentric system was pre- planets sometimes appear to have moved in the reverse sented, by the Renaissance mathematician, astronomer, direction for a while, relative to the background stars. and Catholic cleric Nicolaus Copernicus, leading to As these motions became better understood, more elabothe Copernican Revolution. In the following century, rate descriptions were required, the most famous of which Johannes Kepler elaborated upon and expanded this was the geocentric Ptolemaic system, which achieved its model to include elliptical orbits, and Galileo Galilei pre- full expression in the 2nd century. The Ptolemaic system sented supporting observations made using a telescope. was a sophisticated astronomical system that managed to With the observations of William Herschel, Friedrich calculate the positions for the planets to a fair degree of 212


19.1. EARLY DEVELOPMENTS

213

accuracy.[4] Ptolemy himself, in his Almagest, points out that any model for describing the motions of the planets is merely a mathematical device, and since there is no actual way to know which is true, the simplest model that gets the right numbers should be used.[5] However, he rejected the idea of a spinning earth as absurd as he believed it would create huge winds. His planetary hypotheses were sufficiently real that the distances of moon, sun, planets and stars could be determined by treating orbits’ celestial spheres as contiguous realities. This made the stars’ distance less than 20 Astronomical Units,[6] a regression, since Aristarchus of Samos's heliocentric scheme had centuries earlier necessarily placed the stars Aristarchus’s 3rd century BC calculations on the relative sizes of at least two orders of magnitude more distant. the Earth, Sun and Moon, from a 10th-century CE Greek copy

19.1.1

Greek and Hellenistic world

See also: Greek astronomy

Pythagoreans The non-geocentric model of the Universe was proposed by the Pythagorean philosopher Philolaus (d. 390 BC), who taught that at the center of the Universe was a “central fire”, around which the Earth, Sun, Moon and Planets revolved in uniform circular motion. This system postulated the existence of a counter-earth collinear with the Earth and central fire, with the same period of revolution around the central fire as the Earth. The Sun revolved around the central fire once a year, and the stars were stationary. The Earth maintained the same hidden face towards the central fire, rendering both it and the “counter-earth” invisible from Earth. The Pythagorean concept of uniform circular motion remained unchallenged for approximately the next 2000 years, and it was to the Pythagoreans that Copernicus referred to show that the notion of a moving Earth was neither new nor revolutionary.[7] Kepler gave an alternative explanation of the Pythagoreans’ “central fire” as the Sun, “as most sects purposely hid[e] their teachings”.[8] Heraclides of Pontus (4th century BC) said that the rotation of the Earth explained the apparent daily motion of the celestial sphere. It used to be thought that he believed Mercury and Venus to revolve around the Sun, which in turn (along with the other planets) revolves around the Earth.[9] Macrobius Ambrosius Theodosius (AD 395–423) later described this as the “Egyptian System,” stating that “it did not escape the skill of the Egyptians,” though there is no other evidence it was known in ancient Egypt.[10][11] Aristarchus of Samos

Like Eratosthenes, Aristarchus calculated the size of the Earth, and measured the size and distance of the Moon and Sun, in a treatise which has survived. From his estimates, he concluded that the Sun was six to seven times wider than the Earth and thus hundreds of times more voluminous. His writings on the heliocentric system are lost, but some information is known from surviving descriptions and critical commentary by his contemporaries, such as Archimedes. Some have suggested that his calculation of the relative size of the Earth and Sun led Aristarchus to conclude that it made more sense for the Earth to be moving than for the huge Sun to be moving around it. Though the original text has been lost, a reference in Archimedes' book The Sand Reckoner describes another work by Aristarchus in which he advanced an alternative hypothesis of the heliocentric model. Archimedes wrote: You King Gelon are aware the 'universe' is the name given by most astronomers to the sphere the center of which is the center of the Earth, while its radius is equal to the straight line between the center of the Sun and the center of the Earth. This is the common account as you have heard from astronomers. But Aristarchus has brought out a book consisting of certain hypotheses, wherein it appears, as a consequence of the assumptions made, that the universe is many times greater than the 'universe' just mentioned. His hypotheses are that the fixed stars and the Sun remain unmoved, that the Earth revolves about the Sun on the circumference of a circle, the Sun lying in the middle of the orbit, and that the sphere of fixed stars, situated about the same center as the Sun, is so great that the circle in which he supposes the Earth to revolve bears such a proportion to the distance of the fixed stars as the center of the sphere bears to its surface.[12]

The first person known to have proposed a heliocentric Aristarchus believed the stars to be very far away, and system, however, was Aristarchus of Samos (c. 270 BC). saw this as the reason why there was no visible parallax,


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that is, an observed movement of the stars relative to each other as the Earth moved around the Sun. The stars are in fact much farther away than the distance that was generally assumed in ancient times, which is why stellar parallax is only detectable with telescopes. Archimedes says that Aristarchus made the stars’ distance larger, suggesting that he was answering the natural objection that Heliocentrism requires stellar parallactic oscillations. He apparently agreed to the point but placed the stars so distant as to make the parallactic motion invisibly minuscule. Thus Heliocentrism opened the way for realization that the universe was larger than the geocentrists taught.[13]

Seleucus of Seleucia Since Plutarch mentions the “followers of Aristarchus” in passing, it is likely that there were other astronomers in the Classical period who also espoused Heliocentrism, but whose work was lost. The only other astronomer from antiquity known by name who is known to have supported Aristarchus’ heliocentric model was Seleucus of Seleucia (b. 190 BC), a Hellenistic astronomer who flourished a century after Aristarchus in the Seleucid empire.[14] Seleucus adopted the heliocentric system of Aristarchus and is said to have proved the heliocentric theory.[15] According to Bartel Leendert van der Waerden, Seleucus may have proved the heliocentric theory by determining the constants of a geometric model for the heliocentric theory and by developing methods to compute planetary positions using this model. He may have used early trigonometric methods that were available in his time, as he was a contemporary of Hipparchus.[16] A fragment of a work by Seleucus has survived in Arabic translation, which was referred to by Rhazes (b. 865).[17] Alternatively, his explanation may have involved the phenomenon of tides,[18] which he supposedly theorized to be caused by the attraction to the Moon and by the revolution of the Earth around the Earth-Moon 'center of mass’.

19.1.2

Medieval Europe

There were occasional speculations about Heliocentrism in Europe before Copernicus. In Roman Carthage, the pagan Martianus Capella (5th century A.D.) expressed the opinion that the planets Venus and Mercury did not go about the Earth but instead circled the Sun.[19] Capella’s model was discussed in the Early Middle Ages by various anonymous 9th-century commentators[20] and Copernicus mentions him as an influence on his own work.[21] During the Late Middle Ages, Bishop Nicole Oresme discussed the possibility that the Earth rotated on its axis, while Cardinal Nicholas of Cusa in his Learned Ignorance asked whether there was any reason to assert that

Nicholas of Cusa, 15th century, asked whether there was any reason to assert that any point was the center of the universe.

the Sun (or any other point) was the center of the universe. In parallel to a mystical definition of God, Cusa wrote that “Thus the fabric of the world (machina mundi) will quasi have its center everywhere and circumference nowhere.”[22]

19.1.3 India See also: Indian astronomy and Hindu cosmology Aryabhata (476–550), in his magnum opus Aryabhatiya (499), propounded a planetary model in which the Earth was taken to be spinning on its axis and the periods of the planets were given with respect to the Sun. He accurately calculated many astronomical constants, such as the periods of the planets, times of the solar and lunar eclipses, and the instantaneous motion of the Moon.[23][24] Early followers of Aryabhata’s model included Varahamihira, Brahmagupta, and Bhaskara II. Nilakantha Somayaji (1444–1544), in his Aryabhatiyabhasya, a commentary on Aryabhata’s Aryabhatiya, developed a computational system for a partially heliocentric planetary model, in which the planets orbit the Sun, which in turn orbits the Earth, similar to the Tychonic system later proposed by Tycho Brahe in the late 16th century. In the Tantrasangraha (1500), he further revised his planetary system, which was mathematically more accurate at predicting the heliocentric orbits of the interior planets than both the Tychonic and Copernican models,[23][25] but like Indian astronomy in general fell short of proposing models of the universe.[26] Nilakan-


19.2. COPERNICAN REVOLUTION tha’s planetary system also incorporated the Earth’s rotation on its axis.[27] Most astronomers of the Kerala school of astronomy and mathematics seem to have accepted his planetary model.[28][29]

19.1.4

Medieval Islamic world

215 Masudic Canon, he set forth the principles that the Earth is at the center of the universe and that it has no motion of its own.[40] He was aware that if the Earth rotated on its axis, this would be consistent with his astronomical parameters,[41] but he considered it a problem of natural philosophy rather than mathematics.[36][42]

In the 12th century, some Islamic astronomers developed See also: Astronomy in medieval Islam and Islamic cos- complete alternatives to the Ptolemaic system (although not heliocentric), such as Nur ad-Din al-Bitruji, who mology Ptolemaic model as mathematical, and Muslim astronomers generally accepted the Ptolemaic considered the not physical.[43][44] Al-Bitruji’s alternative system spread through most of Europe in the 13th century, with debates and refutations of his ideas continued up to the 16th century.[44]

An illustration from al-Biruni's astronomical works, explains the different phases of the moon, with respect to the position of the sun. Al-Biruni suggested that if the Earth rotated on its axis this would be consistent with astronomical theory. He discussed Heliocentrism but considered it a problem of natural philosophy.

system and the geocentric model,[30] but by the 10th century texts appeared regularly whose subject matter was doubts concerning Ptolemy (shukūk).[31] Several Muslim scholars questioned the Earth’s apparent immobility[32][33] and centrality within the universe.[34] Some accepted that the Earth rotates around its axis, such as the 10th-century astronomer Abu Sa'id al-Sijzi (d. circa 1020).[35][36] According to Al-Biruni, Sijzi invented an astrolabe called al-zūraqī based on a belief held by some of his contemporaries “That the motion we see is due to the Earth’s movement and not to that of the sky.”[36][37] The prevalence of this view is further confirmed by a reference from the 13th century which states: According to the Geometers [or engineers] (muhandisīn), the earth is in constant circular motion, and what appears to be the motion of the heavens is actually due to the motion of the earth and not the stars.[36] Early in the 11th century Alhazen wrote a scathing critique of Ptolemy's model in his Doubts on Ptolemy (c. 1028), which some have interpreted to imply he was criticizing Ptolemy’s geocentrism,[38] but most agree that he was actually criticizing the details of Ptolemy’s model rather than his geocentrism.[39] Abu Rayhan Biruni (b. 973) discussed the possibility of whether the Earth rotated about its own axis and around the Sun, but in his

At the Maragha and Samarkand observatories, the Earth’s rotation was discussed by al-Kātibī (d. 1277),[45] Tusi (b. 1201) and Qushji (b. 1403). The arguments and evidence used by Tusi and Qushji resemble those used by Copernicus to support the Earth’s motion.[32][33] However, it remains a fact that the Maragha school never made the big leap to Heliocentrism.[46] Some historians maintain that the thought of the Maragha school influenced Copernicus, in particular the mathematical devices known as the Urdi lemma and the Tusi couple.[42][47][48][49][50] Copernicus used such devices in the same planetary models as found in Arabic sources.[51] Furthermore, the exact replacement of the equant by two epicycles used by Copernicus in the Commentariolus was found in an earlier work by Ibn alShatir (d. c. 1375) of Damascus.[52] Ibn al-Shatir’s lunar and Mercury models are also identical to those of Copernicus.[53] However, this remains speculative as no researcher has yet proven that Copernicus knew about Ibn al-Shatir’s work or the Maragha school.[46][54][55] It has been argued that Copernicus could have independently discovered the Tusi couple or took the idea from Proclus's Commentary on the First Book of Euclid,[56] which Copernicus cited.[57] Another possible source for Copernicus’s knowledge of this mathematical device is the Questiones de Spera of Nicole Oresme, who described how a reciprocating linear motion of a celestial body could be produced by a combination of circular motions similar to those proposed by al-Tusi.[58] Nevertheless, Copernicus cited some of the Islamic astronomers whose theories and observations he used in De Revolutionibus, namely al-Battani, Thabit ibn Qurra, al-Zarqali, Ibn Rushd, and al-Bitruji.[59]

19.2 Copernican revolution 19.2.1 Astronomical model Main articles: Copernican heliocentrism and Copernican revolution In the 16th century, Nicolaus Copernicus's De revolutionibus presented a discussion of a heliocentric model of the universe in much the same way as Ptolemy's Almagest


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19.2.2 Religious attitudes to Heliocentrism Heliocentrism had been in conflict with religion before Copernicus. One of the few pieces of information we have about the reception of Aristarchus’s heliocentric system comes from a passage in Plutarch's dialogue, Concerning the Face which Appears in the Orb of the Moon. According to one of Plutarch’s characters in the dialogue, the philosopher Cleanthes had held that Aristarchus should be charged with impiety for “moving the hearth of the world”.[63]

Circulation of Commentariolus (before 1515) The first information about the heliocentric views of Nicolaus Copernicus was circulated in manuscript completed some time before May 1, 1514.[64] Although only in manuscript, Copernicus’ ideas were well known among astronomers and others. His ideas contradicted the thenNicolaus Copernicus, 16th century, described the first computa- prevailing understanding of the Bible. In the King James Bible First Chronicles 16:30 state that “the world also tional system explicitly tied to a heliocentric model shall be stable, that it be not moved.” Psalm 104:5 says, "[the Lord] Who laid the foundations of the earth, that it should not be removed for ever.” Ecclesiastes 1:5 states that “The sun also ariseth, and the sun goeth down, and had presented his geocentric model in the 2nd century. hasteth to his place where he arose.” Copernicus discussed the philosophical implications of his proposed system, elaborated it in geometrical detail, Nonetheless, in 1533, Johann Albrecht Widmannstetter used selected astronomical observations to derive the pa- delivered in Rome a series of lectures outlining Coperby rameters of his model, and wrote astronomical tables nicus’ theory. The lectures were heard with interest [65] Pope Clement VII and several Catholic cardinals. On which enabled one to compute the past and future positions of the stars and planets. In doing so, Copernicus November 1, 1536, Archbishop of Capua Nikolaus von moved Heliocentrism from philosophical speculation to Schönberg wrote a letter to Copernicus from Rome enpredictive geometrical astronomy. In reality, Coperni- couraging him to publish a full version of his theory. cus’s system did not predict the planets’ positions any bet- However, in 1539, Martin Luther said: ter than the Ptolemaic system.[60] This theory resolved the issue of planetary retrograde motion by arguing that such motion was only perceived and apparent, rather than real: “There is talk of a new astrologer who it was a parallax effect, as an object that one is passing wants to prove that the earth moves and goes seems to move backwards against the horizon. This isaround instead of the sky, the sun, the moon, sue was also resolved in the geocentric Tychonic system; just as if somebody were moving in a carriage the latter, however, while eliminating the major epicycles, or ship might hold that he was sitting still and retained as a physical reality the irregular back-and-forth at rest while the earth and the trees walked and motion of the planets, which Kepler characterized as a moved. But that is how things are nowadays: "pretzel".[61] when a man wishes to be clever he must . . . inCopernicus cited Aristarchus in an early (unpublished) manuscript of De Revolutionibus (which still survives), stating: “Philolaus believed in the mobility of the earth, and some even say that Aristarchus of Samos was of that opinion.”[62] However, in the published version he restricts himself to noting that in works by Cicero he had found an account of the theories of Hicetas and that Plutarch had provided him with an account of the Pythagoreans Heraclides Ponticus, Philolaus, and Ecphantus. These authors had proposed a moving earth, which did not, however, revolve around a central sun.

vent something special, and the way he does it must needs be the best! The fool wants to turn the whole art of astronomy upside-down. However, as Holy Scripture tells us, so did Joshua bid the sun to stand still and not the earth.”[66]

This was reported in the context of a conversation at the dinner table and not a formal statement of faith. Melanchthon, however, opposed the doctrine over a period of years.[67][68]


19.2. COPERNICAN REVOLUTION Publication of de Revolutionibus (1543) Nicolaus Copernicus published the definitive statement of his system in De Revolutionibus in 1543. Copernicus began to write it in 1506 and finished it in 1530, but did not publish it until the year of his death. Although he was in good standing with the Church and had dedicated the book to Pope Paul III, the published form contained an unsigned preface by Osiander defending the system and arguing that it was useful for computation even if its hypotheses were not necessarily true. Possibly because of that preface, the work of Copernicus inspired very little debate on whether it might be heretical during the next 60 years. There was an early suggestion among Dominicans that the teaching of Heliocentrism should be banned, but nothing came of it at the time. Some years after the publication of De Revolutionibus John Calvin preached a sermon in which he denounced those who “pervert the order of nature” by saying that “the sun does not move and that it is the earth that revolves and that it turns”.[69] On the other hand, Calvin is not responsible for another famous quotation which has often been misattributed to him: “Who will venture to place the authority of Copernicus above that of the Holy Spirit?" It has long been established that this line cannot be found in any of Calvin’s works.[70][71][72] It has been suggested[73] that the quotation was originally sourced from the works of Lutheran theologian Abraham Calovius.

Tycho Brahe’s geo-heliocentric system c. 1587

In this depiction of the Tychonic system, the objects on blue orbits (the Moon and the Sun) revolve around the Earth. The objects on orange orbits (Mercury, Venus, Mars, Jupiter, and Saturn) revolve around the Sun. Around all is a sphere of fixed stars, located just beyond Saturn.

217 Prior to the publication of De Revolutionibus, the most widely accepted system had been proposed by Ptolemy, in which the Earth was the center of the universe and all celestial bodies orbited it. Tycho Brahe, arguably the most accomplished astronomer of his time, advocated against Copernicus’s heliocentric system and for an alternative to the Ptolemaic geocentric system: a geo-heliocentric system now known as the Tychonic system in which the five then known planets orbit the sun, while the sun and the moon orbit the earth. Tycho appreciated the Copernican system, but objected to the idea of a moving Earth on the basis of physics, astronomy, and religion. The Aristotelian physics of the time (modern Newtonian physics was still a century away) offered no physical explanation for the motion of a massive body like Earth, whereas it could easily explain the motion of heavenly bodies by postulating that they were made of a different sort substance called aether that moved naturally. So Tycho said that the Copernican system "... expertly and completely circumvents all that is superfluous or discordant in the system of Ptolemy. On no point does it offend the principle of mathematics. Yet it ascribes to the Earth, that hulking, lazy body, unfit for motion, a motion as quick as that of the aethereal torches, and a triple motion at that.”[74] Likewise, Tycho took issue with the vast distances to the stars that Aristarchus and Copernicus had assumed in order to explain the lack of any visible parallax. Tycho had measured the apparent sizes of stars (now known to be illusory – see stellar magnitude), and used geometry to calculate that in order to both have those apparent sizes and be as far away as Heliocentrism required, stars would have to be huge (much larger than the sun; the size of Earth’s orbit or larger). Regarding this Tycho wrote, “Deduce these things geometrically if you like, and you will see how many absurdities (not to mention others) accompany this assumption [of the motion of the earth] by inference.”[75] He also cited the Copernican system’s “opposition to the authority of Sacred Scripture in more than one place” as a reason why one might wish to reject it, and observed that his own geoheliocentric alternative “offended neither the principles of physics nor Holy Scripture”.[76] The Jesuit astronomers in Rome were at first unreceptive to Tycho’s system; the most prominent, Clavius, commented that Tycho was “confusing all of astronomy, because he wants to have Mars lower than the Sun.”[77] However, after the advent of the telescope showed problems with some geocentric models (by demonstrating that Venus circles the sun, for example), the Tychonic system and variations on that system became very popular among geocentrists, and the Jesuit astronomer Giovanni Battista Riccioli would continue Tycho’s use of physics, stellar astronomy (now with a telescope), and religion to argue against Heliocentrism and for Tycho’s system well into the seventeenth century (see Riccioli).


218 Publication of Starry messenger (1610)

CHAPTER 19. HELIOCENTRISM writings on Heliocentrism to the attention of the Inquisition, because they appeared to violate Holy Scripture and the decrees of the Council of Trent.[79][80] Cardinal and Inquisitor Robert Bellarmine was called upon to adjudicate, and wrote in April that treating Heliocentrism as a real phenomenon would be “a very dangerous thing,” irritating philosophers and theologians, and harming “the Holy Faith by rendering Holy Scripture as false.”[81]

In January 1616 Msgr. Francesco Ingoli addressed an essay to Galileo disputing the Copernican system. Galileo later stated that he believed this essay to have been instrumental in the ban against Copernicanism that followed in February.[82] According to Maurice Finocchiaro, Ingoli had probably been commissioned by the Inquisition to write an expert opinion on the controversy, and the essay provided the “chief direct basis” for the ban.[83] The essay focused on eighteen physical and mathematical arguments against Heliocentrism. It borrowed primarily from the arguments of Tycho Brahe, and it notedly mentioned the problem that Heliocentrism requires the stars to be much larger than the sun. Ingoli wrote that the great distance to the stars in the heliocentric theory “clearly proves ... the fixed stars to be of such size, as they may surpass or equal the size of the orbit circle of the Earth itself.”[84] Ingoli included four theological arguments in the essay, In the 17th century AD Galileo Galilei opposed the Roman but suggested to Galileo that he focus on the physical Catholic Church by his strong support for Heliocentrism and mathematical arguments. Galileo did not write a response to Ingoli until 1624.[85] Galileo was able to look at the night sky with the newly invented telescope. Then he published his discoveries In February 1616, the Inquisition assembled a commitin Sidereus Nuncius including (among other things) the tee of theologians, known as qualifiers, who delivered moons of Jupiter and that Venus exhibited a full range of their unanimous report condemning Heliocentrism as phases. These discoveries were not consistent with the “foolish and absurd in philosophy, and formally heretical Ptolemeic model of the solar system. As the Jesuit as- since it explicitly contradicts in many places the sense of tronomers confirmed Galileo’s observations, the Jesuits Holy Scripture.” The Inquisition also determined that the Earth’s motion “receives the same judgement in philosomoved toward Tycho’s teachings.[78] phy and ... in regard to theological truth it is at least erroneous in faith.”[86] Bellarmine personally ordered Galileo Publication of Letter to the Grand Duchess (1615) In a Letter to the Grand Duchess Christina, Galileo defended Heliocentrism, and claimed it was not contrary to Scriptures (see Galileo affair). He took Augustine's position on Scripture: not to take every passage literally when the scripture in question is a book of poetry and songs, not a book of instructions or history. The writers of the Scripture wrote from the perspective of the terrestrial world, and from that vantage point the sun does rise and set. In fact, it is the Earth’s rotation which gives the impression of the sun in motion across the sky.

“to abstain completely from teaching or defending this doctrine and opinion or from discussing it... to abandon completely... the opinion that the sun stands still at the center of the world and the earth moves, and henceforth not to hold, teach, or defend it in any way whatever, either orally or in writing.” — Bellarmine and the Inquisition’s injunction against Galileo, 1616[87]

In March, after the Inquisition’s injunction against Galileo, the papal Master of the Sacred Palace, 1616 ban against Copernicanism Congregation of the Index, and Pope banned all books and letters advocating the Copernican system, which they Main article: Galileo affair called “the false Pythagorean doctrine, altogether contrary to Holy Scripture.”[87][88] In 1618 the Holy Office In February 1615, prominent Dominicans including recommended that a modified version of Copernicus’ De Thomaso Caccini and Niccolò Lorini brought Galileo’s Revolutionibus be allowed for use in calendric calcula-


19.2. COPERNICAN REVOLUTION tions, though the original publication remained forbidden until 1758.[88]

219 “appreciated that the reference to heresy in connection with Galileo or Copernicus had no general or theological significance.”

Publication of Epitome astronomia Copernicanae (1617–1621) Subsequent developments In Astronomia nova (1609), Johannes Kepler had used an elliptical orbit to explain the motion of Mars. In Epitome astronomiae Copernicanae he developed a heliocentric model of the solar system in which all the planets have elliptical orbits. This provided significantly increased accuracy in predicting the position of the planets. Kepler’s ideas were not immediately accepted. Galileo for example completely ignored Kepler’s work. Kepler proposed Heliocentrism as a physical description of the solar system and Epitome astronomia Copernicanae was placed on the index of prohibited books despite Kepler being a Protestant.

René Descartes postponed, and ultimately never finished, his treatise The World, which included a heliocentric model,[92] but the Galileo affair did little to slow the spread of Heliocentrism across Europe, as Kepler’s Epitome of Copernican Astronomy became increasingly influential in the coming decades.[93] By 1686 the model was well enough established that the general public was reading about it in Conversations on the Plurality of Worlds, published in France by Bernard le Bovier de Fontenelle and translated into English and other languages in the coming years. It has been called “one of the first great popularizations of science.”[92]

In 1687, Isaac Newton published Philosophiæ Naturalis Publication of Dialogue concerning the two chief Principia Mathematica, which provided an explanation world systems for Kepler’s laws in terms of universal gravitation and what came to be known as Newton’s laws of motion. This Pope Urban VIII encouraged Galileo to publish the pros placed Heliocentrism on a firm theoretical foundation, aland cons of Heliocentrism. Galileo’s response, Dialogue though Newton’s Heliocentrism was of a somewhat modconcerning the two chief world systems, clearly advocated ern kind. Already in the mid-1680s he recognized the Heliocentrism, despite his declaration in the preface that “deviation of the Sun” from the centre of gravity of the solar system.[94] For Newton it was not precisely the centre of the Sun or any other body that could be considered I will endeavour to show that all experiat rest, but “the common centre of gravity of the Earth, ments that can be made upon the Earth are the Sun and all the Planets is to be esteem'd the Ceninsufficient means to conclude for its mobiltre of the World”, and this centre of gravity “either is at ity but are indifferently applicable to the Earth, rest or moves uniformly forward in a right line”. Newmovable or immovable...[89] ton adopted the “at rest” alternative in view of common consent that the centre, wherever it was, was at rest.[95] and his straightforward statement, I might very rationally put it in dispute, whether there be any such centre in nature, or no; being that neither you nor any one else hath ever proved, whether the World be finite and figurate, or else infinite and interminate; yet nevertheless granting you, for the present, that it is finite, and of a terminate Spherical Figure, and that thereupon it hath its centre...[89] Some ecclesiastics also interpreted the book as characterizing the Pope as a simpleton, since his viewpoint in the dialogue was advocated by the character Simplicio. Urban VIII became hostile to Galileo and he was again summoned to Rome.[90] Galileo’s trial in 1633 involved making fine distinctions between “teaching” and “holding and defending as true”. For advancing heliocentric theory Galileo was forced to recant Copernicanism and was put under house arrest for the last few years of his life.

Meanwhile, the Church remained opposed to Heliocentrism as a literal description, but this did not by any means imply opposition to all astronomy; indeed, it needed observational data to maintain its calendar. In support of this effort it allowed the cathedrals themselves to be used as solar observatories called meridiane; i.e., they were turned into “reverse sundials", or gigantic pinhole cameras, where the Sun’s image was projected from a hole in a window in the cathedral’s lantern onto a meridian line. In 1664, Pope Alexander VII published his Index Librorum Prohibitorum Alexandri VII Pontificis Maximi jussu editus (Index of Prohibited Books, published by order of Alexander VII, P.M.) which included all previous condemnations of heliocentric books.[96]

In the mid-eighteenth century the Church’s opposition began to fade. An annotated copy of Newton’s Principia was published in 1742 by Fathers le Seur and Jacquier of the Franciscan Minims, two Catholic mathematicians, with a preface stating that the author’s work assumed Heliocentrism and could not be explained without the theory. According to J. L. Heilbron,[91] informed contemporaries In 1758 the Catholic Church dropped the general prohiof Galileo’s: bition of books advocating Heliocentrism from the Index


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of Forbidden Books.[97] Pope Pius VII approved a decree entific view (in accordance with the theory of Relativin 1822 by the Sacred Congregation of the Inquisition to ity) that where two bodies in space are in motion relative allow the printing of heliocentric books in Rome. to one another, it is impossible scientifically to ascertain The Roman Catholic Church currently operates the which revolves around which, or which is stationary and Vatican Observatory, home to multiple award winning the other in motion. Therefore, to say that there is, or can the scholars, showing their ultimate acceptance of Heliocen- be, “scientific proof” that the earth revolves around[103] sun is quite an unscientific and uncritical statement.” trism by furthering the field. Heliocentrism and Judaism Already in the Talmud, Greek philosophy and science under general name “Greek wisdom” were considered dangerous. They were put under ban then and later for some periods. For example, in 13-5 a beit din (rabbinical court) in Barcelona forbade men younger than 25 from studying secular philosophy or the natural sciences (although an exception was made for those who studied medicine). Possibly due to this the system of Nicolaus Copernicus did not cause furious resistance, although it was found to be contradicting verses of Tanakh (Jewish Bible). The first to mention the new system was Maharal of Prague, although he did not mention Copernicus, the author of the system. In his book “Be'er ha-Golah”, in 1593 Maharal used the appearance of the new system to show that scientific theories are not reliable enough – even astronomy was turned upside-down.[98]

19.3 The view of modern science Kepler’s laws of planetary motion were used as arguments in favor of the heliocentric hypothesis. Three apparent proofs of the heliocentric hypothesis were provided in 1727 by James Bradley, in 1838 by Friedrich Wilhelm Bessel and in 1851 by Foucault. Bessel proved that the parallax of a star was greater than zero by measuring the parallax of 0.314 arcseconds of a star named 61 Cygni. In the same year Friedrich Georg Wilhelm Struve and Thomas Henderson measured the parallaxes of other stars, Vega and Alpha Centauri.

The thinking that the heliocentric view was also not true in a strict sense was achieved in steps. That the Sun was not the center of the universe, but one of innumerable stars, was strongly advocated by the mystic Giordano Bruno. Over the course of the 18th and 19th centuries, the status of the Sun as merely one star among many beCopernicus is mentioned for the first time in Hebrew came increasingly obvious. By the 20th century, even bein the books of David Gans (1541–1613), who worked fore the discovery that there are many galaxies, it was no with Tycho Brahe and Johannes Kepler. Gans wrote two longer an issue. books on astronomy: a short one “Magen David” (1612) and a full one “Nehmad veNaim” (published only in The concept of an absolute velocity, including being “at 1743). He described objectively three systems: Ptolemy, rest” as a particular case, is ruled out by the principle of relativity, also eliminating any obvious “center” of the Copernicus and of Tycho Brahe without taking sides. universe as a natural origin of coordinates. Some forms In 1629 a new Hebrew book “Elim” by Joseph Solomon of Mach’s principle consider the frame at rest with reDelmedigo (1591–1655) appeared. The author says that spect to the distant masses in the universe to have special the arguments of Copernicus are so strong, that only an properties. imbecile will not accept them.[99] Delmedigo studied at Even if the discussion is limited to the solar system, the Padua and was acquainted with Galileo.[100] Sun is not at the geometric center of any planet’s orbit, The following wave of Hebrew literature on the subject but rather approximately at one focus of the elliptical oris from the 18th century. Most of its authors were for bit. Furthermore, to the extent that a planet’s mass cannot Copernicus, although David Nieto and Tobias Cohn were be neglected in comparison to the Sun’s mass, the center exceptions. These two authors gave the same reason for of gravity of the solar system is displaced slightly away opposing Heliocentrism—namely, contradiction of the from the center of the Sun.[95] (The masses of the planBible—although Nieto merely rejected the new system ets, mostly Jupiter, amount to 0.14% of that of the Sun.) on those grounds without much passion, whereas HacoTherefore, a hypothetical astronomer on an extrasolar hen went so far as to call Copernicus “a first-born of Saplanet would observe a small “wobble” in the Sun’s motan”. Hacohen also mentions the fact that the Sages of tion. Talmud derived the Hebrew name of Earth from the verb “run”.[100] In later periods there were no explicit attacks on Helio- 19.3.1 centrism, although some Rabbis were not sure about the point.[101][102]

Modern use of geocentric and heliocentric

In the 20th century R. M.M. Schneerson suggested that In modern calculations the terms “geocentric” and “hethe theory of relativity makes the question obsolete, as liocentric” are often used to refer to reference frames. In he writes; “on the basis of the presently accepted sci- such systems the origin in the center of mass of the Earth,


19.5. NOTES of the Earth–Moon system, of the Sun, of the Sun plus the major planets, or of the entire solar system can be selected; see center-of-mass frame. Right Ascension and Declination are examples of geocentric coordinates, used in Earth-based observations, while the heliocentric latitude and longitude are used for orbital calculations. This leads to such terms as “heliocentric velocity" and “heliocentric angular momentum". In this heliocentric picture, any planet of the Solar System can be used as a source of mechanical energy because it moves relatively to the Sun. A smaller body (either artificial or natural) may gain heliocentric velocity due to gravity assist – this effect can change the body’s mechanical energy in heliocentric reference frame (although it will not changed in the planetary one). However, such selection of “geocentric” or “heliocentric” frames is merely a matter of computation. It does not have philosophical implications and does not constitute a distinct physical or scientific model. From the point of view of General Relativity, inertial reference frames do not exist at all, and any practical reference frame is only an approximation to the actual space-time, which can have higher or lower precision.

19.4 See also • Geocentric model • Celestial spheres • Copernican Revolution (metaphor) • Copernican principle

19.5 Notes [1] The Shorter Oxford English Dictionary (6th ed., 2007) [2] Dreyer (1953), pp.135–48; Linton (2004), pp.38–9). The work of Aristarchus’s in which he proposed his heliocentric system has not survived. We only know of it now from a brief passage in Archimedes's The Sand Reckoner. [3] according to Lucio Russo, the heliocentric view was expounded in Hipparchus's work on gravity. (source: Lucio Rosso, The Forgotten Revolution, How Science was Born in 300BC and Why it had to be Reborn, pp 293-296) [4] Debus, Allen G. (1987), Man and nature in the Renaissance, Cambridge University Press, p. 76, ISBN 0-52129328-6, Chapter V, page 76 [5] In Book 1 section 7 he admits that a model in which the earth revolves with respect to the stars would be simpler but doesn't go as far as considering a heliocentric system.

221

[9] Eastwood, B. S. (November 1, 1992), “Heraclides and Heliocentrism – Texts Diagrams and Interpretations”, Journal for the History of Astronomy, 23: 233, Bibcode:1992JHA....23..233E [10] Otto E. Neugebauer (1975), A history of ancient mathematical astronomy, Berlin/Heidelberg/New York: Springer, p. 695, ISBN 3-540-06995-X [11] Rufus, W. Carl (1923), “The astronomical system of Copernicus”, Popular Astronomy, 31: 510–521 [512], Bibcode:1923PA.....31..510R, at pp. 511-512 [12] Arenarius, I., 4–7 [13] D.Rawlins, Aristarchus’s vast universe: ancient vision, contends that all of Aristarchus’s huge astronomical estimates of distance were based upon his gauging the limit of human visual discrimination to be approximately a ten thousandth of a radian which is about right. [14] Murdin, Paul, Murdin, Paul, ed., Seleucus of Seleucia (c. 190 BC-?), Institute of Physics Bibcode:2000eaa..bookE3998., Publishing, doi:10.1888/0333750888, ISBN 0-333-75088-8, retrieved 2009-08-08 [15] Index of Ancient Greek Philosophers-Scientists, Ics.forth.gr, retrieved 2009-08-08 [16] Bartel, B. L. (1987), “The Heliocentric System in Greek, Persian and Hindu Astronomy”, Annals of the New York Academy of Sciences, 500 (1): 525–545 [527–529], Bibcode:1987NYASA.500..525V, doi:10.1111/j.17496632.1987.tb37224.x. [17] Shlomo Pines (1986), Studies in Arabic versions of Greek texts and in mediaeval science, 2, Brill Publishers, pp. viii & 201–17, ISBN 965-223-626-8 [18] Lucio Russo, Flussi e riflussi, Feltrinelli, Milano, 2003, ISBN 88-07-10349-4. [19] William Stahl, trans., Martianus Capella and the Seven Liberal Arts, vol. 2, The Marriage of Philology and Mercury, 854, 857, New York: Columbia Univ. Pr, 1977, pp. 332–3 [20] Eastwood, Bruce S. (2007), Ordering the Heavens: Roman Astronomy and Cosmology in the Carolingian Renaissance, Leiden: Brill, pp. 244–259, ISBN 978-90-04-16186-3 [21] Eastwood, Bruce S. (1982), “Kepler as Historian of Science: Precursors of Copernican Heliocentrism according to De revolutionibus I, 10”, Proceedings of the American Philosophical Society, 126: 367–394. [22] Nicholas of Cusa, De docta ignorantia, 2.12, p. 103, cited in Koyré (1957), p. 17. [23] Joseph (2000).

[6] Dennis Duke, Ptolemy’s Universe

[24] Thurston (1994).

[7] Boyer, C. A History of Mathematics. Wiley, p. 54.

[25] Ramasubramanian, K. (1998), “Model of planetary motion in the works of Kerala astronomers”, Bulletin of the Astronomical Society of India, 26: 11–31 [23–4], Bibcode:1998BASI...26...11R

[8] Johannes Kepler (1618–21), Epitome of Copernican Astronomy, Book IV, Part 1.2


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[26] K. Ramasubramanian, et al. (1994), p. 788 [27] Amartya Kumar Dutta (May 2006), "Āryabhata and axial rotation of earth”, Resonance, Springer, 11 (5): 58–72 [70–1], doi:10.1007/BF02839373, ISSN 0973-712X [28] George G. Joseph (2000), p. 408. [29] Ramasubramanian, K.; Srinivas, M. D.; Sriram, M. S. (1994), “Modification of the earlier Indian planetary theory by the Kerala astronomers (c. 1500 AD) and the implied heliocentric picture of planetary motion”, Current Science, 66: 784–790. [30] Sabra, A. I. (1998). “Configuring the Universe: Aporetic, Problem Solving, and Kinematic Modeling as Themes of Arabic Astronomy”. Perspectives on Science. 6 (3): 288– 330. at pp. 317–18: All Islamic astronomers from Thabit ibn Qurra in the ninth century to Ibn al-Shatir in the fourteenth, and all natural philosophers from al-Kindi to Averroes and later, are known to have accepted ... the Greek picture of the world as consisting of two spheres of which one, the celestial sphere ... concentrically envelops the other. [31] Hoskin, Michael (1999-03-18). The Cambridge Concise History of Astronomy. Cambridge University Press. p. 60. ISBN 9780521576000. [32] Ragep, F. Jamil (2001a), “Tusi and Copernicus: The Earth’s Motion in Context”, Science in Context, Cambridge University Press, 14 (1–2): 145–163, doi:10.1017/s0269889701000060 [33] Ragep, F. Jamil; Al-Qushji, Ali (2001b), “Freeing Astronomy from Philosophy: An Aspect of Islamic Influence on Science”, Osiris, 2nd Series, 16 (Science in Theistic Contexts: Cognitive Dimensions): 49–64 & 66–71, Bibcode:2001Osir...16...49R, doi:10.1086/649338 [34] Adi Setia (2004), “Fakhr Al-Din Al-Razi on Physics and the Nature of the Physical World: A Preliminary Survey”, Islam & Science, 2, retrieved 2010-03-02 [35] Alessandro Bausani (1973). “Cosmology and Religion in Islam”. Scientia/Rivista di Scienza. 108 (67): 762. [36] Young, M. J. L., ed. (2006-11-02). Religion, Learning and Science in the 'Abbasid Period. Cambridge University Press. p. 413. ISBN 9780521028875. [37] Nasr, Seyyed Hossein (1993-01-01). An Introduction to Islamic Cosmological Doctrines. SUNY Press. p. 135. ISBN 9781438414195. [38] Qadir (1989), p. 5–10. [39] Nicolaus Copernicus, Stanford Encyclopedia of Philosophy (2004). [40] E. S. Kennedy, “Al-Bīrūnī's Masudic Canon”, Al-Abhath, 24 (1971): 59–81; reprinted in David A. King and Mary Helen Kennedy, ed., Studies in the Islamic Exact Sciences, Beirut, 1983, pp. 573–595.

[41] G. Wiet, V. Elisseeff, P. Wolff, J. Naudu (1975). History of Mankind, Vol 3: The Great medieval Civilisations, p. 649. George Allen & Unwin Ltd, UNESCO. [42] Saliba (1999). [43] Samsó, Julio (2007). “Biṭrūjī: Nūr al‐Dīn Abū Isḥāq [Abū Jaʿfar] Ibrāhīm ibn Yūsuf al‐Biṭrūjī". In Thomas Hockey; et al. The Biographical Encyclopedia of Astronomers. New York: Springer. pp. 133–4. ISBN 978-0-38731022-0. (PDF version) [44] Samsó, Julio (1970–80). “Al-Bitruji Al-Ishbili, Abu Ishaq”. Dictionary of Scientific Biography. New York: Charles Scribner’s Sons. ISBN 0-684-10114-9. [45] Hikmat al-'Ain, p. 78 [46] Toby E.Huff(1993):The rise of early modern science: Islam, China, and the West [47] Roberts, V.; Kennedy, E. S. (1959). “The Planetary Theory of Ibn al-Shatir”. Isis. 50: 232–234. doi:10.1086/348774. [48] Guessoum, N. (June 2008), “Copernicus and Ibn Al-Shatir: does the Copernican revolution have Islamic roots?", The Observatory, 128: 231–239 [238], Bibcode:2008Obs...128..231G [49] A. I. Sabra (1998). [50] E. S. Kennedy (Autumn 1966), “Late Medieval Planetary Theory”, Isis, University of Chicago Press, 57 (3): 365– 378 [377], doi:10.1086/350144, JSTOR 228366 [51] Saliba, George (1995-07-01). A History of Arabic Astronomy: Planetary Theories During the Golden Age of Islam. NYU Press. ISBN 9780814780237. [52] Swerdlow, Noel M. (1973-12-31). “The Derivation and First Draft of Copernicus’s Planetary Theory: A Translation of the Commentariolus with Commentary”. Proceedings of the American Philosophical Society. 117 (6): 424. ISSN 0003-049X. JSTOR 986461. [53] King, David A. (2007). “Ibn al‐Shāṭir: ʿAlāʾ al‐Dīn ʿAlī ibn Ibrāhīm”. In Thomas Hockey; et al. The Biographical Encyclopedia of Astronomers. New York: Springer. pp. 569–70. ISBN 978-0-387-31022-0. (PDF version) [54] N.K. Singh, M. Zaki Kirmani,Encyclopaedia of Islamic science and scientists [55] Viktor Blåsjö, “A Critique of the Arguments for Maragha Influence on Copernicus”, Journal for the History of Astronomy, 45 (2014), 183-195 ADS. [56] Veselovsky, I. N. (1973), “Copernicus and Nasir al-Din al-Tusi”, Journal for the History of Astronomy, 4: 128– 30, Bibcode:1973JHA.....4..128V. [57] Neugebauer, Otto (1975), A History of Ancient Mathematical Astronomy, 2, Berlin / Heidelberg / New York: Springer-Verlag, p. 1035, ISBN 0-387-06995-X [58] Kren, Claudia (1971), “The Rolling Device of Naṣir alDīn al-Ṭūsī in the De spera of Nicole Oresme”, Isis, 62 (4): 490–498, doi:10.1086/350791.


19.5. NOTES

[59] Freely, John (2015-03-30). Light from the East: How the Science of Medieval Islam Helped to Shape the Western World. I.B.Tauris. p. 179. ISBN 9781784531386.

223

[76] Gingerich, O. & Voelkel, J. R., J. Hist. Astron., Vol. 29, 1998, page 1, 24 [77] Fantoli, 2003, p. 109

[60] Henry, John (2001). Moving heaven and earth : Copernicus and the solar system. Cambridge: Icon. p. 87. ISBN 978-1-84046-251-7.

[78] Arthur Koestler, The Sleepwalkers (Penguin Arkana, 1989 p. 433)

[61] Gingerich, (2004, p. 51)

[79] Langford (1992), p.56-57

[62] Gingerich, O. “Did Copernicus Owe a Debt to Aristarchus?" Journal for the History of Astronomy, Vol.16, NO.1/FEB, P. 37, 1985. As mentioned earlier in this article, Philolaus had the Earth moving round a Central Fire which was not the Sun, so Copernicus’s reference to Aristarchus’s model as possibly geodynamic does not necessarily imply that he thought it was heliocentric. [63] Dreyer (1953, p. 138); Plutarch (1957, p. 55) (on-line copy available). According to a footnote in the latter reference, Diogenes Laertius listed a work of Cleanthes’ (apparently now lost) with the title Against Aristarchus (Plutarch, 1957, p. 54). [64] A library catalogue of a 16th-century historian, Matthew of Miechow, bears that date and contains a reference to the manuscript, so it must have begun circulating before that date (Koyré, 1973, p.85; Gingerich, 2004, p.32). [65] Speller (2008, p.51) [66] “Religious Objections to Copernicus”.

[80] Drake (1978, p.240), Sharratt (1994, pp.110−111), Favaro (1907, 19:297−298) (Italian). [81] Sharratt (1994, pp.110−115) [82] Graney (2015, pp. 68-69) Ingoli’s essay was published in English translation for the first time in 2015. [83] Finocchiaro (2010, pp. 72) [84] Graney (2015, pp. 71) [85] Graney (2015, pp. 66-76, 164-175, 187-195) [86] Favaro (1907, 19:320), Domínguez (2014); arXiv:1402. 6168 Original text of the decision [87] Heilbron (2010), p.218 [88] Finochiario, Maurice (2007). Retrying Galileo. University of California Press. [89] The Systeme of the World: in Four Dialogues (1661) Thomas Salusbury translation of Dialogo sopra i Due Massi Sistemi del Mondo (1632)

[67] Melanchthon, Elements of Physics, 1st. edition, 1549 [68] Revolution in Science, I. Bernard Cohen, page 497. [69] Rosen (1995, p.159). Rosen disputes the earlier conclusion of another scholar that this was referring specifically to Copernicus’s theory. According to Rosen, Calvin had very likely never heard of Copernicus and was referring instead to “the traditional geokinetic cosmology”. [70] Rosen, Edward (1960), Calvin’s attitude toward Copernicus in Journal of the History of Ideas, volume 21, no. 3, July, pp.431–441. Reprinted in Rosen (1995, pp.161– 171). [71] Gingerich, Owen (2004), The Book Nobody Read. New York: Walker and Co. [72] Hooykaas, R. (1973). Religion and the rise of modern science. Reprint, Edinburgh: Scottish Academic Press, 1977. [73] Bye, Dan J. (2007). McGrath vs Russell on Calvin vs Copernicus: a case of the pot calling the kettle black? in The Freethinker, volume 127, no. 6, June, pp.8–10. Available online here. [74] Owen Gingerich, The eye of heaven: Ptolemy, Copernicus, Kepler, New York: American Institute of Physics, 1993, 181, ISBN 0-88318-863-5 [75] Blair, Ann, “Tycho Brahe’s critique of Copernicus and the Copernican system”, Journal of the History of Ideas, 51, 1990, 364.

[90] Arthur Koestler, The Sleepwalkers (Penguin Arkana, 1989 p. 491) [91] Heilbronn (1999, p.203) [92] Weintraub, David A. Is Pluto a Planet, p. 66, Princeton University Press, 2007 [93] “Kepler’s Laws of Planetary Motion: 1609–1666”, J. L. Russell, British Journal for the History of Science, Vol. 2, No. 1, June 1964 [94] Curtis Wilson, “The Newtonian achievement in astronomy”, pages 233–274 in R Taton & C Wilson (eds) (1989), The General History of Astronomy, Volume 2A, at page 233 [95] (text quotations from 1729 translation of Newton Principia, Book 3 (1729 vol.2) at pages 232–233). [96] “The Pontifical Decrees Against the Doctrine of the Earth’s Movement, and the Ultramontane Defence of Them”, Rev. William Roberts, 1885, London [97] John L.Heilbron, Censorship of Astronomy in Italy after Galileo (in McMullin, Ernan ed., The Church and Galileo, University of Notre Dame Press, Notre Dame, 2005, p. 307, IN. ISBN 0-268-03483-4) [98] Noah J. Efron. Jewish Thought and Scientific Discovery in Early Modern Europe. Journal of the History of Ideas, Vol. 58, No. 4 (Oct., 1997), pp. 719–732 [99] Sefer Elim, Amsterdam, 1629, стр. 304


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[100] Copernicus in the Hebraic Literature from the Sixteenth to the Eighteenth Century Journal of the History of Ideas, vol. 38, No. 2 (Apr. – Jun., 1977), pp. 211–226. (André Neher)

• Graney, Christopher M. (2015), Setting Aside All Authority: Giovanni Battista Riccioli and the Science against Copernicus in the Age of Galileo, University of Notre Dame Press, ISBN 978-0268029883

[101] “Shvut Yakov” 3:20 (r. Y. Reisner from Prague 1710– 1789)

• Heath, T.L. (1913). Aristarchus of Samos, the ancient Copernicus: a history of Greek astronomy to Aristarchus, Oxford, Clarendon. ISBN 0-48624188-2 (1981 Dover reprint).

[102] Hatam Sopher (1762–1839) “Kovetz Tshuvot”, 26 [103] ""Igrot Kodesh” v. 7, p.134, letter number 1996”. Otzar770.com. Retrieved 2012-12-04.

19.6 External links • Does Heliocentrism Mean That the Sun is Stationary? • Heliocentric Pantheon • The Copernican Model: a Sun Centered Solar System

19.7 References • Baker, A. and Chapter, L. (2002), “Part 4: The Sciences”. In M. M. Sharif, “A History of Muslim Philosophy”, Philosophia Islamica. • Drake, Stillman (1978). Galileo At Work. Chicago: University of Chicago Press. ISBN 0-226-16226-5. • Dreyer, J.L.E. (1953), A History of Astronomy from Thales to Kepler, New York, NY: Dover Publications, ISBN 0-486-60079-3 • Fantoli, Annibale (2003). Galileo — For Copernicanism and the Church, 3rd English edition, tr. George V. Coyne, SJ. Vatican Observatory Publications, Notre Dame, IN. ISBN 88-209-7427-4. • Favaro, Antonio, ed. (1890–1909). Le Opere di Galileo Galilei, Edizione Nazionale [The Works of Galileo Galilei, National Edition] (in Italian). Florence: Barbera. ISBN 88-09-20881-1. A searchable online copy is available on the Institute and Museum of the History of Science, Florence, and a brief overview of Le Opere is available at Finn’s fine books, and here.

• Heilbron, John L. (1999), The Sun in the Church: Cathedrals as Solar Observatories, Cambridge, MA: Harvard University Press, ISBN 0674005368 • Heilbron, John L. (2005). “Censorship of Astronomy in Italy after Galileo”. In McMullin, Ernan. The Church and Galileo. University of Notre Dame Press, Notre Dame. ISBN 0-268-03483-4. • Heilbron, John L. (2010). “Biography of Galileo”. Galileo. Oxford University Press, Oxford. • Joseph, George G. (2000). The Crest of the Peacock: Non-European Roots of Mathematics, 2nd edition. Penguin Books, London. ISBN 0-691-00659-8. • Koestler, Arthur, (1959) The Sleepwalkers: A History of Man’s Changing Vision of the Universe, Penguin Books; 1986 edition: ISBN 0-14-055212-X, 1990 reprint: ISBN 0-14-019246-8 • Koyré, Alexandre (1957). From the Closed World to the Infinite Universe. Baltimore: Johns Hopkins Univ. Pr. • Koyré, Alexandre (1973). The Astronomical Revolution: Copernicus – Kepler – Borelli. Ithaca, NY: Cornell University Press. ISBN 0-8014-0504-1. • Langford, Jerome K., O.P. (1998) [1966]. Galileo, Science and the Church (third ed.). St. Augustine’s Press. ISBN 1-890318-25-6.. Original edition by Desclee (New York, NY, 1966) • Linton, Christopher M. (2004), From Eudoxus to Einstein—A History of Mathematical Astronomy, Cambridge: Cambridge University Press, ISBN 978-0-521-82750-8 • Plutarch (1957), Plutarch’s Moralia in Fifteen Volumes, XII, Loeb Classical Library edition, translated by Harold Cherniss and William C. Helmbold, London: William Heinemann

• Finocchiaro, Maurice (2010), Defending Copernicus and Galileo: Critical Reasoning in the two Affairs, Springer, ISBN 978-9048132003

• Qadir, Asghar (1989). Relativity: An Introduction to the Special Theory. World Scientific. ISBN 9971-50612-2.

• Gingerich, Owen (2004). The Book Nobody Read. London: William Heinemann. ISBN 0-434-013153.

• Rosen, Edward (1995), Copernicus and his Successors, London: Hambledon Press, ISBN 1-85285071-X


19.7. REFERENCES • Sabra, A. I. (1998), “Configuring the Universe: Aporetic, Problem Solving, and Kinematic Modeling as Themes of Arabic Astronomy”, Perspectives on Science, 6: 288–330. • Saliba, George (1999). Whose Science is Arabic Science in Renaissance Europe? Columbia University. • The Shorter Oxford English Dictionary (6th ed.), Oxford, UK: Oxford University Press, 2007, ISBN 978-0-199-20687-2 • Sharratt, Michael (1994). Galileo: Decisive Innovator. Cambridge: Cambridge University Press. ISBN 0-521-56671-1. • Speller, Jules (2008), Galileo’s Inquisition Trial Revisited, Frankfurt am Main: Peter Lang, ISBN 9783-631-56229-1 • Taton, René; Wilson, Curtis, eds. (1989), Planetary astronomy from the Renaissance to the rise of astrophysics Part A: Tycho Brahe to Newton, Cambridge: Cambridge University Press, ISBN 0-521-24254-1, retrieved 2009-11-06 • Thurston, Hugh (1994). Early Astronomy. Springer-Verlag, New York. ISBN 0-387-94107X.

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Chapter 20

Johannes Kepler “Kepler” redirects here. For the European cargo spacecraft, see Johannes Kepler ATV. For the space observatory, see Kepler (spacecraft). For other uses, see Kepler (disambiguation). Johannes Kepler (German: [ˈkɛplɐ]; December 27, 1571 – November 15, 1630) was a German mathematician, astronomer, and astrologer. A key figure in the 17th century scientific revolution, he is best known for his laws of planetary motion, based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican Astronomy. These works also provided one of the foundations for Isaac Newton's theory of universal gravitation. Kepler was a mathematics teacher at a seminary school in Graz, Austria, where he became an associate of Prince Hans Ulrich von Eggenberg. Later he became an assistant to the astronomer Tycho Brahe, and eventually he was the imperial mathematician to Emperor Rudolf II and his two successors Matthias and Ferdinand II. He was also a mathematics teacher in Linz, Austria, and an adviser to General Wallenstein. Additionally, he did fundamental work in the field of optics, invented an improved version of the refracting telescope (the Keplerian telescope), and was mentioned in the telescopic discoveries of his contemporary Galileo Galilei. Kepler lived in an era when there was no clear distinction between astronomy and astrology, but there was a strong division between astronomy (a branch of mathematics within the liberal arts) and physics (a branch of natural philosophy). Kepler also incorporated religious arguments and reasoning into his work, motivated by the religious conviction and belief that God had created the world according to an intelligible plan that is accessible through the natural light of reason.[1] Kepler described his new astronomy as “celestial physics”,[2] as “an excursion into Aristotle's Metaphysics",[3] and as “a supplement to Aristotle’s On the Heavens",[4] transforming the ancient tradition of physical cosmology by treating astronomy as part of a universal mathematical physics.[5] Kepler’s birthplace, in Weil der Stadt

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20.2. GRAZ (1594–1600)

227 students. Under the instruction of Michael Maestlin, Tübingen’s professor of mathematics from 1583 to 1631,[10] he learned both the Ptolemaic system and the Copernican system of planetary motion. He became a Copernican at that time. In a student disputation, he defended heliocentrism from both a theoretical and theological perspective, maintaining that the Sun was the principal source of motive power in the universe.[11] Despite his desire to become a minister, near the end of his studies Kepler was recommended for a position as teacher of mathematics and astronomy at the Protestant school in Graz. He accepted the position in April 1594, at the age of 23.[12]

The Great Comet of 1577, which Kepler witnessed as a child, attracted the attention of astronomers across Europe

20.1 Early years

20.2 Graz (1594–1600) 20.2.1 Mysterium Cosmographicum

Kepler was born on December 27, the feast day of St. John the Evangelist, 1571, at the Free Imperial City of Weil der Stadt (now part of the Stuttgart Region in the German state of Baden-Württemberg, 30 km west of Stuttgart’s center). His grandfather, Sebald Kepler, had been Lord Mayor of that town but, by the time Johannes was born, he had two brothers and one sister and the Kepler family fortune was in decline. His father, Heinrich Kepler, earned a precarious living as a mercenary, and he left the family when Johannes was five years old. He was believed to have died in the Eighty Years’ War in the Netherlands. His mother Katharina Guldenmann, an innkeeper’s daughter, was a healer and herbalist. Born prematurely, Johannes claimed to have been weak and sickly as a child. Nevertheless, he often impressed travelers at his grandfather’s inn with his phenomenal mathematical faculty.[6] He was introduced to astronomy at an early age, and developed a love for it that would span his entire life. At age six, he observed the Great Comet of 1577, writing that he “was taken by [his] mother to a high place to look at it.”[7] At age nine, he observed another astronomical event, a lunar eclipse in 1580, recording that he remembered being “called outdoors” to see it and that the moon “appeared quite red”.[7] However, childhood smallpox left him with weak vision and crippled hands, limiting his ability in the observational aspects of astronomy.[8] In 1589, after moving through grammar school, Latin school, and seminary at Maulbronn, Kepler attended Tübinger Stift at the University of Tübingen. There, he studied philosophy under Vitus Müller[9] and theology under Jacob Heerbrand (a student of Philipp Melanchthon at Wittenberg), who also taught Michael Maestlin while he was a student, until he became Chancellor at Tübingen in 1590.[10] He proved himself to be a superb mathematician and earned a reputation as a skillful astrologer, casting horoscopes for fellow

Kepler’s Platonic solid model of the solar system, from Mysterium Cosmographicum (1596)

Kepler’s first major astronomical work, Mysterium Cosmographicum (The Cosmographic Mystery) [1596], was the first published defense of the Copernican system. Kepler claimed to have had an epiphany on July 19, 1595, while teaching in Graz, demonstrating the periodic conjunction of Saturn and Jupiter in the zodiac: he realized that regular polygons bound one inscribed and one circumscribed circle at definite ratios, which, he reasoned, might be the geometrical basis of the universe. After failing to find a unique arrangement of polygons that fit known astronomical observations (even with extra planets added to the system), Kepler began experimenting with 3-dimensional polyhedra. He found that each of the five Platonic solids could be inscribed and circumscribed by spherical orbs; nesting these solids,


228 each encased in a sphere, within one another would produce six layers, corresponding to the six known planets— Mercury, Venus, Earth, Mars, Jupiter, and Saturn. By ordering the solids selectively—octahedron, icosahedron, dodecahedron, tetrahedron, cube—Kepler found that the spheres could be placed at intervals corresponding to the relative sizes of each planet’s path, assuming the planets circle the Sun. Kepler also found a formula relating the size of each planet’s orb to the length of its orbital period: from inner to outer planets, the ratio of increase in orbital period is twice the difference in orb radius. However, Kepler later rejected this formula, because it was not precise enough.[13]

CHAPTER 20. JOHANNES KEPLER Though the details would be modified in light of his later work, Kepler never relinquished the Platonist polyhedralspherist cosmology of Mysterium Cosmographicum. His subsequent main astronomical works were in some sense only further developments of it, concerned with finding more precise inner and outer dimensions for the spheres by calculating the eccentricities of the planetary orbits within it. In 1621, Kepler published an expanded second edition of Mysterium, half as long again as the first, detailing in footnotes the corrections and improvements he had achieved in the 25 years since its first publication.[16] In terms of the impact of Mysterium, it can be seen as an important first step in modernizing the theory proposed by Nicolaus Copernicus in his "De Revolutionibus orbium coelestium". Whilst Copernicus sought to advance a heliocentric system in this book, he resorted to Ptolemaic devices (viz., epicycles and eccentric circles) in order to explain the change in planets’ orbital speed, and also continued to use as a point of reference the center of the earth’s orbit rather than that of the sun “as an aid to calculation and in order not to confuse the reader by diverging too much from Ptolemy.” Modern astronomy owes much to “Mysterium Cosmographicum”, despite flaws in its main thesis, “since it represents the first step in cleansing the Copernican system of the remnants of the Ptolemaic theory still clinging to it.” [17]

20.2.2 Marriage to Barbara Müller

Close-up of an inner section of the model

As he indicated in the title, Kepler thought he had revealed God’s geometrical plan for the universe. Much of Kepler’s enthusiasm for the Copernican system stemmed from his theological convictions about the connection between the physical and the spiritual; the universe itself was an image of God, with the Sun corresponding to the Father, the stellar sphere to the Son, and the intervening space between to the Holy Spirit. His first manuscript of Mysterium contained an extensive chapter reconciling he- Portraits of Kepler and his wife in oval medallions liocentrism with biblical passages that seemed to support geocentrism.[14] In December 1595, Kepler was introduced to Barbara With the support of his mentor Michael Maestlin, Kepler Müller, a 23-year-old widow (twice over) with a young received permission from the Tübingen university senate daughter, Regina Lorenz, and he began courting her. to publish his manuscript, pending removal of the Bible Müller, heiress to the estates of her late husbands, was exegesis and the addition of a simpler, more understand- also the daughter of a successful mill owner. Her father able description of the Copernican system as well as Ke- Jobst initially opposed a marriage despite Kepler’s nobilpler’s new ideas. Mysterium was published late in 1596, ity; though he had inherited his grandfather’s nobility, Keand Kepler received his copies and began sending them to pler’s poverty made him an unacceptable match. Jobst prominent astronomers and patrons early in 1597; it was relented after Kepler completed work on Mysterium, but not widely read, but it established Kepler’s reputation as the engagement nearly fell apart while Kepler was away a highly skilled astronomer. The effusive dedication, to tending to the details of publication. However, Protestant powerful patrons as well as to the men who controlled his officials—who had helped set up the match—pressured position in Graz, also provided a crucial doorway into the the Müllers to honor their agreement. Barbara and Jopatronage system.[15] hannes were married on April 27, 1597.[18]


20.3. PRAGUE (1600–1612) In the first years of their marriage, the Keplers had two children (Heinrich and Susanna), both of whom died in infancy. In 1602, they had a daughter (Susanna); in 1604, a son (Friedrich); and in 1607, another son (Ludwig).[19]

229 causes the motion of planets), he established a speculative system connecting astrological aspects and astronomical distances to weather and other earthly phenomena. By 1599, however, he again felt his work limited by the inaccuracy of available data—just as growing religious tension was also threatening his continued employment in Graz. In December of that year, Tycho invited Kepler to visit him in Prague; on January 1, 1600 (before he even received the invitation), Kepler set off in the hopes that Tycho’s patronage could solve his philosophical problems as well as his social and financial ones.[22]

20.3 Prague (1600–1612) 20.3.1 Work for Tycho Brahe

House of Kepler and Barbara Müller in Gössendorf, near Graz (1597–1599)

20.2.3

Other research

Following the publication of Mysterium and with the blessing of the Graz school inspectors, Kepler began an ambitious program to extend and elaborate his work. He planned four additional books: one on the stationary aspects of the universe (the Sun and the fixed stars); one on the planets and their motions; one on the physical nature of planets and the formation of geographical features (focused especially on Earth); and one on the effects of the heavens on the Earth, to include atmospheric optics, meteorology, and astrology.[20] He also sought the opinions of many of the astronomers to whom he had sent Mysterium, among them Reimarus Ursus (Nicolaus Reimers Bär)—the imperial mathematician to Rudolph II and a bitter rival of Tycho Brahe. Ursus did not reply directly, but republished Kepler’s flattering letter to pursue his priority dispute over (what is now called) the Tychonic system with Tycho. Despite this black mark, Tycho also began corresponding with Kepler, starting with a harsh but legitimate critique of Kepler’s system; among a host of objections, Tycho took issue with the use of inaccurate numerical data taken from Copernicus. Through their letters, Tycho and Kepler discussed a broad range of astronomical problems, dwelling on lunar phenomena and Copernican theory (particularly its theological viability). But without the significantly more accurate data of Tycho’s observatory, Kepler had no way to address many of these issues.[21] Instead, he turned his attention to chronology and “harmony,” the numerological relationships among music, mathematics and the physical world, and their astrological consequences. By assuming the Earth to possess a soul (a property he would later invoke to explain how the sun

Tycho Brahe

On February 4, 1600, Kepler met Tycho Brahe and his assistants Franz Tengnagel and Longomontanus at Benátky nad Jizerou (35 km from Prague), the site where Tycho’s new observatory was being constructed. Over the next two months he stayed as a guest, analyzing some of Tycho’s observations of Mars; Tycho guarded his data closely, but was impressed by Kepler’s theoretical ideas and soon allowed him more access. Kepler planned to test his theory[23] from Mysterium Cosmographicum based on the Mars data, but he estimated that the work would take up to two years (since he was not allowed to simply copy


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the data for his own use). With the help of Johannes Jessenius, Kepler attempted to negotiate a more formal employment arrangement with Tycho, but negotiations broke down in an angry argument and Kepler left for Prague on April 6. Kepler and Tycho soon reconciled and eventually reached an agreement on salary and living arrangements, and in June, Kepler returned home to Graz to collect his family.[24]

Lutheran faith unhindered. The emperor nominally provided an ample income for his family, but the difficulties of the over-extended imperial treasury meant that actually getting hold of enough money to meet financial obligations was a continual struggle. Partly because of financial troubles, his life at home with Barbara was unpleasant, marred with bickering and bouts of sickness. Court life, however, brought Kepler into contact with other prominent scholars (Johannes Matthäus Wackher von Wackhenfels, Jost Bürgi, David Fabricius, Martin Bachazek, and Johannes Brengger, among others) and astronomical work proceeded rapidly.[29]

Political and religious difficulties in Graz dashed his hopes of returning immediately to Brahe; in hopes of continuing his astronomical studies, Kepler sought an appointment as mathematician to Archduke Ferdinand. To that end, Kepler composed an essay—dedicated to Ferdinand—in which he proposed a force-based theory 20.3.3 of lunar motion: “In Terra inest virtus, quae Lunam ciet” (“There is a force in the earth which causes the moon to move”).[25] Though the essay did not earn him a place in Ferdinand’s court, it did detail a new method for measuring lunar eclipses, which he applied during the July 10 eclipse in Graz. These observations formed the basis of his explorations of the laws of optics that would culminate in Astronomiae Pars Optica.[26]

Astronomiae Pars Optica

On August 2, 1600, after refusing to convert to Catholicism, Kepler and his family were banished from Graz. Several months later, Kepler returned, now with the rest of his household, to Prague. Through most of 1601, he was supported directly by Tycho, who assigned him to analyzing planetary observations and writing a tract against Tycho’s (by then deceased) rival, Ursus. In September, Tycho secured him a commission as a collaborator on the new project he had proposed to the emperor: the Rudolphine Tables that should replace the Prutenic Tables of Erasmus Reinhold. Two days after Tycho’s unexpected death on October 24, 1601, Kepler was appointed his successor as imperial mathematician with the responsibility to complete his unfinished work. The next 11 years as imperial mathematician would be the most productive of his life.[27]

20.3.2

Advisor to Emperor Rudolph II

Kepler’s primary obligation as imperial mathematician was to provide astrological advice to the emperor. Though Kepler took a dim view of the attempts of contemporary astrologers to precisely predict the future or divine specific events, he had been casting well-received detailed horoscopes for friends, family, and patrons since his time as a student in Tübingen. In addition to horoscopes for allies and foreign leaders, the emperor sought Kepler’s advice in times of political trouble. Rudolph was actively interested in the work of many of his court scholars (including numerous alchemists) and kept up with Kepler’s work in physical astronomy as well.[28]

A plate from Astronomiae Pars Optica, illustrating the structure of eyes

As he slowly continued analyzing Tycho’s Mars observations—now available to him in their entirety— and began the slow process of tabulating the Rudolphine Tables, Kepler also picked up the investigation of the laws of optics from his lunar essay of 1600. Both lunar and solar eclipses presented unexplained phenomena, such as unexpected shadow sizes, the red color of a total lunar eclipse, and the reportedly unusual light surrounding a total solar eclipse. Related issues of atmospheric refraction applied to all astronomical observations. Through most of 1603, Kepler paused his other work to focus on optical theory; the resulting manuscript, Officially, the only acceptable religious doctrines in presented to the emperor on January 1, 1604, was Prague were Catholic and Utraquist, but Kepler’s posi- published as Astronomiae Pars Optica (The Optical Part tion in the imperial court allowed him to practice his of Astronomy). In it, Kepler described the inverse-square


20.3. PRAGUE (1600–1612) law governing the intensity of light, reflection by flat and curved mirrors, and principles of pinhole cameras, as well as the astronomical implications of optics such as parallax and the apparent sizes of heavenly bodies. He also extended his study of optics to the human eye, and is generally considered by neuroscientists to be the first to recognize that images are projected inverted and reversed by the eye’s lens onto the retina. The solution to this dilemma was not of particular importance to Kepler as he did not see it as pertaining to optics, although he did suggest that the image was later corrected “in the hollows of the brain” due to the “activity of the Soul.”[30] Today, Astronomiae Pars Optica is generally recognized as the foundation of modern optics (though the law of refraction is conspicuously absent).[31] With respect to the beginnings of projective geometry, Kepler introduced the idea of continuous change of a mathematical entity in this work. He argued that if a focus of a conic section were allowed to move along the line joining the foci, the geometric form would morph or degenerate, one into another. In this way, an ellipse becomes a parabola when a focus moves toward infinity, and when two foci of an ellipse merge into one another, a circle is formed. As the foci of a hyperbola merge into one another, the hyperbola becomes a pair of straight lines. He also assumed that if a straight line is extended to infinity it will meet itself at a single point at infinity, thus having the properties of a large circle.[32]

20.3.4

231 pecially regarding the emperor. It was in this context, as the imperial mathematician and astrologer to the emperor, that Kepler described the new star two years later in his De Stella Nova. In it, Kepler addressed the star’s astronomical properties while taking a skeptical approach to the many astrological interpretations then circulating. He noted its fading luminosity, speculated about its origin, and used the lack of observed parallax to argue that it was in the sphere of fixed stars, further undermining the doctrine of the immutability of the heavens (the idea accepted since Aristotle that the celestial spheres were perfect and unchanging). The birth of a new star implied the variability of the heavens. In an appendix, Kepler also discussed the recent chronology work of the Polish historian Laurentius Suslyga; he calculated that, if Suslyga was correct that accepted timelines were four years behind, then the Star of Bethlehem—analogous to the present new star—would have coincided with the first great conjunction of the earlier 800-year cycle.[33]

The Supernova of 1604

Remnant of Kepler’s Supernova SN 1604

In October 1604, a bright new evening star (SN 1604) appeared, but Kepler did not believe the rumors until he saw it himself. Kepler began systematically observing the nova. Astrologically, the end of 1603 marked the beginning of a fiery trigon, the start of the about 800-year cycle of great conjunctions; astrologers associated the two previous such periods with the rise of Charlemagne (c. 800 years earlier) and the birth of Christ (c. 1600 years earlier), and thus expected events of great portent, es-

The location of the stella nova, in the foot of Ophiuchus, is marked with an N (8 grid squares down, 4 over from the left).

20.3.5 Astronomia nova The extended line of research that culminated in Astronomia nova (A New Astronomy)—including the first two laws of planetary motion—began with the analysis, under Tycho’s direction, of Mars’ orbit. Kepler calculated and recalculated various approximations of Mars’


232 orbit using an equant (the mathematical tool that Copernicus had eliminated with his system), eventually creating a model that generally agreed with Tycho’s observations to within two arcminutes (the average measurement error). But he was not satisfied with the complex and still slightly inaccurate result; at certain points the model differed from the data by up to eight arcminutes. The wide array of traditional mathematical astronomy methods having failed him, Kepler set about trying to fit an ovoid orbit to the data.[34] Within Kepler’s religious view of the cosmos, the Sun (a symbol of God the Father) was the source of motive force in the solar system. As a physical basis, Kepler drew by analogy on William Gilbert’s theory of the magnetic soul of the Earth from De Magnete (1600) and on his own work on optics. Kepler supposed that the motive power (or motive species)[35] radiated by the Sun weakens with distance, causing faster or slower motion as planets move closer or farther from it.[36][37] Perhaps this assumption entailed a mathematical relationship that would restore astronomical order. Based on measurements of the aphelion and perihelion of the Earth and Mars, he created a formula in which a planet’s rate of motion is inversely proportional to its distance from the Sun. Verifying this relationship throughout the orbital cycle, however, required very extensive calculation; to simplify this task, by late 1602 Kepler reformulated the proportion in terms of geometry: planets sweep out equal areas in equal times—Kepler’s second law of planetary motion.[38]

Diagram of the geocentric trajectory of Mars through several periods of apparent retrograde motion (Astronomia nova, Chapter 1, 1609)

He then set about calculating the entire orbit of Mars, using the geometrical rate law and assuming an egg-shaped ovoid orbit. After approximately 40 failed attempts, in early 1605 he at last hit upon the idea of an ellipse, which he had previously assumed to be too simple a solution for

CHAPTER 20. JOHANNES KEPLER earlier astronomers to have overlooked.[39] Finding that an elliptical orbit fit the Mars data, he immediately concluded that all planets move in ellipses, with the sun at one focus—Kepler’s first law of planetary motion. Because he employed no calculating assistants, however, he did not extend the mathematical analysis beyond Mars. By the end of the year, he completed the manuscript for Astronomia nova, though it would not be published until 1609 due to legal disputes over the use of Tycho’s observations, the property of his heirs.[40]

20.3.6 Dioptrice, Somnium manuscript, and other work In the years following the completion of Astronomia Nova, most of Kepler’s research was focused on preparations for the Rudolphine Tables and a comprehensive set of ephemerides (specific predictions of planet and star positions) based on the table (though neither would be completed for many years). He also attempted (unsuccessfully) to begin a collaboration with Italian astronomer Giovanni Antonio Magini. Some of his other work dealt with chronology, especially the dating of events in the life of Jesus, and with astrology, especially criticism of dramatic predictions of catastrophe such as those of Helisaeus Roeslin.[41] Kepler and Roeslin engaged in a series of published attacks and counter-attacks, while physician Philip Feselius published a work dismissing astrology altogether (and Roeslin’s work in particular). In response to what Kepler saw as the excesses of astrology on the one hand and overzealous rejection of it on the other, Kepler prepared Tertius Interveniens [Third-party Interventions]. Nominally this work—presented to the common patron of Roeslin and Feselius—was a neutral mediation between the feuding scholars, but it also set out Kepler’s general views on the value of astrology, including some hypothesized mechanisms of interaction between planets and individual souls. While Kepler considered most traditional rules and methods of astrology to be the “evilsmelling dung” in which “an industrious hen” scrapes, there was an “occasional grain-seed, indeed, even a pearl or a gold nugget” to be found by the conscientious scientific astrologer.[42] Conversely, Sir Oliver Lodge observed that Kepler was somewhat disdainful of astrology, as Kepler was “continually attacking and throwing sarcasm at astrology, but it was the only thing for which people would pay him, and on it after a fashion he lived.”[43] In the first months of 1610, Galileo Galilei—using his powerful new telescope—discovered four satellites orbiting Jupiter. Upon publishing his account as Sidereus Nuncius [Starry Messenger], Galileo sought the opinion of Kepler, in part to bolster the credibility of his observations. Kepler responded enthusiastically with a short published reply, Dissertatio cum Nuncio Sidereo [Conversation with the Starry Messenger]. He endorsed Galileo’s


20.3. PRAGUE (1600–1612)

233

Karlova street in Old Town, Prague – house where Kepler lived. Museum

observations and offered a range of speculations about the meaning and implications of Galileo’s discoveries and telescopic methods, for astronomy and optics as well as cosmology and astrology. Later that year, Kepler published his own telescopic observations of the moons in Narratio de Jovis Satellitibus, providing further support of Galileo. To Kepler’s disappointment, however, Galileo never published his reactions (if any) to Astronomia Nova.[44]

One of the diagrams from Strena Seu de Nive Sexangula, illustrating the Kepler conjecture

nium was to describe what practicing astronomy would be like from the perspective of another planet, to show the feasibility of a non-geocentric system. The manuscript, which disappeared after changing hands several times, described a fantastic trip to the moon; it was part allegory, part autobiography, and part treatise on interplanetary travel (and is sometimes described as the first work of science fiction). Years later, a distorted version of the story may have instigated the witchcraft trial against his mother, as the mother of the narrator consults a demon to learn the means of space travel. Following her eventual acquittal, Kepler composed 223 footnotes to the story—several times longer than the actual text—which explained the allegorical aspects as well as the considerable scientific content (particularly regarding lunar geography) hidden within the text.[47]

After hearing of Galileo’s telescopic discoveries, Kepler also started a theoretical and experimental investigation of telescopic optics using a telescope borrowed from Duke Ernest of Cologne.[45] The resulting manuscript was completed in September 1610 and published as Dioptrice in 1611. In it, Kepler set out the theoretical basis of double-convex converging lenses and double-concave diverging lenses—and how they are combined to produce a Galilean telescope—as well as the concepts of real vs. virtual images, upright vs. inverted images, and the effects of focal length on magnification and reduction. He also described an improved telescope— now known as the astronomical or Keplerian telescope— in which two convex lenses can produce higher magnification than Galileo’s combination of convex and concave 20.3.7 lenses.[46]

Work in mathematics and physics

Around 1611, Kepler circulated a manuscript of As a New Year’s gift that year (1611), he also composed what would eventually be published (posthumously) as for his friend and some-time patron, Baron Wackher von Somnium [The Dream]. Part of the purpose of Som- Wackhenfels, a short pamphlet entitled Strena Seu de Nive


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Sexangula (A New Year’s Gift of Hexagonal Snow). In this treatise, he published the first description of the hexagonal symmetry of snowflakes and, extending the discussion into a hypothetical atomistic physical basis for the symmetry, posed what later became known as the Kepler conjecture, a statement about the most efficient arrangement for packing spheres.[48][49]

20.3.8

Personal and political troubles

In 1611, the growing political-religious tension in Prague came to a head. Emperor Rudolph—whose health was failing—was forced to abdicate as King of Bohemia by his brother Matthias. Both sides sought Kepler’s astrological advice, an opportunity he used to deliver conciliatory political advice (with little reference to the stars, except in general statements to discourage drastic action). However, it was clear that Kepler’s future prospects in the court of Matthias were dim.[50]

A statue of Kepler in Linz

church over his theological scruples. His first publication in Linz was De vero Anno (1613), an expanded treatise on the year of Christ’s birth; he also participated in deliberations on whether to introduce Pope Gregory's reformed calendar to Protestant German lands; that year he also Also in that year, Barbara Kepler contracted Hungarian wrote the influential mathematical treatise Nova sterespotted fever, then began having seizures. As Bar- ometria doliorum vinariorum, on measuring the volume bara was recovering, Kepler’s three children all fell sick of containers such as wine barrels, published in 1615.[53] with smallpox; Friedrich, 6, died. Following his son’s death, Kepler sent letters to potential patrons in Württemberg and Padua. At the University of Tübingen in 20.4.1 Second marriage Württemberg, concerns over Kepler’s perceived Calvinist heresies in violation of the Augsburg Confession and On October 30, 1613, Kepler married the 24-year-old the Formula of Concord prevented his return. The Susanna Reuttinger. Following the death of his first wife University of Padua—on the recommendation of the de- Barbara, Kepler had considered 11 different matches parting Galileo—sought Kepler to fill the mathematics over two years (a decision process formalized later as the professorship, but Kepler, preferring to keep his family in marriage problem).[54] He eventually returned to ReutGerman territory, instead travelled to Austria to arrange tinger (the fifth match) who, he wrote, “won me over with a position as teacher and district mathematician in Linz. love, humble loyalty, economy of household, diligence, However, Barbara relapsed into illness and died shortly and the love she gave the stepchildren.”[55] The first three after Kepler’s return.[51] children of this marriage (Margareta Regina, Katharina, Kepler postponed the move to Linz and remained in and Sebald) died in childhood. Three more survived into Prague until Rudolph’s death in early 1612, though be- adulthood: Cordula (born 1621); Fridmar (born 1623); tween political upheaval, religious tension, and family and Hildebert (born 1625). According to Kepler’s biogra[56] tragedy (along with the legal dispute over his wife’s es- phers, this was a much happier marriage than his first. tate), Kepler could do no research. Instead, he pieced together a chronology manuscript, Eclogae Chronicae, from correspondence and earlier work. Upon succession as 20.4.2 Epitome of Copernican Astronomy, calendars, and the witch trial of his Holy Roman Emperor, Matthias re-affirmed Kepler’s pomother sition (and salary) as imperial mathematician but allowed him to move to Linz.[52] For more details on this topic, see Epitome astronomiae Copernicanae. had in20.4 Linz and elsewhere (1612– Since completing the Astronomia nova, Kepler tended to compose an astronomy textbook.[57] In 1615, 1630) he completed the first of three volumes of Epitome astronomiae Copernicanae (Epitome of Copernican AstronIn Linz, Kepler’s primary responsibilities (beyond com- omy); the first volume (books I–III) was printed in 1617, pleting the Rudolphine Tables) were teaching at the dis- the second (book IV) in 1620, and the third (books V– trict school and providing astrological and astronomical VII) in 1621. Despite the title, which referred simply to services. In his first years there, he enjoyed financial secu- heliocentrism, Kepler’s textbook culminated in his own rity and religious freedom relative to his life in Prague— ellipse-based system. The Epitome became Kepler’s most though he was excluded from Eucharist by his Lutheran influential work. It contained all three laws of plane-


20.4. LINZ AND ELSEWHERE (1612–1630)

235

Kepler’s Figure 'M' from the Epitome, showing the world as belonging to just one of any number of similar stars.

tary motion and attempted to explain heavenly motions through physical causes.[58] Though it explicitly extended the first two laws of planetary motion (applied to Mars in Astronomia nova) to all the planets as well as the Moon and the Medicean satellites of Jupiter,[59] it did not explain how elliptical orbits could be derived from observational data.[60] As a spin-off from the Rudolphine Tables and the related Ephemerides, Kepler published astrological calendars, which were very popular and helped offset the costs of producing his other work—especially when support from the Imperial treasury was withheld. In his calendars—six between 1617 and 1624—Kepler forecast planetary positions and weather as well as political events; the latter were often cannily accurate, thanks to his keen grasp of contemporary political and theological tensions. By 1624, however, the escalation of those tensions and the ambiguity of the prophecies meant political trouble for Kepler himself; his final calendar was publicly burned in Graz.[61] In 1615, Ursula Reingold, a woman in a financial dispute with Kepler’s brother Christoph, claimed Kepler’s mother Katharina had made her sick with an evil brew. The dispute escalated, and in 1617 Katharina was accused of witchcraft; witchcraft trials were relatively common in central Europe at this time. Beginning in August 1620, she was imprisoned for fourteen months. She was released in October 1621, thanks in part to the extensive legal defense drawn up by Kepler. The accusers had no stronger evidence than rumors. Katharina was subjected to territio verbalis, a graphic description of the torture awaiting her as a witch, in a final attempt to make her confess. Throughout the trial, Kepler postponed his other work to focus on his “harmonic theory”. The result, published in 1619, was Harmonices Mundi (“Harmony of the World”).[62]

Geometrical harmonies in the perfect solids from Harmonices Mundi (1619)

20.4.3 Harmonices Mundi Main article: Harmonices Mundi Kepler was convinced “that the geometrical things have provided the Creator with the model for decorating the whole world”.[63] In Harmony, he attempted to explain the proportions of the natural world—particularly the astronomical and astrological aspects—in terms of music.[64] The central set of “harmonies” was the musica universalis or “music of the spheres”, which had been studied by Pythagoras, Ptolemy and many others before Kepler; in fact, soon after publishing Harmonices Mundi, Kepler was embroiled in a priority dispute with Robert Fludd, who had recently published his own harmonic theory.[65] Kepler began by exploring regular polygons and regular solids, including the figures that would come to be known as Kepler’s solids. From there, he extended his harmonic analysis to music, meteorology, and astrology; harmony resulted from the tones made by the souls of heavenly


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bodies—and in the case of astrology, the interaction between those tones and human souls. In the final portion of the work (Book V), Kepler dealt with planetary motions, especially relationships between orbital velocity and orbital distance from the Sun. Similar relationships had been used by other astronomers, but Kepler—with Tycho’s data and his own astronomical theories—treated them much more precisely and attached new physical significance to them.[66]

In 1623, Kepler at last completed the Rudolphine Tables, which at the time was considered his major work. However, due to the publishing requirements of the emperor and negotiations with Tycho Brahe’s heir, it would not be printed until 1627. In the meantime, religious tension — the root of the ongoing Thirty Years’ War — once again put Kepler and his family in jeopardy. In 1625, agents of the Catholic Counter-Reformation placed most of Kepler’s library under seal, and in 1626 the city of Linz was for Among many other harmonies, Kepler articulated what besieged. Kepler moved to Ulm, where he arranged the printing of the Tables at his own expense.[70] came to be known as the third law of planetary motion. He then tried many combinations until he discovered In 1628, following the military successes of the Emperor that (approximately) "The square of the periodic times Ferdinand’s armies under General Wallenstein, Kepler are to each other as the cubes of the mean distances.” became an official advisor to Wallenstein. Though not Although he gives the date of this epiphany (March 8, the general’s court astrologer per se, Kepler provided as1618), he does not give any details about how he arrived tronomical calculations for Wallenstein’s astrologers and at this conclusion.[67] However, the wider significance occasionally wrote horoscopes himself. In his final years, for planetary dynamics of this purely kinematical law Kepler spent much of his time traveling, from the impewas not realized until the 1660s. When conjoined with rial court in Prague to Linz and Ulm to a temporary home Christiaan Huygens' newly discovered law of centrifugal in Sagan, and finally to Regensburg. Soon after arriving force, it enabled Isaac Newton, Edmund Halley, and per- in Regensburg, Kepler fell ill. He died on November 15, haps Christopher Wren and Robert Hooke to demonstrate 1630, and was buried there; his burial site was lost afindependently that the presumed gravitational attraction ter the Swedish army destroyed the churchyard.[71] Only between the Sun and its planets decreased with the square Kepler’s self-authored poetic epitaph survived the times: of the distance between them.[68] This refuted the traditional assumption of scholastic physics that the power of Mensus eram coelos, nunc terrae metior umbras gravitational attraction remained constant with distance Mens coelestis erat, corporis umbra iacet. whenever it applied between two bodies, such as was assumed by Kepler and also by Galileo in his mistaken universal law that gravitational fall is uniformly accelerated, I measured the skies, now the shadows I meaand also by Galileo’s student Borrelli in his 1666 celestial sure mechanics.[69] Skybound was the mind, earthbound the body rests.[72]

20.4.4 Rudolphine Tables and his last years

20.5 Reception of his astronomy Kepler’s laws were not immediately accepted. Several major figures such as Galileo and René Descartes completely ignored Kepler’s Astronomia nova. Many astronomers, including Kepler’s teacher, Michael Maestlin, objected to Kepler’s introduction of physics into his astronomy. Some adopted compromise positions. Ismael Boulliau accepted elliptical orbits but replaced Kepler’s area law with uniform motion in respect to the empty focus of the ellipse, while Seth Ward used an elliptical orbit with motions defined by an equant.[73][74][75]

Kepler’s horoscope for General Wallenstein

Several astronomers tested Kepler’s theory, and its various modifications, against astronomical observations. Two transits of Venus and Mercury across the face of the sun provided sensitive tests of the theory, under circumstances when these planets could not normally be observed. In the case of the transit of Mercury in 1631, Kepler had been extremely uncertain of the parameters for Mercury, and advised observers to look for the transit the day before and after the predicted date. Pierre Gassendi


20.6. HISTORICAL AND CULTURAL LEGACY

237

observed the transit on the date predicted, a confirmation of Kepler’s prediction.[76] This was the first observation of a transit of Mercury. However, his attempt to observe the transit of Venus just one month later was unsuccessful due to inaccuracies in the Rudolphine Tables. Gassendi did not realize that it was not visible from most of Europe, including Paris.[77] Jeremiah Horrocks, who observed the 1639 Venus transit, had used his own observations to adjust the parameters of the Keplerian model, predicted the transit, and then built apparatus to observe the transit. He remained a firm advocate of the Keplerian model.[78][79][80] Epitome of Copernican Astronomy was read by astronomers throughout Europe, and following Kepler’s death it was the main vehicle for spreading Kepler’s ideas. Between 1630 and 1650, it was the most widely used astronomy textbook, winning many converts to ellipsebased astronomy.[58] However, few adopted his ideas on the physical basis for celestial motions. In the late 17th century, a number of physical astronomy theories drawing from Kepler’s work—notably those of Giovanni Alfonso Borelli and Robert Hooke—began to incorporate attractive forces (though not the quasi-spiritual motive species postulated by Kepler) and the Cartesian concept of inertia.[81] This culminated in Isaac Newton’s Principia Mathematica (1687), in which Newton derived Kepler’s laws of planetary motion from a force-based theory of universal gravitation.[82] The GDR stamp featuring Kepler

20.6 Historical and cultural legacy tronomy such as Jean-Étienne Montucla's 1758 Histoire des mathématiques and Jean-Baptiste Delambre's 1821 Histoire de l'astronomie moderne. These and other histories written from an Enlightenment perspective treated Kepler’s metaphysical and religious arguments with skepticism and disapproval, but later Romantic-era natural philosophers viewed these elements as central to his success. William Whewell, in his influential History of the Inductive Sciences of 1837, found Kepler to be the archetype of the inductive scientific genius; in his Philosophy of the Inductive Sciences of 1840, Whewell held Kepler up as the embodiment of the most advanced forms of scientific method. Similarly, Ernst Friedrich Apelt— the first to extensively study Kepler’s manuscripts, after their purchase by Catherine the Great—identified Kepler as a key to the "Revolution of the sciences". Apelt, who Monument to Tycho Brahe and Kepler in Prague, Czech Republic saw Kepler’s mathematics, aesthetic sensibility, physical ideas, and theology as part of a unified system of thought, produced the first extended analysis of Kepler’s life and work.[83]

20.6.1

History of science

Beyond his role in the historical development of astronomy and natural philosophy, Kepler has loomed large in the philosophy and historiography of science. Kepler and his laws of motion were central to early histories of as-

Alexandre Koyré's work on Kepler was, after Apelt, the first major milestone in historical interpretations of Kepler’s cosmology and its influence. In the 1930s and 1940s, Koyré, and a number of others in the first generation of professional historians of science, described


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the "Scientific Revolution" as the central event in the history of science, and Kepler as a (perhaps the) central figure in the revolution. Koyré placed Kepler’s theorization, rather than his empirical work, at the center of the intellectual transformation from ancient to modern worldviews. Since the 1960s, the volume of historical Kepler scholarship has expanded greatly, including studies of his astrology and meteorology, his geometrical methods, the role of his religious views in his work, his literary and rhetorical methods, his interaction with the broader cultural and philosophical currents of his time, and even his role as an historian of science.[84]

20.6.3 Popular science and historical fiction Kepler has acquired a popular image as an icon of scientific modernity and a man before his time; science popularizer Carl Sagan described him as “the first astrophysicist and the last scientific astrologer”.[89]

The debate over Kepler’s place in the Scientific Revolution has produced a wide variety of philosophical and popular treatments. One of the most influential is Arthur Koestler's 1959 The Sleepwalkers, in which Kepler is unambiguously the hero (morally and theologically as well Philosophers of science—such as Charles Sanders Peirce, as intellectually) of the revolution.[90] Norwood Russell Hanson, Stephen Toulmin, and Karl A well-received, if fanciful, historical novel by John Popper—have repeatedly turned to Kepler: examples of Banville, Kepler (1981), explored many of the themes deincommensurability, analogical reasoning, falsification, veloped in Koestler’s non-fiction narrative and in the phiand many other philosophical concepts have been found losophy of science.[91] Somewhat more fanciful is a recent in Kepler’s work. Physicist Wolfgang Pauli even used work of nonfiction, Heavenly Intrigue (2004), suggesting Kepler’s priority dispute with Robert Fludd to explore that Kepler murdered Tycho Brahe to gain access to his the implications of analytical psychology on scientific data.[92] [85] investigation.

20.6.2

Editions and translations

Modern translations of a number of Kepler’s books appeared in the late-nineteenth and early-twentieth centuries, the systematic publication of his collected works began in 1937 (and is nearing completion in the early 21st century). An edition in eight volumes, Kepleri Opera omnia, was prepared by Christian Frisch (1807–1881), during 1858 to 1871, on the occasion of Kepler’s 300th birthday. Frisch’s edition only included Kepler’s Latin, with a Latin commentary. A new edition was planned beginning in 1914 by Walther von Dyck (1856–1934). Dyck compiled copies of Kepler’s unedited manuscripts, using international diplomatic contacts to convince the Soviet authorities to lend him the manuscripts kept in Leningrad for photographic reproduction. These manuscripts contained several works by Kepler that had not been available to Frisch. Dyck’s photographs remain the basis for the modern editions of Kepler’s unpublished manuscripts. Max Caspar (1880–1956) published his German translation of Kepler’s Mysterium Cosmographicum in 1923. Both Dyck and Caspar were influenced in their interest in Kepler by mathematician Alexander von Brill (1842– 1935). Caspar became Dyck’s collaborator, succeeding him as project leader in 1934, establishing the KeplerKommission in the following year. Assisted by Martha List (1908–1992) and Franz Hammer (1898–1979), Caspar continued editorial work during World War II. Max Caspar also published a biography of Kepler in 1948.[86] The commission was later chaired by Volker Bialas (during 1976–2003) and Ulrich Grigull (during 1984–1999) and Roland Bulirsch (1998–2014).[87][88]

20.6.4 Veneration and eponymy In Austria, Kepler left behind such a historical legacy that he was one of the motifs of a silver collector’s coin: the 10-euro Johannes Kepler silver coin, minted on September 10, 2002. The reverse side of the coin has a portrait of Kepler, who spent some time teaching in Graz and the surrounding areas. Kepler was acquainted with Prince Hans Ulrich von Eggenberg personally, and he probably influenced the construction of Eggenberg Castle (the motif of the obverse of the coin). In front of him on the coin is the model of nested spheres and polyhedra from Mysterium Cosmographicum.[93] The German composer Paul Hindemith wrote an opera about Kepler entitled Die Harmonie der Welt, and a symphony of the same name was derived from music for the opera. Philip Glass wrote an opera called Kepler based on Kepler’s life (2009). Kepler is honored together with Nicolaus Copernicus with a feast day on the liturgical calendar of the Episcopal Church (USA) on May 23.[94] Main article: List of things named after Johannes Kepler Directly named for Kepler’s contribution to science are Kepler’s laws of planetary motion, Kepler’s Supernova (Supernova 1604, which he observed and described) and the Kepler Solids, a set of geometrical constructions, two of which were described by him, and the Kepler conjecture on sphere packing. • In astronomy: The lunar crater Kepler (Keplerus, named by Giovanni Riccioli, 1651), the asteroid 1134 Kepler (1929), Kepler (crater on Mars) (1973), Kepler Launch Site for model rockets


20.7. WORKS

239 • Astronomia nova (New Astronomy) (1609) • Tertius Interveniens (Third-party Interventions) (1610) • Dissertatio cum Nuncio Sidereo (Conversation with the Starry Messenger) (1610) • Dioptrice (1611) • De nive sexangula (On the Six-Cornered Snowflake) (1611) • De vero Anno, quo aeternus Dei Filius humanam naturam in Utero benedictae Virginis Mariae assumpsit (1614)[97] • Eclogae Chronicae (1615, published with Dissertatio cum Nuncio Sidereo)

The Kepler crater as photographed by Apollo 12 in 1969

(2001), the Kepler Mission, a space photometer launched by NASA in 2009,[95] Johannes Kepler ATV (Automated Transfer Vehicle launched to resupply the ISS in 2011). • Educational institutions: Johannes Kepler University of Linz (1975), Kepler College (Seattle, Washington), besides several institutions of primary and secondary education, such as Johannes Kepler Grammar School,[96] at the site where Kepler lived in Prague, and Kepler Gymnasium, Tübingen

• Nova stereometria doliorum vinariorum (New Stereometry of Wine Barrels) (1615) • Epitome astronomiae Copernicanae (Epitome of Copernican Astronomy) (published in three parts from 1618 to 1621) • Harmonices Mundi (Harmony of the Worlds) (1619) • Mysterium cosmographicum (The Sacred Mystery of the Cosmos), 2nd edition (1621) • Tabulae Rudolphinae (Rudolphine Tables) (1627) • Somnium (The Dream) (1634)

A critical edition of Kepler’s collected works (Johannes • Streets or squares named after him: Keplerplatz Kepler Gesammelte Werke, KGW) in 22 volumes is beVienna (station of Vienna U-Bahn), Keplerstraße ing edited by the Kepler-Kommission (founded 1935) on in Hanau near Frankfurt am Main, Keplerstraße in behalf of the Bayerische Akademie der Wissenschaften. Munich, Germany, Keplerstraße and Keplerbrücke in Graz, Austria. Vol. 1: Mysterium Cosmographicum. De Stella Nova. Ed. M. Caspar. 1938, 2nd ed. 1993. • The Kepler Mountains and Kepler Track in FiordPaperback ISBN 3-406-01639-1. land National Park, South Island, New Zealand; Vol. 2: Astronomiae pars optica. Ed. F. HamKepler Challenge (1988). mer. 1939, Paperback ISBN 3-406-01641-3. • Kepler, a high end graphics processing microarchiVol. 3: Astronomia Nova. Ed. M. Caspar. tecture introduced by Nvidia in 2012. 1937. IV, 487 p. 2. ed. 1990. Paperback

20.7 Works • Mysterium Cosmographicum (The Sacred Mystery of the Cosmos) (1596) • De Fundamentis Astrologiae Certioribus (On Firmer Fundaments of Astrology; 1601) • Astronomiae Pars Optica (The Optical Part of Astronomy) (1604) • De Stella nova in pede Serpentarii (On the New Star in Ophiuchus’s Foot) (1606)

ISBN 3-406-01643-X. Semi-parchment ISBN 3-406-01642-1. Vol. 4: Kleinere Schriften 1602–1611. Dioptrice. Ed. M. Caspar, F. Hammer. 1941. ISBN 3-406-01644-8. Vol. 5: Chronologische Schriften. Ed. F. Hammer. 1953. Out-of-print. Vol. 6: Harmonice Mundi. Ed. M. Caspar. 1940, 2nd ed. 1981, ISBN 3-406-01648-0. Vol. 7: Epitome Astronomiae Copernicanae. Ed. M. Caspar. 1953, 2nd ed. 1991. ISBN 3406-01650-2, Paperback ISBN 3-406-016510.


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CHAPTER 20. JOHANNES KEPLER Vol. 8: Mysterium Cosmographicum. Editio altera cum notis. De Cometis. Hyperaspistes. Commentary F. Hammer. 1955. Paperback ISBN 3-406-01653-7. Vol 9: Mathematische Schriften. Ed. F. Hammer. 1955, 2nd ed. 1999. Out-of-print. Vol. 10: Tabulae Rudolphinae. Ed. F. Hammer. 1969. ISBN 3-406-01656-1. Vol. 11,1: Ephemerides novae motuum coelestium. Commentary V. Bialas. 1983. ISBN 3-406-01658-8, Paperback ISBN 3406-01659-6. Vol. 11,2: Calendaria et Prognostica. Astronomica minora. Somnium. Commentary V. Bialas, H. Grössing. 1993. ISBN 3-40637510-3, Paperback ISBN 3-406-37511-1. Vol. 12: Theologica. Hexenprozeß. TacitusÜbersetzung. Gedichte. Commentary J. Hübner, H. Grössing, F. Boockmann, F. Seck. Directed by V. Bialas. 1990. ISBN 3-40601660-X, Paperback ISBN 3-406-01661-8.

• Vols. 13–18: Letters: Vol. 13: Briefe 1590–1599. Ed. M. Caspar. 1945. 432 p. ISBN 3406-01663-4. Vol. 14: Briefe 1599–1603. Ed. M. Caspar. 1949. Out-of-print. 2nd ed. in preparation. Vol 15: Briefe 1604–1607. Ed. M. Caspar. 1951. 2nd ed. 1995. ISBN 3-406-01667-7. Vol. 16: Briefe 1607–1611. Ed. M. Caspar. 1954. ISBN 3-40601668-5. Vol. 17: Briefe 1612–1620. Ed. M. Caspar. 1955. ISBN 3-40601671-5. Vol. 18: Briefe 1620–1630. Ed. M. Caspar. 1959. ISBN 3-40601672-3. Vol. 19: Dokumente zu Leben und Werk. Commentary M. List. 1975. ISBN 978-3-40601674-5. Vols. 20–21: manuscripts Vol. 20,1: Manuscripta astronomica (I). Apologia, De motu Terrae, Hipparchus etc. Commentary V. Bialas. 1988. ISBN 3-406-315011. Paperback ISBN 3-406-31502X. Vol. 20,2: Manuscripta astronomica (II). Commentaria in Theoriam

Martis. Commentary V. Bialas. 1998. Paperback ISBN 3-40640593-2. Vol. 21,1: Manuscripta astronomica (III) et mathematica. De Calendario Gregoriano. In preparation. Vol. 21,2: Manuscripta varia. In preparation. Vol. 22: General index, in preparation. The Kepler-Kommission also publishes Bibliographia Kepleriana (2nd ed. List, 1968), a complete bibliography of editions of Kepler’s works, with a supplementary volume to the second edition (ed. Hamel 1998).

20.8 See also • Cavalieri’s principle • History of astronomy • History of physics • Kepler orbit • Kepler problem • Kepler triangle • Kepler’s laws of planetary motion • Kepler–Bouwkamp constant • List of things named after Johannes Kepler • Scientific revolution

20.9 Notes and references [1] Barker and Goldstein. “Theological Foundations of Kepler’s Astronomy”, pp. 112–13. [2] Kepler. New Astronomy, title page, tr. Donohue, pp. 26– 7 [3] Kepler. New Astronomy, p. 48 [4] Epitome of Copernican Astronomy in Great Books of the Western World, Vol 15, p. 845 [5] Stephenson. Kepler’s Physical Astronomy, pp. 1–2; Dear, Revolutionizing the Sciences, pp. 74–78 [6] Caspar. Kepler, pp. 29–36; Connor. Kepler’s Witch, pp. 23–46. [7] Koestler. The Sleepwalkers, p. 234 (translated from Kepler’s family horoscope). [8] Caspar. Kepler, pp. 36–38; Connor. Kepler’s Witch, pp. 25–27.


20.9. NOTES AND REFERENCES

[9] Connor, James A. Kepler’s Witch (2004), p. 58. [10] Barker, Peter; Goldstein, Bernard R. “Theological Foundations of Kepler’s Astronomy”, Osiris, 2nd Series, Vol. 16, Science in Theistic Contexts: Cognitive Dimensions (2001), p. 96. [11] Westman, Robert S. “Kepler’s Early Physico-Astrological Problematic,” Journal for the History of Astronomy, 32 (2001): 227–36. [12] Caspar. Kepler, pp. 38–52; Connor. Kepler’s Witch, pp. 49–69. [13] Caspar. Kepler, pp. 60–65; see also: Barker and Goldstein, “Theological Foundations of Kepler’s Astronomy.”

241

[36] “Kepler’s decision to base his causal explanation of planetary motion on a distance-velocity law, rather than on uniform circular motions of compounded spheres, marks a major shift from ancient to modern conceptions of science ... [Kepler] had begun with physical principles and had then derived a trajectory from it, rather than simply constructing new models. In other words, even before discovering the area law, Kepler had abandoned uniform circular motion as a physical principle.” Peter Barker and Bernard R. Goldstein, “Distance and Velocity in Kepler’s Astronomy”, Annals of Science, 51 (1994): 59–73, at p. 60. [37] Koyré, The Astronomical Revolution, pp. 199–202. [38] Caspar, Kepler, pp. 129–132

[14] Barker and Goldstein. “Theological Foundations of Kepler’s Astronomy,” pp. 99–103, 112–113.

[39] Caspar, Kepler, p. 133

[15] Caspar. Kepler, pp. 65–71.

[40] Caspar, Kepler, pp. 131–140; Koyré, The Astronomical Revolution, pp. 277–279

[16] Field. Kepler’s Geometrical Cosmology, Chapter IV, p 73ff.

[41] Caspar, Kepler, pp. 178–81

[17] Dreyer, J.L.E. A History of Astronomy from Thales to Kepler, Dover Publications, 1953, pp. 331, 377–379. [18] Caspar, Kepler. pp. 71–75. [19] Connor. Kepler’s Witch, pp. 89–100, 114–116; Caspar. Kepler, pp. 75–77 [20] Caspar. Kepler, pp. 85–86. [21] Caspar, Kepler, pp. 86–89 [22] Caspar, Kepler, pp. 89–100

[42] Caspar, Kepler, pp. 181–85. The full title is Tertius Interveniens, das ist Warnung an etliche Theologos, Medicos vnd Philosophos, sonderlich D. Philippum Feselium, dass sie bey billicher Verwerffung der Sternguckerischen Aberglauben nict das Kindt mit dem Badt aussschütten vnd hiermit jhrer Profession vnwissendt zuwider handlen, translated by C. Doris Hellman as "Tertius Interveniens, that is warning to some theologians, medics and philosophers, especially D. Philip Feselius, that they in cheap condemnation of the star-gazer’s superstition do not throw out the child with the bath and hereby unknowingly act contrary to their profession.”

[24] Caspar, Kepler, pp. 100–08.

[43] Lodge, O.J., Johann Kepler in “The World of Mathematics”, Vol. 1 (1956) Ed. Newman, J.R., Simon and Schuster, pp. 231.

[25] Caspar, Kepler, p. 110.

[44] Caspar, Kepler, pp. 192–197

[26] Caspar, Kepler, pp. 108–11.

[45] Koestler, The Sleepwalkers p. 384

[27] Caspar, Kepler, pp. 111–22.

[46] Caspar, Kepler, pp. 198–202

[28] Caspar, Kepler, pp. 149–53

[47] Lear, Kepler’s Dream, pp. 1–78

[29] Caspar, Kepler, pp. 146–148, 159–177

[48] Schneer, “Kepler’s New Year’s Gift of a Snowflake,” pp. 531–45

[23] Using Tycho’s data, see 'Two views of a system'

[30] Finger, “Origins of Neuroscience,” p 74. Oxford University Press, 2001. [31] Caspar, Kepler, pp. 142–146

[49] Kepler, Johannes (1966) [1611]. Hardie, Colin, ed. De nive sexangula [The Six-sided Snowflake]. Oxford: Clarendon Press. OCLC 974730.

[32] Morris Kline, Mathematical Thought from Ancient to Modern Times, p 299. Oxford University Press, 1972.

[50] Caspar, Kepler, pp. 202–204

[33] Caspar, Kepler, pp. 153–157

[51] Connor, Kepler’s Witch, pp. 222–226; Caspar, Kepler, pp. 204–07

[34] Caspar, Kepler, pp. 123–128 [52] Caspar, Kepler, pp. 208–11 [35] On motive species, see Lindberg, “The Genesis of Kepler’s Theory of Light,” pp. 38–40.

[53] Caspar, Kepler, pp. 209–20, 227–240


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[54] Ferguson, Thomas S. (1989), “Who solved the secretary problem ?", Statistical Science, 4 (3): 282–289, doi:10.1214/ss/1177012493, JSTOR 2245639, When the celebrated German astronomer, Johannes Kepler (1571– 1630), lost his first wife to cholera in 1611, he set about finding a new wife using the same methodical thoroughness and careful consideration of the data that he used in finding the orbit of Mars to be an ellipse ... The process consumed much of his attention and energy for nearly 2 years ... [55] Quotation from Connor, Kepler’s Witch, p 252, translated from an October 23, 1613 letter from Kepler to an anonymous nobleman [56] Caspar, Kepler, pp. 220–223; Connor, Kepler’s Witch, pp. 251–54. [57] Caspar, Kepler, pp. 239–240, 293–300 [58] Gingerich, “Kepler, Johannes” from Dictionary of Scientific Biography, pp. 302–04 [59] By 1621 or earlier, Kepler recognized that Jupiter’s moons obey his third law. Kepler contended that rotating massive bodies communicate their rotation to their satellites, so that the satellites are swept around the central body; thus the rotation of the Sun drives the revolutions of the planets and the rotation of the Earth drives the revolution of the Moon. In Kepler’s era, no one had any evidence of Jupiter’s rotation. However, Kepler argued that the force by which a central body causes its satellites to revolve around it, weakens with distance; consequently, satellites that are farther from the central body revolve slower. Kepler noted that Jupiter’s moons obeyed this pattern and he inferred that a similar force was responsible. He also noted that the orbital periods and semi-major axes of Jupiter’s satellites were roughly related by a 3/2 power law, as are the orbits of the six (then known) planets. However, this relation was approximate: the periods of Jupiter’s moons were known within a few percent of their modern values, but the moons’ semi-major axes were determined less accurately. Kepler discussed Jupiter’s moons in his Epitome Astronomiae Copernicanae [Summary of Copernican Astronomy] (Linz (“Lentiis ad Danubium”), (Austria): Johann Planck, 1622), book 4, part 2, page 554. (For a more modern and legible edition, see: Christian Frisch, ed., Joannis Kepleri Astronomi Opera Omnia, vol. 6 (Frankfurt-am-Main, (Germany): Heyder & Zimmer, 1866), page 361.) Original : 4) Confirmatur vero fides hujus rei comparatione quatuor Jovialium et Jovis cum sex planetis et Sole. Etsi enim de corpore Jovis, an et ipsum circa suum axem convertatur, non ea documenta habemus, quae nobis suppetunt in corporibus Terrae et praecipue Solis, quippe a sensu ipso: at illud sensus testatur, plane ut est cum sex planetis circa Solem, sic etiam se rem habere cum quatuor Jovialibus, ut circa corpus Jovis quilibet, quo longius ab illo potest excurrere, hoc tardius redeat, et id quidem proportione non eadem, sed majore, hoc est sescupla proportionis intervallorum cujusque a Jove: quae plane ipsissima

est, qua utebantur supra sex planetae. Intervalla enim quatuor Jovialium a Jove prodit Marius in suo Mundo Joviali ista: 3, 5, 8, 13 (vel 14 Galilaeo) ... Periodica vero tempora prodit idem Marius ista: dies 1. h. 18 1/2, dies 3 h. 13 1/3, dies 7 h. 3, dies 16 h. 18: ubique proportio est major quam dupla, major igitur quam intervallorum 3, 5, 8, 13 vel 14, minor tamen quam quadratorum, qui duplicant proportiones intervallorum, sc. 9, 25, 64, 169 vel 196, sicut etiam sescupla sunt majora simplis, minora vero duplis. Translation : (4) However, the credibility of this [argument] is proved by the comparison of the four [moons] of Jupiter and Jupiter with the six planets and the Sun. Because, regarding the body of Jupiter, whether it turns around its axis, we don't have proofs for what suffices for us [regarding the rotation of ] the body of the Earth and especially of the Sun, certainly [as reason proves to us]: but reason attests that, just as it is clearly [true] among the six planets around the Sun, so also it is among the four [moons] of Jupiter, because around the body of Jupiter any [satellite] that can go farther from it orbits slower, and even that [orbit’s period] is not in the same proportion, but greater [than the distance from Jupiter]; that is, 3/2 (sescupla ) of the proportion of each of the distances from Jupiter, which is clearly the very [proportion] as [is used for] the six planets above. In his [book] The World of Jupiter [Mundus Jovialis, 1614], [Simon] Mayr [1573–1624] presents these distances, from Jupiter, of the four [moons] of Jupiter: 3, 5, 8, 13 (or 14 [according to] Galileo) ... Mayr presents their time periods: 1 day 18 1/2 hours, 3 days 13 1/3 hours, 7 days 3 hours, 16 days 18 hours: for all [of these data] the proportion is greater than double, thus greater than [the proportion] of the distances 3, 5, 8, 13 or 14, although less than [the proportion] of the squares, which double the proportions of the distances, namely 9, 25, 64, 169 or 196, just as [a power of] 3/2 is also greater than 1 but less than 2. [60] Wolf, A History of Science, Technology and Philosophy, pp. 140–41; Pannekoek, A History of Astronomy, p 252 [61] Caspar, Kepler, pp. 239, 300–01, 307–08 [62] Caspar, Kepler, pp. 240–264; Connor, Kepler’s Witch, chapters I, XI-XIII; Lear, Kepler’s Dream, pp. 21–39 [63] Quotation from Caspar, Kepler, pp. 265–266, translated from Harmonices Mundi [64] The opening of the movie Mars et Avril by Martin Villeneuve is based on German astronomer Johannes Kepler’s cosmological model from the 17th century, Harmonices Mundi, in which the harmony of the universe is determined by the motion of celestial bodies. Benoît Charest also composed the score according to this theory.


20.10. SOURCES

[65] Caspar, Kepler, pp. 264–66, 290–93 [66] Caspar, Kepler, pp. 266–90 [67] Miller, Arthur I. (March 24, 2009). Deciphering the cosmic number: the strange friendship of Wolfgang Pauli and Carl Jung. W. W. Norton & Company. p. 80. ISBN 978-0-393-06532-9. Retrieved March 7, 2011. [68] Westfall, Never at Rest, pp. 143, 152, 402–03; Toulmin and Goodfield, The Fabric of the Heavens, p 248; De Gandt, 'Force and Geometry in Newton’s Principia', chapter 2; Wolf, History of Science, Technology and Philosophy, p. 150; Westfall, The Construction of Modern Science, chapters 7 and 8 [69] Koyré, The Astronomical Revolution, p. 502 [70] Caspar, Kepler, pp. 308–328 [71] Caspar, Kepler, pp. 332–351, 355–61 [72] Koestler, The Sleepwalkers, p. 427. [73] For a detailed study of the reception of Kepler’s astronomy see Wilbur Applebaum, “Keplerian Astronomy after Kepler: Researches and Problems,” History of Science, 34(1996): 451–504. [74] Koyré, The Astronomical Revolution, pp. 362–364 [75] North, History of Astronomy and Cosmology, pp. 355–60 [76] Helden, Albert van (1976). “The Importance of the Transit of Mercury of 1631”. Journal for the History of Astronomy. 7: 1–10. Bibcode:1976JHA.....7....1V. [77] HM Nautical Almanac Office (June 10, 2004). “1631 Transit of Venus”. Archived from the original on October 1, 2006. Retrieved August 28, 2006. [78] Allan Chapman, “Jeremiah Horrocks, the transit of Venus, and the 'New Astronomy' in early 17th-century England,” Quarterly Journal of the Royal Astronomical Society, 31 (1990): 333–357. [79] North, History of Astronomy and Cosmology, pp. 348– 349 [80] Wilbur Applebaum and Robert Hatch, “Boulliau, Mercator, and Horrock’s Venus in sole visa: Three Unpublished Letters,” Journal for the History of Astronomy, 14(1983): 166–179 [81] Lawrence Nolan (ed.), The Cambridge Descartes Lexicon, Cambridge University Press, 2016, “Inertia.” [82] Kuhn, The Copernican Revolution, pp. 238, 246–252 [83] Jardine, “Koyré's Kepler/Kepler’s Koyré,” pp. 363–367 [84] Jardine, “Koyré's Kepler/Kepler’s Koyré,” pp. 367–372; Shapin, The Scientific Revolution, pp. 1–2

243

[88] kepler-kommission.de. Ulf Hashagen, Walther von Dyck (1856–1934). Mathematik, Technik und Wissenschaftsorganisation an der TH München, Stuttgart, 2003. [89] Quote from Carl Sagan, Cosmos: A Personal Voyage, episode III: “The Harmony of the Worlds”. Kepler was hardly the first to combine physics and astronomy; however, according to the traditional (though disputed) interpretation of the Scientific Revolution, he would be the first astrophysicist in the era of modern science. [90] Stephen Toulmin, Review of The Sleepwalkers in The Journal of Philosophy, Vol. 59, no. 18 (1962), pp. 500– 503 [91] William Donahue, “A Novelist’s Kepler,” Journal for the History of Astronomy, Vol. 13 (1982), pp. 135–136; “Dancing the grave dance: Science, art and religion in John Banville’s Kepler,” English Studies, Vol. 86, no. 5 (October 2005), pp. 424–438 [92] Marcelo Gleiser, “Kepler in the Dock”, review of Gilder and Gilder’s Heavenly Intrigue, Journal for the History of Astronomy, Vol. 35, pt. 4 (2004), pp. 487–489 [93] “Eggenberg Palace coin”. September 9, 2009.

Austrian Mint.

Retrieved

[94] “Calendar of the Church Year according to the Episcopal Church”. Charles Wohlers. Retrieved October 17, 2014. [95] Ng, Jansen (July 3, 2009). “Kepler Mission Sets Out to Find Planets Using CCD Cameras”. DailyTech. Retrieved July 3, 2009. [96] “GJK.cz”. GJK.cz. Retrieved October 17, 2014. [97] "... in 1614, Johannes Kepler published his book “De vero anno quo aeternus dei filius humanum naturam in utero benedictae Virginis Mariae assumpsit”, on the chronology related to the Star of Bethlehem.”, The Star of Bethlehem, Kapteyn Astronomical Institute

• The most complete biography of Kepler is Max Caspar’s Kepler. Though there are a number of more recent biographies, most are based on Caspar’s work with minimal original research; much of the information cited from Caspar can also be found in the books by Arthur Koestler, Kitty Ferguson, and James A. Connor. Owen Gingerich’s The Eye of Heaven builds on Caspar’s work to place Kepler in the broader intellectual context of early-modern astronomy. Many later studies have focused on particular elements of his life and work. Kepler’s mathematics, cosmological, philosophical and historical views have been extensively analyzed in books and journal articles, though his astrological work—and its relationship to his astronomy—remains understudied.

[85] Pauli, “The Influence of Archetypical Ideas” [86] Gingerich, introduction to Caspar’s Kepler, pp. 3–4 [87] Ulrich Grigull, “Sechzig Jahre Kepler-Kommission”, in: Sitzungsberichte der Bayerischen Akademie der Wissenschaften [Sitzung vom 5. Juli 1996], 1996.

20.10 Sources • Andersen, Hanne; Peter Barker; and Xiang Chen. The Cognitive Structure of Scientific Revolutions,


244

CHAPTER 20. JOHANNES KEPLER chapter 6: “The Copernican Revolution.” New York: Cambridge University Press, 2006. ISBN 0521-85575-6

• Armitage, Angus. John Kepler, Faber, 1966. • Banville, John. Kepler, Martin, Secker and Warburg, London, 1981 (fictionalised biography) • Barker, Peter and Bernard R. Goldstein: “Theological Foundations of Kepler’s Astronomy”. Osiris, Volume 16. Science in Theistic Contexts. University of Chicago Press, 2001, pp. 88–113 • Caspar, Max. Kepler; transl. and ed. by C. Doris Hellman; with a new introduction and references by Owen Gingerich; bibliographic citations by Owen Gingerich and Alain Segonds. New York: Dover, 1993. ISBN 0-486-67605-6 • Connor, James A. Kepler’s Witch: An Astronomer’s Discovery of Cosmic Order Amid Religious War, Political Intrigue, and the Heresy Trial of His Mother. HarperSanFrancisco, 2004. ISBN 0-06-052255-0 • De Gandt, Francois. Force and Geometry in Newton’s Principia, Translated by Curtis Wilson, Princeton University Press 1995. ISBN 0-69103367-6 • Dreyer, J. L. E. A History of Astronomy from Thales to Kepler. Dover Publications Inc, 1967. ISBN 0486-60079-3 • Ferguson, Kitty. The nobleman and his housedog: Tycho Brahe and Johannes Kepler: the strange partnership that revolutionized science. London: Review, 2002. ISBN 0-7472-7022-8 – published in the US as: Tycho & Kepler: the unlikely partnership that forever changed our understanding of the heavens. New York: Walker, 2002. ISBN 0-8027-1390-4 • Field, J. V.. Kepler’s geometrical cosmology. Chicago University Press, 1988. ISBN 0-22624823-2 • Gilder, Joshua and Anne-Lee Gilder: Heavenly Intrigue: Johannes Kepler, Tycho Brahe, and the Murder Behind One of History’s Greatest Scientific Discoveries, Doubleday (May 18, 2004). ISBN 0-385-50844-1 Reviews bookpage.com, crisismagazine.com • Gingerich, Owen. The Eye of Heaven: Ptolemy, Copernicus, Kepler. American Institute of Physics, 1993. ISBN 0-88318-863-5 (Masters of modern physics; v. 7) • Gingerich, Owen: “Kepler, Johannes” in Dictionary of Scientific Biography, Volume VII. Charles Coulston Gillispie, editor. New York: Charles Scribner’s Sons, 1973

• Greenbaum and Boockmann: “Kepler’s Astrology”, Culture and Cosmos Vol. 14. Special Double Issue, 2012. • Jardine, Nick: “Koyré's Kepler/Kepler’s Koyré,” History of Science, Vol. 38 (2000), pp. 363–376 • Kepler, Johannes. Johannes Kepler New Astronomy trans. W. Donahue, forward by O. Gingerich, Cambridge University Press 1993. ISBN 0-52130131-9 • Kepler, Johannes and Christian Frisch. Joannis Kepleri Astronomi Opera Omnia (John Kepler, Astronomer; Complete Works), 8 vols.(1858–1871). vol. 1, 1858, vol. 2, 1859, vol. 3, 1860, vol. 6, 1866, vol. 7, 1868, Frankfurt am Main and Erlangen, Heyder & Zimmer, – Google Books • Kepler, Johannes, et al. Great Books of the Western World. Volume 16: Ptolemy, Copernicus, Kepler, Chicago: Encyclopædia Britannica, Inc., 1952. (contains English translations by of Kepler’s Epitome, Books IV & V and Harmonices Book 5) • Koestler, Arthur. The Sleepwalkers: A History of Man’s Changing Vision of the Universe. (1959). ISBN 0-14-019246-8 • Koyré, Alexandre: Galilean Studies Harvester Press 1977. ISBN 0-85527-354-2 • Koyré, Alexandre: The Astronomical Revolution: Copernicus-Kepler-Borelli Ithaca, NY: Cornell University Press, 1973. ISBN 0-8014-0504-1; Methuen, 1973. ISBN 0-416-76980-2; Hermann, 1973. ISBN 2-7056-5648-0 • Kuhn, Thomas S. The Copernican Revolution: Planetary Astronomy in the Development of Western Thought. Cambridge, MA: Harvard University Press, 1957. ISBN 0-674-17103-9 • Lindberg, David C.: “The Genesis of Kepler’s Theory of Light: Light Metaphysics from Plotinus to Kepler.” Osiris, N.S. 2. University of Chicago Press, 1986, pp. 5–42. • Lear, John. Kepler’s Dream. Berkeley: University of California Press, 1965 • M.T.K Al-Tamimi. “Great collapse Kepler’s first law”, Natural Science, 2 (2010), ISSN 2150-4091 • North, John. The Fontana History of Astronomy and Cosmology, Fontana Press, 1994. ISBN 0-00686177-6 • Pannekoek, Anton: A History of Astronomy, Dover Publications Inc 1989. ISBN 0-486-65994-1


20.11. EXTERNAL LINKS

245

• Pauli, Wolfgang. Wolfgang Pauli — Writings on physics and philosophy, translated by Robert Schlapp and edited by P. Enz and Karl von Meyenn (Springer Verlag, Berlin, 1994). See section 21, The influence of archetypical ideas on the scientific theories of Kepler, concerning Johannes Kepler and Robert Fludd (1574–1637). ISBN 3-540-56859-X

• JohannesKepler.Info Kepler information and community website, launched on December 27, 2009

• Schneer, Cecil: “Kepler’s New Year’s Gift of a Snowflake.” Isis, Volume 51, No. 4. University of Chicago Press, 1960, pp. 531–545.

• De Stella Nova in Pede Serpentarii (“On the new star in Ophiuchus’s foot”) in full text facsimile at Linda Hall Library

• Shapin, Steven. The Scientific Revolution. Chicago: University of Chicago Press, 1996. ISBN 0-22675020-5

• The Correspondence of Johannes Kepler in EMLO

• Stephenson, Bruce. Kepler’s physical astronomy. New York: Springer, 1987. ISBN 0-387-96541-6 (Studies in the history of mathematics and physical sciences; 13); reprinted Princeton:Princeton Univ. Pr., 1994. ISBN 0-691-03652-7 • Stephenson, Bruce. The Music of the Heavens: Kepler’s Harmonic Astronomy, Princeton University Press, 1994. ISBN 0-691-03439-7 • Toulmin, Stephen and June Goodfield. The Fabric of the Heavens: The Development of Astronomy and Dynamics. Pelican, 1963. • Voelkel, James R. The Composition of Kepler’s Astronomia nova, Princeton University Press, 2001. ISBN 0-691-00738-1 • Westfall, Richard S.. The Construction of Modern Science: Mechanism and Mechanics. John Wiley and Sons, 1971. ISBN 0-471-93531-X; reprinted Cambridge University Press, 1978. ISBN 0-52129295-6 • Westfall, Richard S. Never at Rest: A Biography of Isaac Newton. Cambridge University Press, 1981. ISBN 0-521-23143-4 • Wolf, A. A History of Science, Technology and Philosophy in the 16th and 17th centuries. George Allen & Unwin, 1950.

20.11 External links

• Harmonices mundi (“The Harmony of the Worlds”) in fulltext facsimile; Carnegie-Mellon University • Liscia, Daniel A. Di. “Johannes Kepler”. Stanford Encyclopedia of Philosophy.

• Walter W. Bryant. Kepler at Project Gutenberg (1920 book, part of Men of Science series) • Electronic facsimile-editions of the rare book collection at the Vienna Institute of Astronomy • Johannes Kepler at DMOZ • Audio – Cain/Gay (2010) Astronomy Cast Johannes Kepler and His Laws of Planetary Motion • Christianson, Gale E., Kepler’s Somnium: Science Fiction and the Renaissance Scientist • Kollerstrom, Nicholas, Kepler’s Belief in Astrology • References for Johannes Kepler • Plant, David, Kepler and the “Music of the Spheres” • Kepler, Napier, and the Third Law at MathPages • Calderón Urreiztieta, Carlos. Harmonice Mundi • Animated and multimedia version of Book V • Reading the mind of God 1997 drama based on his life by Patrick Gabridge • Johannes Kepler 2010 drama based on his life by Robert Lalonde • O'Connor, John J.; Robertson, Edmund F., “Johannes Kepler”, MacTutor History of Mathematics archive, University of St Andrews. • Online Galleries, History of Science Collections, University of Oklahoma Libraries High resolution images of works by and/or portraits of Johannes Kepler in .jpg and .tiff format.

• Works by Johannes Kepler at Project Gutenberg From the Lessing J. Rosenwald Collection at the Library • Works by or about Johannes Kepler at Internet of Congress: Archive • Full text of Kepler. by Walter Bryant (public domain biography)

• Tabvlæ Rudolphinæ qvibvs astronomicæ scientiæ ... Typis J. Saurii, 1627.

• Kommission zur Herausgabe der Werke von Johannes Kepler (with links to digital scans of the published volumes)

• Books by Johannes Kepler that are available in digital facsimile from the website of the Linda Hall Library:


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CHAPTER 20. JOHANNES KEPLER • (1604) Ad vitellionem paralipomena • (1606) De stella nova in pede Serpentarii • (1611) Dioptrice • (1618) Epitome astronomiae Copernicanæ


Chapter 21

De revolutionibus orbium coelestium De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres) is the seminal work on the heliocentric theory of the Renaissance astronomer Nicolaus Copernicus (1473–1543). The book, first printed in 1543 in Nuremberg, Holy Roman Empire, offered an alternative model of the universe to Ptolemy's geocentric system, which had been widely accepted since ancient times.

21.1 History

description matches the Commentariolus, so Copernicus must have begun work on his new system by that time.[1] Most historians believe that he wrote the Commentariolus after his return from Italy, possibly only after 1510. At this time, Copernicus anticipated that he could reconcile the motion of the Earth with the perceived motions of the planets easily, with fewer motions than were necessary in the Alfonsine Tables, the version of the Ptolemaic system current at the time. In particular, the heliocentric Copernican model made use of the Urdi Lemma developed in the 13th century by Mu'ayyad al-Din al-'Urdi, the first of the Maragha astronomers to develop a non-Ptolemaic model of planetary motion.[2] Observations of Mercury by Bernhard Walther (1430– 1504) of Nuremberg, a pupil of Regiomontanus, were made available to Copernicus by Johannes Schöner, 45 observations in total, 14 of them with longitude and latitude. Copernicus used three of them in De revolutionibus, giving only longitudes, and erroneously attributing them to Schöner. Copernicus’ values differed slightly from the ones published by Schöner in 1544 in Observationes XXX annorum a I. Regiomontano et B. Walthero Norimbergae habitae, [4°, Norimb. 1544]. A manuscript of De revolutionibus in Copernicus’ own hand has survived. After his death, it was given to his pupil, Rheticus, who for publication had only been given a copy without annotations. Via Heidelberg, it ended up in Prague, where it was rediscovered and studied in the 19th century. Close examination of the manuscript, including the different types of paper used, helped scholars construct an approximate timetable for its composition. Apparently Copernicus began by making a few astronomical observations to provide new data to perfect his models. He may have begun writing the book while still engaged in observations. By the 1530s a substantial part of the book was complete, but Copernicus hesitated to publish.

Heliocentric model of the solar system in Copernicus' manuscript

Copernicus initially outlined his system in a short, untitled, anonymous manuscript that he distributed to several friends, referred to as the Commentariolus. A physician’s library list dating to 1514 includes a manuscript whose

In 1539 Georg Joachim Rheticus, a young mathematician from Wittenberg, arrived in Frauenburg (Frombork) to study with him. Rheticus read Copernicus’ manuscript and immediately wrote a non-technical summary of its main theories in the form of an open letter addressed to Schöner, his astrology teacher in Nürnberg; he published this letter as the Narratio Prima in Danzig in 1540.

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Rheticus’ friend and mentor Achilles Gasser published a second edition of the Narratio in Basel in 1541. Due to its friendly reception, Copernicus finally agreed to publication of more of his main work—in 1542, a treatise on trigonometry, which was taken from the second book of the still unpublished De revolutionibus. Rheticus published it in Copernicus’ name. Under strong pressure from Rheticus, and having seen that the first general reception of his work had not been unfavorable, Copernicus finally agreed to give the book to his close friend, Bishop Tiedemann Giese, to be delivered to Rheticus in Wittenberg for printing by Johannes Petreius at Nürnberg (Nuremberg). It was published just before Copernicus’ death, in 1543.

21.2 Contents

• Book I chapters 1-11 are a general vision of the heliocentric theory, and a summarized exposition of his cosmology. The world (heavens) is spherical, as is the earth, and the land and water make a single globe. The celestial bodies, including the earth, have regular circular and everlasting movements. The earth rotates on its axis and around the sun. Answers to why the ancients thought the earth was central. The order of the planets around the sun and their periodicity. Chapters 12-14 give theorems for chord geometry as well as a table of chords. • Book II describes the principles of spherical astronomy as a basis for the arguments developed in the following books and gives a comprehensive catalogue of the fixed stars. • Book III describes his work on the precession of the equinoxes and treats the apparent movements of the Sun and related phenomena. • Book IV is a similar description of the Moon and its orbital movements. • Book V explains how to calculate the positions of the wandering stars based on the heliocentric model and gives tables for the five planets. • Book VI deals with the digression in latitude from the ecliptic of the five planets. Copernicus argued that the universe comprised eight spheres. The outermost consisted of motionless, fixed stars, with the Sun motionless at the center. The known planets revolved about the Sun, each in its own sphere, in the order: Mercury, Venus, Earth, Mars, Jupiter, Saturn. The Moon, however, revolved in its sphere around the Earth. What appeared to be the daily revolution of the Sun and fixed stars around the Earth was actually the Earth’s daily rotation on its own axis. For philosophical reasons, Copernicus clung to the belief that all the orbits of celestial bodies must be perfect circles[4] and to a belief in the unobserved crystalline spheres. This forced Copernicus to retain the Ptolemaic system’s complex system of epicycles, to account for the observed deviations from circularity and to square his calculations with observations. Despite Copernicus’ adherence to these aspects of ancient astronomy, his radical shift from a geocentric to a heliocentric cosmology was a serious blow to Aristotle's science—and helped usher in the Scientific Revolution.

Title page, 2nd edition, Basel, Officina Henricpetrina, 1566

The book is dedicated to Pope Paul III in a preface that 21.3 Ad lectorem argues that mathematics, not physics, should be the basis for understanding and accepting his new theory. Rheticus left Nürnberg to take up his post as professor in De revolutionibus is divided into six “books” (sections or Leipzig. The Lutheran preacher Andreas Osiander had parts), following closely the layout of Ptolemy’s Almagest taken over the task of supervising the printing and pubwhich it updated and replaced:[3] lication. In an effort to reduce the controversial impact


21.3. AD LECTOREM

249 sis for computation. However, since different hypotheses are sometimes offered for one and the same ... the astronomer will take as his first choice that hypothesis which is the easiest to grasp. The philosopher will perhaps rather seek the semblance of the truth. But neither of them will understand or state anything certain, unless it has been divinely revealed to him ... Let no one expect anything certain from astronomy, which cannot furnish it, lest he accept as the truth ideas conceived for another purpose, and depart this study a greater fool than when he entered.[6] As even Osiander’s defenders point out, the Ad lectorem “expresses views on the aim and nature of scientific theories at variance with Copernicus’ claims for his own theory”.[7]

Many view Osiander’s letter as a betrayal of science and Copernicus, and an attempt to pass his own thoughts off as those of the book’s author. An example of this type of claim can be seen in the Catholic Encyclopedia, which states “Fortunately for him [the dying Copernicus], he could not see what Osiander had done. This reformer, Title page, 3rd ed., Amsterdam, Nicolaus Mulerius, publisher, knowing the attitude of Luther and Melanchthon against 1617 the heliocentric system ... without adding his own name, replaced the preface of Copernicus by another strongly of the book Osiander added his own unsigned letter Ad contrasting in spirit with that of Copernicus.”[8] lectorem de hypothesibus huius operis (To the reader conWhile Osiander’s motives behind the letter have been cerning the hypotheses of this work)[5] printed in front questioned by many, he has been defended by historian of Copernicus’ preface which was a dedicatory letter to Bruce Wrightsman, who points out he was not an enPope Paul III and which kept the title “Praefatio authoemy of science. Osiander had many scientific connecris” (to acknowledge that the unsigned letter was not by tions including “Johannes Schoner, Rheticus’s teacher, the book’s author). whom Osiander recommended for his post at the NurnOsiander’s letter stated that Copernicus’ system was berg Gymnasium; Peter Apian of Ingolstadt University; mathematics intended to aid computation and not an at- Hieronymous Schreiber...Joachim Camerarius...Erasmus tempt to declare literal truth: Reinhold...Joachim Rheticus...and finally, Hieronymous Cardan.”[7] it is the duty of an astronomer to compose the history of the celestial motions through careful and expert study. Then he must conceive and devise the causes of these motions or hypotheses about them. Since he cannot in any way attain to the true causes, he will adopt whatever suppositions enable the motions to be computed correctly ... The present author has performed both these duties excellently. For these hypotheses need not be true nor even probable. On the contrary, if they provide a calculus consistent with the observations, that alone is enough ... For this art, it is quite clear, is completely and absolutely ignorant of the causes of the apparent [movement of the heavens]. And if any causes are devised by the imagination, as indeed very many are, they are not put forward to convince anyone that they are true, but merely to provide a reliable ba-

The historian Wrightsman put forward that Osiander did not sign the letter because he “was such a notorious [Protestant] reformer whose name was well-known and infamous among Catholics”,[7] so that signing would have likely caused negative scrutiny of the work of Copernicus (a loyal Catholic canon and scholar). Copernicus himself had communicated to Osiander his “own fears that his work would be scrutinized and criticized by the 'peripatetics and theologians’,”[7] and he had already been in trouble with his bishop, Johannes Dantiscus, on account of his former relationship with his mistress and friendship with Dantiscus’s enemy and suspected heretic, Alexander Scultetus. It was also possible that Protestant Nurnberg could fall to the forces of the Holy Roman Emperor and since “the books of hostile theologians could be burned...why not scientific works with the names of hated theologians affixed to them?[7] " Wrightsman also holds that this is why Copernicus did not mention his top student, Rheticus (a Lutheran) in the book’s dedication to


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the Pope.[7]

Osiander was tempered by the influence of Nicholas of Cusa's and his idea of coincidentia oppositorum. Rather than having Pico’s focus on human effort, Osiander followed Cusa’s idea that understanding the Universe and its Creator only came from divine inspiration rather than intellectual organization. From these influences, Osiander held that in the area of philosophical speculation and scientific hypothesis there are “no heretics of the intellect”, but when one gets past speculation into truth-claims the Bible is the ultimate measure. By holding Copernicianism was mathematical speculation, Osiander held that it would be silly to hold it up against the accounts of the Bible.

Osiander’s interest in astronomy was theological, hoping for “improving the chronology of historical events and thus providing more accurate apocalyptic interpretations of the Bible... [he shared in] the general awareness that the calendar was not in agreement with astronomical movement and therefore, needed to be corrected by devising better models on which to base calculations.” In an era before the telescope, Osiander (like most of the era’s mathematical astronomers) attempted to bridge the “fundamental incompatibility between Ptolemaic astronomy and Aristotlian physics, and the need to preserve both”, by taking an 'instrumentalist' position. Only the handful of “Philosophical purists like the Averroists... de- Pico’s influence on Osiander did not escape Rheticus, manded physical consistency and thus sought for realist who reacted strongly against the Ad lectorem. As historian models.”[7] Robert S. Westman puts it, “The more profound source Copernicus was hampered by his insistence on preserv- of Rheticus’s ire however, was Osiander’s view of astroning the idea that celestial bodies had to travel in per- omy as a disciple fundamentally incapable of knowing fect spheres – he “was still attached to classical ideas anything with certainty. For Rheticus, this extreme posiof circular motion around deferents and epicycles, and tion surely must have resonated uncomfortably with Pico attack on the foundations of divinatory spheres.”[9] This was particularly troubling concerning della Mirandola’s [10] astrology.” the Earth because he “attached the Earth’s axis rigidly to a Sun-centered sphere. The unfortunate consequence was that the terrestrial rotation axis then maintained the same inclination with respect to the Sun as the sphere turned, eliminating the seasons.”[9] To explain the seasons, he had to propose a third motion, “an annual contrary conical sweep of the terrestrial axis”.[9] It was not until the Great Comet of 1577, which moved as if there were no spheres to crash through, did the idea come under question. In 1609, Kepler fixed Copernicus’ theory by stating that the planets orbit the sun not in circles, but ellipses. Only after Kepler’s refinement of Copernicus’ theory was the need for deferents and epicycles abolished. In his work, Copernicus “used conventional, hypothetical devices like epicycles...as all astronomers had done since antiquity. ...hypothetical constructs solely designed to 'save the phenomena' and aid computation”.[7] Ptolemy’s theory contained a hypothesis about the epicycle of Venus that was viewed as absurd if seen as anything other than a geometrical device (its brightness and distance should have varied greatly, but they don't). “In spite of this defect in Ptolemy’s theory, Copernicus’ hypothesis predicts approximately the same variations.”[7] Because of the use of similar terms and similar deficiencies, Osiander could see “little technical or physical truth-gain”[7] between one system and the other. It was this attitude towards technical astronomy that had allowed it to “function since antiquity, despite its inconsistencies with the principles of physics and the philosophical objections of Averroists.”[7] Writing Ad lectorem, Osiander was influenced by Pico della Mirandola's idea that humanity “orders [an intellectual] cosmos out of the chaos of opinions.”[7] From Pico’s writings, Osiander “learned to extract and synthesize insights from many sources without becoming the slavish follower of any of them.”[7] The effect of Pico on

In his Disputations, Pico had made a devastating attack on astrology. Because those who were making astrological predictions relied on astronomers to tell them where the planets were, they also became a target. Pico held that since astronomers who calculate planetary positions could not agree among themselves, how were they to be held as reliable? While Pico could bring into concordance writers like Aristotle, Plato, Plotinus, Averroes, Avicenna, and Aquinas, the lack of consensus he saw in astronomy was a proof to him of its fallibility alongside astrology. Pico pointed out that the astronomers’ instruments were imprecise and any imperfection of even a degree made them worthless for astrology, people should not trust astrologists because they should not trust the numbers from astronomers. Pico pointed out that astronomers couldn't even tell where the sun appeared in the order of the planets as they orbited the earth (some put it close to the moon, others among the planets). How, Pico asked, could astrologists possibly claim they could read what was going on when the astronomers they relied on could offer no precision on even basic questions? As Westman points out, to Rheticus “it would seem that Osiander now offered new grounds for endorsing Pico’s conclusions: not merely was the disagreement among astronomers grounds for mistrusting the sort of knowledge that they produced, but now Osiander proclaimed that astronomers might construct a world deduced from (possibly) false premises. Thus the conflict between Piconian skepticism and secure principles for the science of the stars was built right into the complex dedicatory apparatus of De Revolutionibus itself.”[10] According to the notes of Michael Maestlin, “Rheticus...became embroiled in a very bitter wrangle with the printer [over the Ad lectorem]. Rheticus...suspected Osiander had prefaced the work; if he knew this for certain, he declared, he would


21.4. RECEPTION

251

rough up the fellow so violently that in future he would When the book was finally published, demand was low, mind his own business.”[11] with an initial print run of 400 failing to sell out.[17] Objecting to the Ad lectorem, Tiedemann Giese urged the Copernicus had made the book extremely technical, unNuremberg city council to issue a correction, but this was readable to all but the most advanced astronomers of the into their ranks before stirnot done, and the matter was forgotten. Jan Broscius, a day, allowing it to disseminate [18] ring great controversy. And, like Osiander, contemposupporter of Copernicus, also despaired of the Ad lecrary mathematicians and astronomers encouraged its autorem, writing “Ptolemy’s hypothesis is the earth rests. dience to view it as a useful mathematical fiction with no Copernicus’ hypothesis is that the earth is in motion. Can physical reality, thereby somewhat shielding it from aceither, therefore, be true? ... Indeed, Osiander deceives [19] much with that preface of his ... Hence, someone may cusations of blasphemy. well ask: How is one to know which hypothesis is truer, Among some astronomers, the book “at once took its the Ptolemaic or the Copernican?"[7] place as a worthy successor to the Almagest of Ptolemy, been the Alpha and Omega of Petreius had sent a copy to Hieronymus Schreiber, which had hitherto [20] astronomers”. Erasmus Reinhold hailed the work in an astronomer from Nürnberg who had substituted for 1542 and by 1551 had developed the Prutenic Tables Rheticus as professor of mathematics in Wittenberg (“Prussian Tables"; Latin: Tabulae prutenicae; German: while Rheticus was in Nürnberg supervising the printing. Preußische Tafeln) using Copernicus’ methods. The Schreiber, who died in 1547, left in his copy of the book Prutenic Tables, published in 1551, were used as a baa note about Osiander’s authorship. Via Michael Mästlin, sis for the calendar reform instituted in 1582 by Pope this copy came to Johannes Kepler, who discovered what Osiander had done[12][13] and methodically demonstrated Gregory XIII. They were also used by sailors and marthat Osiander had indeed added the foreword.[14] The itime explorers, whose 15th-century predecessors had most knowledgeable astronomers of the time had realized used Regiomontanus' Table of the Stars. In England, Robert Recorde, John Dee, Thomas Digges and William that the foreword was Osiander’s doing. Gilbert were among those who adopted his position; Owen Gingerich[15] gives a slightly different version: Ke- in Germany, Christian Wurstisen, Christoph Rothmann pler knew of Osiander’s authorship since he had read and Michael Mästlin, the teacher of Johannes Kepler; in about it in one of Schreiber’s annotations in his copy of De Italy, Giambattista Benedetti and Giordano Bruno whilst Revolutionibus; Maestlin learned of the fact from Kepler. Franciscus Patricius accepted the rotation of the earth. Indeed, Maestlin perused Kepler’s book, up to the point In Spain, rules published in 1561 for the curriculum of of leaving a few annotations in it. However, Maestlin al- the University of Salamanca gave students the choice ready suspected Osiander, because he had bought his De between studying Ptolemy or Copernicus.[21][22] One of revolutionibus from the widow of Philipp Apian; examin- those students, Diego de Zúñiga, published an acceptance ing his books, he had found a note attributing the intro- of Copernican theory in 1584.[23] duction to Osiander. Very soon, nevertheless, Copernicus’ theory was atJohannes Praetorius (1537–1616), who learned of Os- tacked with Scripture and with the common Aristotelian iander’s authorship from Rheticus during a visit to him proofs. In 1549 Melanchthon, Luther’s principal lieuin Kraków, wrote Osiander’s name in the margin of the tenant, wrote against Copernicus, pointing to the theforeword in his copy of De revolutionibus. ory’s apparent conflict with Scripture and advocating that All three early editions of De revolutionibus included Os- “severe measures” be taken to restrain the impiety of Copernicans.[24] The works of Copernicus and Zúñiga— iander’s foreword. the latter for asserting that De revolutionibus was compatible with Catholic faith—were placed on the Index of Forbidden Books by a decree of the Sacred Congregation of March 5, 1616 (more than 70 years after its publica21.4 Reception tion): Even before the 1543 publication of De revolutionibus, rumors circulated about its central theses. Martin Luther is quoted as saying in 1539:

People gave ear to an upstart astrologer who strove to show that the earth revolves, not the heavens or the firmament, the sun and the moon ... This fool wishes to reverse the entire science of astronomy; but sacred Scripture tells us [Joshua 10:13] that Joshua commanded the sun to stand still, and not the earth.[16]

This Holy Congregation has also learned about the spreading and acceptance by many of the false Pythagorean doctrine, altogether contrary to the Holy Scripture, that the earth moves and the sun is motionless, which is also taught by Nicholaus Copernicus’ De revolutionibus orbium coelestium and by Diego de Zúñiga’s In Job ... Therefore, in order that this opinion may not creep any further to the prejudice of Catholic truth, the Congregation has decided that the books by Nicolaus Coperni-


252

CHAPTER 21. DE REVOLUTIONIBUS ORBIUM COELESTIUM cus [De revolutionibus] and Diego de Zúñiga [In Job] be suspended until corrected.[25]

• 1873, Thorn, German translation sponsored by the local Coppernicus Society, with all Copernicus’ textual corrections given as footnotes.

De revolutionibus was not formally banned but merely withdrawn from circulation, pending “corrections” that would clarify the theory’s status as hypothesis. Nine sen- 21.7 Translations tences that represented the heliocentric system as certain were to be omitted or changed. After these corrections English translations of De revolutionibus have included: were prepared and formally approved in 1620 the reading of the book was permitted.[26] But the book was never • On the Revolutions of the Heavenly Spheres, transreprinted with the changes and was available in Catholic lated with an introduction and notes by A.M. Dunjurisdictions only to suitably qualified scholars, by special can, Newton Abbot, David & Charles, ISBN 0request. It remained on the Index until 1758, when Pope 7153-6927-X; New York, Barnes and Noble, 1976, Benedict XIV (1740–58) removed the uncorrected book [27] ISBN 0-06-491279-5. from his revised Index.

21.5 Census of copies Arthur Koestler described De revolutionibus as "The Book That Nobody Read" saying the book “was and is an alltime worst seller”, despite the fact that it was reprinted four times.[28] Owen Gingerich, a writer on both Nicolaus Copernicus and Johannes Kepler, disproved this after a 35-year project to examine every surviving copy of the first two editions. Gingerich showed that nearly all the leading mathematicians and astronomers of the time owned and read the book; however, his analysis of the marginalia shows that they almost all ignored the cosmology at the beginning of the book and were only interested in Copernicus’ new equant-free models of planetary motion in the later chapters. Also, Nicolaus Reimers in 1587 translated the book into German. Gingerich’s efforts and conclusions are recounted in The Book Nobody Read, published in 2004 by Walker & Co. His census[29] included 276 copies of the first edition (by comparison, there are 228 extant copies of the First Folio of Shakespeare) and 325 copies of the second.[30] The research behind this book earned its author the Polish government’s Order of Merit in 1981. Due largely to Gingerich’s scholarship, De revolutionibus has been researched and catalogued better than any other first-edition historic text except for the original Gutenberg Bible.[31] One of the copies now resides at the Archives of the University of Santo Tomas in the Miguel de Benavides Library.

21.6 Editions • 1543, Nuremberg, by Johannes Petreius • 1566, Basel, by Henricus Petrus • 1617, Amsterdam, by Nicolaus Mulerius • 1854, Warsaw, with Polish translation and the authentic preface by Copernicus.

• On the Revolutions; translation and commentary by Edward Rosen, Baltimore, Johns Hopkins University Press, 1992, ISBN 0-8018-4515-7. (Foundations of Natural History. Originally published in Warsaw, Poland, 1978.) • On the Revolutions of the Heavenly Spheres, translated by C.G. Wallis, Annapolis, St John’s College Bookstore, 1939. Republished in volume 16 of the Great Books of the Western World, Chicago, Encyclopædia Britannica, 1952; in the series of the same name, published by the Franklin Library, Franklin Center, Philadelphia, 1985; in volume 15 of the second edition of the Great Books, Encyclopædia Britannica, 1990; and Amherst, N.Y., Prometheus Books, 1995, Great Minds Series—Science, ISBN 1-57392-035-5.

21.8 Notes [1] Gingerich 2004, p. 32 [2] Saliba (1979). [3] Dreyer, John L E (1906). History of the planetary systems from Thales to Kepler. p. 342. [4] Gingerich 2004, p. 23 [5] Wallis’s translation (1952, p.505) [6] David Luban (1994). Legal Modernism. University of Michigan. [7] Andreas Osiander’s Contribution to the Copernican Achievement, by Bruce Wrightsman, Section VII, The Copernican Achievement, ed. Robert S. Westman, University of California Press, Los Angeles, 1975 [8] “Nicolaus Copernicus”. Catholic Encyclopedia. [9] William Tobin (2003). The Life and Science of Léon Foucault: The Man who Proved the Earth Rotates. Cambridge University Press.


21.9. REFERENCES

[10] Robert S. Westman (2011). The Copernican Question: Prognostication, Skepticism, and Celestial Order. Los Angeles, CA: University of California Press. [11] “Galsgow University Library Special Collections Department, Book of the Month, Nicolaus Copernicus De Revolutionibus Nuremberg: 1543 Sp Coll Hunterian Cz.1.13”. [12] Edward Rosen: Three Copernican Treatises: The Commentariolus of Copernicus, The Letter Against Werner, The Narratio Prima of Rheticus, Dover Publications, 2004, ISBN 0-486-43605-5, p. 24. [13] Koestler, 1959, p. 169 [14] Robert Westman, “Three Responses to Copernican Theory”, in Robert Westman, ed., The Copernican Achievement, 1975. [15] Gingerich, O. (2004). The book nobody read. Heinemann, London. pp. 159–164. [16] Quoted in Thomas Kuhn, The Copernican Revolution, Cambridge, Massachusetts, Harvard University Press, 1957, p. 191. [17] Philip Ball, The Devil’s Doctor: Paracelsus and the World of Renaissance Magic and Science, ISBN 978-009-945787-9, p. 354. [18] Thomas Kuhn, The Copernican Revolution, p. 185. [19] Thomas Kuhn, The Copernican Revolution, pp. 186–87. [20] Dreyer & 1906 345 [21] Deming, David (2012). Science and Technology in World History, Volume 3: The Black Death, the Renaissance, the Reformation and the Scientific Revolution. McFarland & Company. p. 138. ISBN 9780786461721. [22] Gilbert, William (1998). “Chapter 23: The Beginning of the Scientific Revolution”. The Renaissance and The Reformation. Carrie. OCLC 817744956. [23] Dreyer & 1906 346-352 [24] Thomas Kuhn, The Copernican Revolution, p. 192. Kuhn writes that Melanchthon emphasized Ecclesiastes 1:4-5 (“The earth abideth forever ... the sun also ariseth, and the sun goeth down, and hasteth to his place where he arose”). [25] Original Latin text and an English translation. Also mentioned by W. R. Shea and M. Artigas in Galileo in Rome (2003), pp. 84–85, ISBN 0-19-516598-5. [26] "Nicolaus Copernicus", Catholic Encyclopedia.

253

21.9 References • Copernicus, Nicolaus (1952), On the Revolutions of the Heavenly Spheres, Great Books of the Western World, 16, translated by Charles Glenn Wallis, Chicago: William Benton, pp. 497–838 • Gassendi, Pierre: The Life of Copernicus, biography (1654), with notes by Olivier Thill (2002), ISBN 159160-193-2 () • Gingerich, Owen (2002). An annotated census of Copernicus’ De revolutionibus (Nuremberg, 1543 and Basel, 1566). Leiden: Brill (Studia copernicana. Brill’s series; v. 2). ISBN 90-04-11466-1. • Gingerich, Owen (2004). The Book Nobody Read : Chasing the Revolutions of Nicolaus Copernicus. New York : Walker. ISBN 0-8027-1415-3. • Hannam, James (2007). “Deconstructing Copernicus”. Medieval Science and Philosophy. Retrieved 2007-08-17. Analyses the varieties of argument used by Copernicus. • Heilbron, J.L.: The Sun in the Church: Cathedrals as Solar Observatories. Cambridge, Massachusetts, Harvard University Press, 1999 ISBN 0-674-854330 • Koestler, Arthur (1959). The Sleepwalkers. Hutchison. • Swerdlow, N.M., O. Neugebauer: Mathematical astronomy in Copernicus’ De revolutionibus. New York : Springer, 1984 ISBN 0-387-90939-7 (Studies in the history of mathematics and physical sciences ; 10) • Vermij, R.H.: The Calvinist Copernicans: The Reception of the New Astronomy in the Dutch Republic, 1575-1750. Amsterdam : Koninklijke Nederlandse Akademie van Wetenschappen, 2002 ISBN 90-6984-340-4 • Westman, R.S., ed.: The Copernican achievement. Berkeley : University of California Press, 1975 ISBN 0-520-02877-5 • Zinner, E.: Entstehung und Ausbreitung der coppernicanischen Lehre. 2. Aufl. durchgesehen und erg. von Heribert M. Nobis und Felix Schmeidler. München : C.H. Beck, 1988 ISBN 3-406-32049-X

[27] "Benedict XIV", Catholic Encyclopedia. [28] Koestler 1959, p194 [29] Gingerich 2002

21.10 External links

[30] Gingerich 2004, p. 121

• De revolutionibus orbium coelestium, from Harvard University.

[31] Peter DeMarco. "Book quest took him around the globe". Boston Globe. April 13, 2004

• De revolutionibus orbium coelestium, from Jagiellon University, Poland.


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• De Revolutionibus Orbium Coelestium, from Rare Book Room. • On the Revolutions, from WebExhibits. translation of part of Book I.

English

• River Campus Libraries, Book of the Month December 2005: De revolutionibus orbium coelestium • De Revolutionibus Orbium Coelestium (1543) From the Rare Book and Special Collection Division at the Library of Congress • De Revolutionibus Orbium Coelestium (1566) From the Rare Book and Special Collection Division at the Library of Congress


Chapter 22

Kepler’s laws of planetary motion For a more historical approach, see in particular the Most planetary orbits are nearly circular, and careful obarticles Astronomia nova and Epitome Astronomiae servation and calculation are required in order to estabCopernicanae. lish that they are actually not perfectly circular ellipses. Using calculations of the orbit of Mars, whose published [2] In astronomy, Kepler's laws of planetary motion are values are somewhat suspect, which indicated elliptical orbits, Johannes Kepler inferred that other heavenly bodthree scientific laws describing the motion of planets ies, including those farther away from the Sun, also have around the Sun. elliptical orbits.

f1 (sun)

A1 planet 2 planet 1

a1

Kepler’s work (published between 1609 and 1619) improved the heliocentric theory of Nicolaus Copernicus, explaining how the planets’ speeds varied, and using elliptical orbits rather than circular orbits with epicycles.[3]

f2

Isaac Newton showed in 1687 that relationships like Kepler’s would apply in the solar system to a good approximation, as consequences of his own laws of motion and law of universal gravitation.

A2

Kepler’s laws are part of the foundation of modern astronomy and physics.[4]

a2 f3

22.1 Comparison to Copernicus Figure 1: Illustration of Kepler’s three laws with two planetary orbits. (1) The orbits are ellipses, with focal points ƒ1 and ƒ2 for the first planet and ƒ1 and ƒ3 for the second planet. The Sun is placed in focal point ƒ1 . (2) The two shaded sectors A1 and A2 have the same surface area and the time for planet 1 to cover segment A1 is equal to the time to cover segment A2 . (3) The total orbit times for planet 1 and planet 2 have a ratio a1 3/2 : a2 3/2 .

Kepler’s laws improve the model of Copernicus. If the eccentricities of the planetary orbits are taken as zero, then Kepler basically agrees with Copernicus: 1. The planetary orbit is a circle 2. The Sun at the center of the orbit 3. The speed of the planet in the orbit is constant

The eccentricities of the orbits of those planets known to Copernicus and Kepler are small, so the foregoing rules 1. The orbit of a planet is an ellipse with the Sun at one give good approximations of planetary motion; but Keof the two foci. pler’s laws fit the observations better than Copernicus’s. 2. A line segment joining a planet and the Sun sweeps Kepler’s corrections are not at all obvious: out equal areas during equal intervals of time.[1] 1. The planetary orbit is not a circle, but an ellipse. 3. The square of the orbital period of a planet is pro2. The Sun is not at the center but at a focal point of portional to the cube of the semi-major axis of its orbit. the elliptical orbit. 255


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CHAPTER 22. KEPLER’S LAWS OF PLANETARY MOTION

3. Neither the linear speed nor the angular speed of the eccentricity of all planets except Mercury[14] ). His first planet in the orbit is constant, but the area speed is law reflected this discovery. constant. Kepler in 1621 and Godefroy Wendelin in 1643 noted that Kepler’s third law applies to the four brightest moons The eccentricity of the orbit of the Earth makes the of Jupiter.[Nb 1] The second law, in the “area law” form, time from the March equinox to the September equinox, was contested by Nicolaus Mercator in a book from 1664, around 186 days, unequal to the time from the September but by 1670 his Philosophical Transactions were in its equinox to the March equinox, around 179 days. A di- favour. As the century proceeded it became more widely ameter would cut the orbit into equal parts, but the plane accepted.[15] The reception in Germany changed noticethrough the sun parallel to the equator of the earth cuts ably between 1688, the year in which Newton’s Principia the orbit into two parts with areas in a 186 to 179 ratio, so was published and was taken to be basically Copernican, the eccentricity of the orbit of the Earth is approximately and 1690, by which time work of Gottfried Leibniz on Kepler had been published.[16] ε≈

π 186 − 179 ≈ 0.015, 4 186 + 179

which is close to the correct value (0.016710219) (see Earth’s orbit). The calculation is correct when perihelion, the date the Earth is closest to the Sun, falls on a solstice. The current perihelion, near January 4, is fairly close to the solstice of December 21 or 22.

22.2 Nomenclature It took nearly two centuries for the current formulation of Kepler’s work to take on its settled form. Voltaire's Eléments de la philosophie de Newton (Elements of Newton’s Philosophy) of 1738 was the first publication to use the terminology of “laws”.[5][6] The Biographical Encyclopedia of Astronomers in its article on Kepler (p. 620) states that the terminology of scientific laws for these discoveries was current at least from the time of Joseph de Lalande.[7] It was the exposition of Robert Small, in An account of the astronomical discoveries of Kepler (1804) that made up the set of three laws, by adding in the third.[8] Small also claimed, against the history, that these were empirical laws, based on inductive reasoning.[6][9] Further, the current usage of “Kepler’s Second Law” is something of a misnomer. Kepler had two versions of it, related in a qualitative sense, the “distance law” and the “area law”. The “area law” is what became the Second Law in the set of three; but Kepler did himself not privilege it in that way.[10]

Newton is credited with understanding that the second law is not special to the inverse square law of gravitation, being a consequence just of the radial nature of that law; while the other laws do depend on the inverse square form of the attraction. Carl Runge and Wilhelm Lenz much later identified a symmetry principle in the phase space of planetary motion (the orthogonal group O(4) acting) which accounts for the first and third laws in the case of Newtonian gravitation, as conservation of angular momentum does via rotational symmetry for the second law.[17]

22.4 Formulary The mathematical model of the kinematics of a planet subject to the laws allows a large range of further calculations.

22.4.1 First law The orbit of every planet is an ellipse with the Sun at one of the two foci.

planet

Sun

22.3 History Johannes Kepler published his first two laws about planetary motion in 1609, having found them by analyzing the astronomical observations of Tycho Brahe.[11][3][12] Kepler’s third law was published in 1619.[13][3] Notably, Kepler had believed in the Copernican model of the solar system, which called for circular orbits, but could not reconcile Brahe’s highly precise observations with a circular fit to Mars’ orbit (Mars coincidentally having the highest

Figure 2: Kepler’s first law placing the Sun at the focus of an elliptical orbit

Mathematically, an ellipse can be represented by the formula:


22.4. FORMULARY

257

rmax b = b rmin p 1 − ε2 The semi-latus rectum p is the harmonic mean between r ᵢ and r ₐₓ: b= √

p

b

r θ

a rmin

rmax

1 1 1 1 − = − rmin p p rmax pa = rmax rmin = b2 The eccentricity ε is the coefficient of variation between r ᵢ and r ₐₓ:

Figure 4: Heliocentric coordinate system (r, θ) for ellipse. Also shown are: semi-major axis a, semi-minor axis b and semi-latus rectum p; center of ellipse and its two foci marked by large dots. For θ = 0°, r = rmin and for θ = 180°, r = rmax.

r=

p , 1 + ε cos θ

ε=

rmax − rmin . rmax + rmin

The area of the ellipse is

A = πab .

The special case of a circle is ε = 0, resulting in r = p = 2 where p is the semi-latus rectum, and ε is the eccentricity r ᵢ = r ₐₓ = a = b and A = πr . of the ellipse, and r is the distance from the Sun to the planet, and θ is the angle to the planet’s current position 22.4.2 Second law from its closest approach, as seen from the Sun. So (r, θ) are polar coordinates. A line joining a planet and the Sun sweeps out equal areas during equal intervals of For an ellipse 0 < ε < 1 ; in the limiting case ε = 0, the [1] time. orbit is a circle with the sun at the centre (i.e. where there is no, or nil, eccentricity). At θ = 0°, perihelion, the distance is minimum

rmin =

p 1+ε

At θ = 90° and at θ = 270° the distance is equal to p . At θ = 180°, aphelion, the distance is maximum (by definition, aphelion is – invariably – perihelion plus 180°)

rmax =

p 1−ε

The semi-major axis a is the arithmetic mean between The same (blue) area is swept out in a fixed time period. The green arrow is velocity. The purple arrow directed towards the r ᵢ and r ₐₓ: Sun is the acceleration. The other two purple arrows are acceleration components parallel and perpendicular to the velocity.

rmax − a = a − rmin

The orbital radius and angular velocity of the planet in the p elliptical orbit will vary. This is shown in the animation: a= 1 − ε2 the planet travels faster when closer to the sun, then slower The semi-minor axis b is the geometric mean between when farther from the sun. Kepler’s second law states that r ᵢ and r ₐₓ: the blue sector has constant area.


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In a small time dt the planet sweeps out a small triangle having base line r and height r dθ and area dA = 12 · r · 1 2 dθ rdθ and so the constant areal velocity is dA dt = 2 r dt . The area enclosed by the elliptical orbit is πab. So the period P satisfies dθ P · 12 r2 = πab dt and the mean motion of the planet around the Sun

n = 2π/P

2. The magnitude of the acceleration is inversely proportional to the square of the planet’s distance from the Sun (the inverse square law). This implies that the Sun may be the physical cause of the acceleration of planets. Newton defined the force acting on a planet to be the product of its mass and the acceleration (see Newton’s laws of motion). So: 1. Every planet is attracted towards the Sun.

satisfies r2 dθ = abn dt.

22.4.3

1. The direction of the acceleration is towards the Sun.

Third law

The square of the orbital period of a planet is directly proportional to the cube of the semimajor axis of its orbit. This captures the relationship between the distance of planets from the Sun, and their orbital periods.

2. The force acting on a planet is in direct proportion to the mass of the planet and in inverse proportion to the square of its distance from the Sun. The Sun plays an unsymmetrical part, which is unjustified. So he assumed, in Newton’s law of universal gravitation: 1. All bodies in the solar system attract one another. 2. The force between two bodies is in direct proportion to the product of their masses and in inverse proportion to the square of the distance between them.

For a brief biography of Kepler and discussion of his third law, see: NASA: Stargaze. As the planets have small masses compared to that of the [13] this third law in a laborious Sun, the orbits conform approximately to Kepler’s laws. Kepler enunciated in 1619 attempt to determine what he viewed as the "music of the Newton’s model improves upon Kepler’s model, and fits spheres" according to precise laws, and express it in terms actual observations more accurately (see two-body probof musical notation.[18] So it was known as the harmonic lem). law.[19] Below comes the detailed calculation of the acceleration According to this law the expression P 2 a−3 has the same of a planet moving according to Kepler’s first and second value for all the planets in the solar system. Here P is laws. the time taken for a planet to complete an orbit round the sun, and a is the mean value between the maximum and minimum distances between the planet and sun (i.e. the 22.5.1 Acceleration vector semimajor axis). See also: Polar coordinate § Vector calculus, and The corresponding formula in Newtonian mechanics is Mechanics of planar particle motion P2 4π 2 4π 2 = ≈ = constant a3 G(M + m) GM where M is the mass of the sun, m is the mass of the planet, and G is the gravitational constant. As the Sun is much heavier than any planet, Kepler’s third law is approximately correct in Newtonian mechanics.

From the heliocentric point of view consider the vector to the planet r = rˆr where r is the distance to the planet and ˆr is a unit vector pointing towards the planet.

dˆr ˆ = ˆr˙ = θ˙θ, dt

ˆ dθ ˙ ˙r = ˆθ = −θˆ dt

ˆ is the unit vector orthogonal to ˆr and pointing where θ in the direction of rotation, and θ is the polar angle, and 22.5 Planetary acceleration where a dot on top of the variable signifies differentiation Isaac Newton computed in his Philosophiæ Naturalis with respect to time. Principia Mathematica the acceleration of a planet mov- Differentiate the position vector twice to obtain the veing according to Kepler’s first and second law. locity vector and the acceleration vector:


22.5. PLANETARY ACCELERATION

259 Differentiating once more

ˆ r˙ = rˆ ˙ r + rˆr˙ = rˆ ˙ r + rθ˙θ, nab n2 a2 b2 ˙ ˆ θ¨θ+r ˆ θ˙ˆθ) ¨ r˙ θ) ˙ θ. ˆp¨ r = nabε cos θ θ˙ = nabε cos θ 2 = ε cos θ. ¨r = (¨ rˆr+r˙ˆr˙ )+(r˙ θ˙θ+r = (¨ r−rθ˙2 )ˆr+(rθ+2 r r2 So The radial acceleration a satisfies r

ˆ ¨r = ar rˆ + aθ θ

par =

where the radial acceleration is

n2 a2 b2 n2 a2 b2 n2 a2 b2 ( p) ε cos θ−p = ε cos θ − . 2 3 2 r r r r

Substituting the equation of the ellipse gives ar = r¨ − rθ˙2 par =

and the transversal acceleration is

p) n2 a 2 2 n2 a2 b2 ( p − 1 − = − b . r2 r r r2

The relation b2 = pa gives the simple final result ˙ aθ = rθ¨ + 2r˙ θ.

22.5.2

ar = −

The inverse square law

n2 a 3 . r2

This means that the acceleration vector r of any planet obeying Kepler’s first and second law satisfies the inverse square law

Kepler’s second law says that

r2 θ˙ = nab r=−

is constant. The transversal acceleration aθ is zero:

α ˆr r2

where

˙ d(r2 θ) ¨ = raθ = 0. = r(2r˙ θ˙ + rθ) dt

α = n2 a 3

So the acceleration of a planet obeying Kepler’s second is a constant, and ˆr is the unit vector pointing from the law is directed towards the sun. Sun towards the planet, and r is the distance between the planet and the Sun. The radial acceleration a is r

( ar = r¨ − rθ˙2 = r¨ − r

nab r2

)2 = r¨ −

n2 a2 b2 . r3

According to Kepler’s third law, α has the same value for all the planets. So the inverse square law for planetary accelerations applies throughout the entire solar system.

The inverse square law is a differential equation. The soKepler’s first law states that the orbit is described by the lutions to this differential equation include the Keplerian motions, as shown, but they also include motions where equation: the orbit is a hyperbola or parabola or a straight line. See Kepler orbit. p = 1 + ε cos θ. r Differentiating with respect to time

pr˙ = −ε sin θ θ˙ r2

or

pr˙ = nab ε sin θ.

22.5.3 Newton’s law of gravitation

By Newton’s second law, the gravitational force that acts on the planet is:

F = mplanet r = −mplanet αr−2ˆr where mplanet is the mass of the planet and α has the same value for all planets in the solar system. According to


260

CHAPTER 22. KEPLER’S LAWS OF PLANETARY MOTION

Newton’s third Law, the Sun is attracted to the planet by The procedure for calculating the heliocentric polar coa force of the same magnitude. Since the force is pro- ordinates (r,θ) of a planet as a function of the time t since portional to the mass of the planet, under the symmetric perihelion, is the following four steps: consideration, it should also be proportional to the mass of the Sun, mSun . So 1. Compute the mean anomaly M = nt where n is the mean motion. n · P = 2π radians where P is the period.

α = GmSun where G is the gravitational constant.

2. Compute the eccentric anomaly E by solving Kepler’s equation:

The acceleration of solar system body number i is, according to Newton’s laws:

ri = G

M = E − ε sin E −2 ˆrij mj rij

3. Compute the true anomaly θ by the equation:

j̸=i

where mj is the mass of body j, rij is the distance between body i and body j, ˆrij is the unit vector from body i towards body j, and the vector summation is over all bodies in the world, besides i itself.

(1 − ε) tan2

θ E = (1 + ε) tan2 2 2

4. Compute the heliocentric distance

In the special case where there are only two bodies in the world, Earth and Sun, the acceleration becomes

r = a(1 − ε cos E).

The important special case of circular orbit, ε = 0, gives θ = E = M. Because the uniform circular motion was considered to be normal, a deviation from this motion was which is the acceleration of the Kepler motion. So this considered an anomaly. Earth moves around the Sun according to Kepler’s laws. The proof of this procedure is shown below. If the two bodies in the world are Moon and Earth the acceleration of the Moon becomes

−2 ˆrEarth,Sun rEarth = GmSun rEarth,Sun

22.6.1 Mean anomaly, M −2 ˆrMoon,Earth rMoon = GmEarth rMoon,Earth

So in this approximation the Moon moves around the Earth according to Kepler’s laws.

circle

In the three-body case the accelerations are −2 −2 ˆrSun,Earth +GmMoon rSun,Moon ˆrSun,Moon rSun = GmEarth rSun,Earth

x

orbit

−2 −2 ˆrEarth,Sun +GmMoon rEarth,Moon ˆrEarth,Moon rEarth = GmSun rEarth,Sun

P

−2 −2 ˆrMoon,Sun +GmEarth rMoon,Earth ˆrMoon,Earth rMoon = GmSun rMoon,Sun

These accelerations are not those of Kepler orbits, and the three-body problem is complicated. But Keplerian approximation is the basis for perturbation calculations. See Lunar theory.

22.6 Position as a function of time

M c

E S

y

θ d

z

FIgure 5: Geometric construction for Kepler’s calculation of θ. The Sun (located at the focus) is labeled S and the planet P. The auxiliary circle is an aid to calculation. Line xd is perpendicular to the base and through the planet P. The shaded sectors are arranged to have equal areas by positioning of point y.

Kepler used his two first laws to compute the position of a planet as a function of time. His method involves the solution of a transcendental equation called Kepler’s equa- The Keplerian problem assumes an elliptical orbit and the tion. four points:


22.6. POSITION AS A FUNCTION OF TIME s the Sun (at one focus of ellipse);

261 as an intermediate variable, and first compute E as a function of M by solving Kepler’s equation below, and then compute the true anomaly θ from the eccentric anomaly E. Here are the details.

z the perihelion c the center of the ellipse p the planet

|zcy| = |zsx| = |zcx| − |scx|

and a = |cz|, distance between center and perihelion, the semimajor axis, ε=

|cs| a ,

a2 M a2 E aε · a sin E = − 2 2 2 Division by a2 /2 gives Kepler’s equation

the eccentricity,

√ b = a 1 − ε2 , the semiminor axis, r = |sp|, the distance between Sun and planet. θ = ∠zsp, the direction to the planet as seen from the Sun, the true anomaly.

M = E − ε · sin E. This equation gives M as a function of E. Determining E for a given M is the inverse problem. Iterative numerical algorithms are commonly used.

The problem is to compute the polar coordinates (r,θ) of Having computed the eccentric anomaly E, the next step the planet from the time since perihelion, t. is to calculate the true anomaly θ. It is solved in steps. Kepler considered the circle with the major axis as a diameter, and x, the projection of the planet to the auxiliary circle y, the point on the circle such that the sector areas |zcy| and |zsx| are equal, M = ∠zcy, the mean anomaly. The sector areas are related by |zsp| = The circular sector area |zcy| =

b a

· |zsx|.

22.6.3 True anomaly, θ Note from the figure that − → → − → cd = − cs + sd so that

a2 M 2 .

a · cos E = a · ε + r · cos θ.

The area swept since perihelion,

Dividing by a and inserting from Kepler’s first law |zsp| =

2

b b b a M abM · |zsx| = · |zcy| = · = , a a a 2 2

r 1 − ε2 is by Kepler’s second law proportional to time since per- a = 1 + ε · cos θ ihelion. So the mean anomaly, M, is proportional to time to get since perihelion, t. 1−ε2 · 1+ε·cos θ ε·(1+ε·cos θ)+(1−ε )·cos θ ε+cos θ = 1+ε·cos θ . 1+ε·cos θ

cos E M = nt,

=

=

ε +

cos θ

2

where n is the mean motion.

22.6.2

Eccentric anomaly, E

When the mean anomaly M is computed, the goal is to compute the true anomaly θ. The function θ = f(M) is, however, not elementary.[20] Kepler’s solution is to use

The result is a usable relationship between the eccentric anomaly E and the true anomaly θ. A computationally more convenient form follows by substituting into the trigonometric identity:

tan2 E = ∠zcx , x as seen from the centre, the eccentric anomaly

Get

x 1 − cos x = . 2 1 + cos x


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CHAPTER 22. KEPLER’S LAWS OF PLANETARY MOTION

Benati, 1651), volume 1, page 492 Scholia III. In the margin beside the relevant paragraph is printed: Vendelini inε+cos θ 1 − 1+ε·cos 1 − cos E geniosa speculatio circa motus & intervalla satellitum Joθ 2 E tan = = ε+cos θ vis. (Wendelin’s clever speculation about the movement 2 1 + cos E 1 + 1+ε·cos θ and distances of Jupiter’s satellites.) (1 + ε · cos θ) − (ε + cos θ) 1 − ε 1 − cos θ 1 − ε In 1621, θ Johannes Kepler had noted that Jupiter’s moons = = · = · tan2(approximately) . obey his third law in his Epitome Astrono(1 + ε · cos θ) + (ε + cos θ) 1 + ε 1 + cos θ 1 + ε miae Copernicanae 2 [Epitome of Copernican Astronomy] (Linz (“Lentiis ad Danubium“), (Austria): Johann Planck, Multiplying by 1 + ε gives the result 1622), book 4, part 2, page 554.

(1 − ε) · tan2

θ E = (1 + ε) · tan2 2 2

This is the third step in the connection between time and position in the orbit.

22.6.4

Distance, r

The fourth step is to compute the heliocentric distance r from the true anomaly θ by Kepler’s first law:

r · (1 + ε · cos θ) = a · (1 − ε2 ) Using the relation above between θ and E the final equation for the distance r is:

r = a · (1 − ε · cos E).

22.7 See also • Circular motion • Free-fall time • Gravity • Kepler orbit • Kepler problem • Kepler’s equation • Laplace–Runge–Lenz vector • Specific relative angular momentum, relatively easy derivation of Kepler’s laws starting with conservation of angular momentum

22.8 Notes [1] Godefroy Wendelin wrote a letter to Giovanni Battista Riccioli about the relationship between the distances of the Jovian moons from Jupiter and the periods of their orbits, showing that the periods and distances conformed to Kepler’s third law. See: Joanne Baptista Riccioli, Almagestum novum … (Bologna (Bononia), (Italy): Victor

22.9 References [1] Bryant, Jeff; Pavlyk, Oleksandr. "Kepler’s Second Law", Wolfram Demonstrations Project. Retrieved December 27, 2009. [2] http://www.nytimes.com/1990/01/23/science/ after-400-years-a-challenge-to-kepler-he-fabricated-his-data-scholar-says. html?pagewanted=1 [3] Holton, Gerald James; Brush, Stephen G. (2001). Physics, the Human Adventure: From Copernicus to Einstein and Beyond (3rd paperback ed.). Piscataway, NJ: Rutgers University Press. pp. 40–41. ISBN 0-8135-2908-5. Retrieved December 27, 2009. [4] See also G. E. Smith, “Newton’s Philosophiae Naturalis Principia Mathematica”, especially the section Historical context ... in The Stanford Encyclopedia of Philosophy (Winter 2008 Edition), Edward N. Zalta (ed.). [5] Voltaire, Eléments de la philosophie de Newton [Elements of Newton’s Philosophy] (London, England: 1738). See, for example: • From p. 162: “Par une des grandes loix de Kepler, toute Planete décrit des aires égales en temp égaux : par une autre loi non moins sûre, chaque Planete fait sa révolution autour du Soleil en telle sort, que si, sa moyenne distance au Soleil est 10. prenez le cube de ce nombre, ce qui sera 1000., & le tems de la révolution de cette Planete autour du Soleil sera proportionné à la racine quarrée de ce nombre 1000.” (By one of the great laws of Kepler, each planet describes equal areas in equal times ; by another law no less certain, each planet makes its revolution around the sun in such a way that if its mean distance from the sun is 10, take the cube of that number, which will be 1000, and the time of the revolution of that planet around the sun will be proportional to the square root of that number 1000.) • From p. 205: “Il est donc prouvé par la loi de Kepler & par celle de Neuton, que chaque Planete gravite vers le Soleil, ... " (It is thus proved by the law of Kepler and by that of Newton, that each planet revolves around the sun … ) [6] Wilson, Curtis (May 1994). “Kepler’s Laws, So-Called” (PDF). HAD News. Washington, DC: Historical Astronomy Division, American Astronomical Society (31): 1–2. Retrieved December 27, 2009.


22.9. REFERENCES

[7] De la Lande, Astronomie, vol. 1 (Paris, France: Desaint & Saillant, 1764). See, for example: • From page 390: " … mais suivant la fameuse loi de Kepler, qui sera expliquée dans le Livre suivant (892), le rapport des temps périodiques est toujours plus grand que celui des distances, une planete cinq fois plus éloignée du soleil, emploie à faire sa révolution douze fois plus de temps ou environ; … " ( … but according to the famous law of Kepler, which will be explained in the following book [i.e., chapter] (paragraph 892), the ratio of the periods is always greater than that of the distances [so that, for example,] a planet five times farther from the sun, requires about twelve times or so more time to make its revolution [around the sun]; … ) • From page 429: “Les Quarrés des Temps périodiques sont comme les Cubes des Distances. 892. La plus fameuse loi du mouvement des planetes découverte par Kepler, est celle du repport qu'il y a entre les grandeurs de leurs orbites, & le temps qu'elles emploient à les parcourir; … " (The squares of the periods are as the cubes of the distances. 892. The most famous law of the movement of the planets discovered by Kepler is that of the relation that exists between the sizes of their orbits and the times that the [planets] require to traverse them; … ) • From page 430: “Les Aires sont proportionnelles au Temps. 895. Cette loi générale du mouvement des planetes devenue si importante dans l'Astronomie, sçavior, que les aires sont proportionnelles au temps, est encore une des découvertes de Kepler; … " (Areas are proportional to times. 895. This general law of the movement of the planets [which has] become so important in astronomy to know, [namely] that areas are proportional to times, is one of Kepler’s discoveries; … ) • From page 435: “On a appellé cette loi des aires proportionnelles aux temps, Loi de Kepler, aussi bien que celle de l'article 892, du nome de ce célebre Inventeur; … " (One called this law of areas proportional to times (the law of Kepler) as well as that of paragraph 892, by the name of that celebrated inventor; … ) [8] Robert Small, An account of the astronomical discoveries of Kepler (London, England: J Mawman, 1804), pp. 298– 299. [9] Robert Small, An account of the astronomical discoveries of Kepler (London, England: J. Mawman, 1804). [10] Bruce Stephenson (1994). Kepler’s Physical Astronomy. Princeton University Press. p. 170. ISBN 0-691-036527. [11] In his Astronomia nova, Kepler presented only a proof that Mars’ orbit is elliptical. Evidence that the other known planets’ orbits are elliptical was presented only in 1621. See: Johannes Kepler, Astronomia nova … (1609), p. 285. After having rejected circular and oval orbits, Kepler concluded that Mars’ orbit must be elliptical. From the top of page 285: “Ergo ellipsis est Planetæ iter; … " (Thus, an ellipse is the planet’s [i.e., Mars’] path; … ) Later on

263

the same page: " … ut sequenti capite patescet: ubi simul etiam demonstrabitur, nullam Planetæ relinqui figuram Orbitæ, præterquam perfecte ellipticam; … " ( … as will be revealed in the next chapter: where it will also then be proved that any figure of the planet’s orbit must be relinquished, except a perfect ellipse; … ) And then: “Caput LIX. Demonstratio, quod orbita Martis, … , fiat perfecta ellipsis: … " (Chapter 59. Proof that Mars’ orbit, … , is a perfect ellipse: … ) The geometric proof that Mars’ orbit is an ellipse appears as Protheorema XI on pages 289– 290. Kepler stated that every planet travels in elliptical orbits having the Sun at one focus in: Johannes Kepler, Epitome Astronomiae Copernicanae [Summary of Copernican Astronomy] (Linz (“Lentiis ad Danubium”), (Austria): Johann Planck, 1622), book 5, part 1, III. De Figura Orbitæ (III. On the figure [i.e., shape] of orbits), pages 658–665. From p. 658: “Ellipsin fieri orbitam planetæ … " (Of an ellipse is made a planet’s orbit … ). From p. 659: " … Sole (Foco altero huius ellipsis) … " ( … the Sun (the other focus of this ellipse) … ). [12] In his Astronomia nova ... (1609), Kepler did not present his second law in its modern form. He did that only in his Epitome of 1621. Furthermore, in 1609, he presented his second law in two different forms, which scholars call the “distance law” and the “area law”. • His “distance law” is presented in: “Caput XXXII. Virtutem quam Planetam movet in circulum attenuari cum discessu a fonte.” (Chapter 32. The force that moves a planet circularly weakens with distance from the source.) See: Johannes Kepler, Astronomia nova … (1609), pp. 165–167. On page 167, Kepler states: " … , quanto longior est αδ quam αε, tanto diutius moratur Planeta in certo aliquo arcui excentrici apud δ, quam in æquali arcu excentrici apud ε.” ( … , as αδ is longer than αε, so much longer will a planet remain on a certain arc of the eccentric near δ than on an equal arc of the eccentric near ε.) That is, the farther a planet is from the Sun (at the point α), the slower it moves along its orbit, so a radius from the Sun to a planet passes through equal areas in equal times. However, as Kepler presented it, his argument is accurate only for circles, not ellipses. • His “area law” is presented in: “Caput LIX. Demonstratio, quod orbita Martis, … , fiat perfecta ellipsis: … " (Chapter 59. Proof that Mars’ orbit, … , is a perfect ellipse: … ), Protheorema XIV and XV, pp. 291–295. On the top p. 294, it reads: “Arcum ellipseos, cujus moras metitur area AKN, debere terminari in LK, ut sit AM.” (The arc of the ellipse, of which the duration is delimited [i.e., measured] by the area AKM, should be terminated in LK, so that it [i.e., the arc] is AM.) In other words, the time that Mars requires to move along an arc AM of its elliptical orbit is measured by the area of the segment AMN of the ellipse (where N is the position of the Sun), which in turn is proportional to the section AKN of the circle that encircles the ellipse and that is tangent to it. Therefore, the area that is swept out by a radius from the Sun to Mars as Mars moves along an arc of its elliptical orbit is proportional to


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the time that Mars requires to move along that arc. Thus, a radius from the Sun to Mars sweeps out equal areas in equal times. In 1621, Kepler restated his second law for any planet: Johannes Kepler, Epitome Astronomiae Copernicanae [Summary of Copernican Astronomy] (Linz (“Lentiis ad Danubium”), (Austria): Johann Planck, 1622), book 5, page 668. From page 668: “Dictum quidem est in superioribus, divisa orbita in particulas minutissimas æquales: accrescete iis moras planetæ per eas, in proportione intervallorum inter eas & Solem.” (It has been said above that, if the orbit of the planet is divided into the smallest equal parts, the times of the planet in them increase in the ratio of the distances between them and the sun.) That is, a planet’s speed along its orbit is inversely proportional to its distance from the Sun. (The remainder of the paragraph makes clear that Kepler was referring to what is now called angular velocity.) [13] Johannes Kepler, Harmonices Mundi [The Harmony of the World] (Linz, (Austria): Johann Planck, 1619), book 5, chapter 3, p. 189. From the bottom of p. 189: “Sed res est certissima exactissimaque quod proportio qua est inter binorum quorumcunque Planetarum tempora periodica, sit præcise sesquialtera proportionis mediarum distantiarum, … " (But it is absolutely certain and exact that the proportion between the periodic times of any two planets is precisely the sesquialternate proportion [i.e., the ratio of 3:2] of their mean distances, … ") An English translation of Kepler’s Harmonices Mundi is available as: Johannes Kepler with E.J. Aiton, A.M. Duncan, and J.V. Field, trans., The Harmony of the World (Philadelphia, Pennsylvania: American Philosophical Society, 1997); see especially p. 411. [14] http://www.windows2universe.org/our_solar_system/ planets_table.html [15] Wilbur Applebaum (13 June 2000). Encyclopedia of the Scientific Revolution: From Copernicus to Newton. Routledge. p. 603. ISBN 978-1-135-58255-5. [16] Roy Porter (25 September 1992). The Scientific Revolution in National Context. Cambridge University Press. p. 102. ISBN 978-0-521-39699-8. [17] Victor Guillemin; Shlomo Sternberg (2006). Variations on a Theme by Kepler. American Mathematical Soc. p. 5. ISBN 978-0-8218-4184-6. [18] Burtt, Edwin. The Metaphysical Foundations of Modern Physical Science. p. 52. [19] Gerald James Holton, Stephen G. Brush (2001). Physics, the Human Adventure. Rutgers University Press. p. 45. ISBN 0-8135-2908-5. [20] MÜLLER, M (1995). “EQUATION OF TIME – PROBLEM IN ASTRONOMY”. Acta Physica Polonica A. Retrieved 23 February 2013.

22.10 Bibliography • Kepler’s life is summarized on pages 523–627 and Book Five of his magnum opus, Harmonice Mundi

(harmonies of the world), is reprinted on pages 635– 732 of On the Shoulders of Giants: The Great Works of Physics and Astronomy (works by Copernicus, Kepler, Galileo, Newton, and Einstein). Stephen Hawking, ed. 2002 ISBN 0-7624-1348-4 • A derivation of Kepler’s third law of planetary motion is a standard topic in engineering mechanics classes. See, for example, pages 161–164 of Meriam, J. L. (1971) [1966]. “Dynamics, 2nd ed”. New York: John Wiley. ISBN 0-471-59601-9.. • Murray and Dermott, Solar System Dynamics, Cambridge University Press 1999, ISBN 0-52157597-4 • V.I. Arnold, Mathematical Methods of Classical Mechanics, Chapter 2. Springer 1989, ISBN 0-38796890-3

22.11 External links • B.Surendranath Reddy; animation of Kepler’s laws: applet • "Derivation of Kepler’s Laws" (from Newton’s laws) at Physics Stack Exchange. • Crowell, Benjamin, Conservation Laws, http://www.lightandmatter.com/area1book2.html, an online book that gives a proof of the first law without the use of calculus. (see section 5.2, p. 112) • David McNamara and Gianfranco Vidali, Kepler’s Second Law – Java Interactive Tutorial, http://www. phy.syr.edu/courses/java/mc_html/kepler.html, an interactive Java applet that aids in the understanding of Kepler’s Second Law. • Audio – Cain/Gay (2010) Astronomy Cast Johannes Kepler and His Laws of Planetary Motion • University of Tennessee’s Dept. Physics & Astronomy: Astronomy 161 page on Johannes Kepler: The Laws of Planetary Motion • Equant compared to Kepler: interactive model • Kepler’s Third Law:interactive model • Solar System Simulator (Interactive Applet) • Kepler and His Laws, educational web pages by David P. Stern


Chapter 23

Giordano Bruno This article is about the Italian philosopher Giordano Bruno. For other uses, see Giordano Bruno (disambiguation). Not to be confused with Bruno Giordano.

23.1 Life

Giordano Bruno (Italian: [dʒorˈdano ˈbruno]; Latin: Iordanus Brunus Nolanus; 1548 – 17 February 1600), born Filippo Bruno, was an Italian Dominican friar, philosopher, mathematician, poet, and astrologer.[3] He is remembered for his cosmological theories, which conceptually extended the then novel Copernican model. He proposed that the stars were just distant suns surrounded by their own exoplanets and raised the possibility that these planets could even foster life of their own (a philosophical position known as cosmic pluralism). He also insisted that the universe is in fact infinite and could have no celestial body at its “center”.

23.1.1 Early years, 1548–1576

Beginning in 1593, Bruno was tried for heresy by the Roman Inquisition on charges including denial of several core Catholic doctrines, including eternal damnation, the Trinity, the divinity of Christ, the virginity of Mary, and transubstantiation. Bruno’s pantheism was also a matter of grave concern.[4] The Inquisition found him guilty, and he was burned at the stake in Rome’s Campo de' Fiori in 1600. After his death, he gained considerable fame, being particularly celebrated by 19th- and early 20th-century commentators who regarded him as a martyr for science,[5] although historians have debated the extent to which his heresy trial was a response to his astronomical views or to other aspects of his philosophy and theology.[6][7][8][9][10] Bruno’s case is still considered a landmark in the history of free thought and the emerging sciences.[11][12][13] In addition to cosmology, Bruno also wrote extensively on the art of memory, a loosely organized group of mnemonic techniques and principles. Historian Frances Yates argues that Bruno was deeply influenced by Arab astrology (particularly the philosophy of Averroes[14] ), Neoplatonism, Renaissance Hermeticism, and legends surrounding the Egyptian god Thoth.[15] Other studies of Bruno have focused on his qualitative approach to mathematics and his application of the spatial concepts of geometry to language.[16]

Born Filippo Bruno in Nola (in Campania, then part of the Kingdom of Naples) in 1548, he was the son of Giovanni Bruno, a soldier, and Fraulissa Savolino. In his youth he was sent to Naples to be educated. He was tutored privately at the Augustinian monastery there, and attended public lectures at the Studium Generale.[17] At the age of 17, he entered the Dominican Order at the monastery of San Domenico Maggiore in Naples, taking the name Giordano, after Giordano Crispo, his metaphysics tutor. He continued his studies there, completing his novitiate, and became an ordained priest in 1572 at age 24. During his time in Naples he became known for his skill with the art of memory and on one occasion traveled to Rome to demonstrate his mnemonic system before Pope Pius V and Cardinal Rebiba. In his later years Bruno claimed that the Pope accepted his dedication to him of the lost work On The Ark of Noah at this time.[18] While Bruno was distinguished for outstanding ability, his taste for free thinking and forbidden books soon caused him difficulties. Given the controversy he caused in later life it is surprising that he was able to remain within the monastic system for eleven years. In his testimony to Venetian inquisitors during his trial, many years later, he says that proceedings were twice taken against him for having cast away images of the saints, retaining only a crucifix, and for having recommended controversial texts to a novice.[19] Such behavior could perhaps be overlooked, but Bruno’s situation became much more serious when he was reported to have defended the Arian heresy, and when a copy of the banned writings of Erasmus, annotated by him, was discovered hidden in the convent privy. When he learned that an indictment was being prepared against him in Naples he fled, shedding his religious habit, at least for a time.[20]

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23.1.2

CHAPTER 23. GIORDANO BRUNO

First years of wandering, 1576– attack on the work of Antoine de la Faye, a distinguished professor. He and the printer were promptly arrested. 1583

Rather than apologizing, Bruno insisted on continuing to Bruno first went to the Genoese port of Noli, then to defend his publication. He was refused the right to take Savona, Turin and finally to Venice, where he published sacrament. Though this right was eventually restored, he his lost work On the Signs of the Times with the permis- left Geneva. sion (so he claimed at his trial) of the Dominican Remi- He went to France, arriving first in Lyon, and thereafter gio Nannini Fiorentino. From Venice he went to Padua, settling for a time (1580–1581) in Toulouse, where he where he met fellow Dominicans who convinced him took his doctorate in theology and was elected by stuto wear his religious habit again. From Padua he went dents to lecture in philosophy. It seems he also attempted to Bergamo and then across the Alps to Chambéry and at this time to return to Catholicism, but was denied abLyon. His movements after this time are obscure.[21] solution by the Jesuit priest he approached. When religious strife broke out in the summer of 1581, he moved to Paris. There he held a cycle of thirty lectures on theological topics and also began to gain fame for his prodigious memory. Bruno’s feats of memory were based, at least in part, on his elaborate system of mnemonics, but some of his contemporaries found it easier to attribute them to magical powers. His talents attracted the benevolent attention of the king Henry III. The king summoned him to the court. Bruno subsequently reported “I got me such a name that King Henry III summoned me one day to discover from me if the memory which I possessed was natural or acquired by magic art. I satisfied him that it did not come from sorcery but from organised knowledge; and, following this, I got a book on memory printed, entitled The Shadows of Ideas, which I dedicated to His Majesty. Forthwith he gave me an Extraordinary Lectureship with a salary.”[24]

The earliest depiction of Bruno is an engraving published in 1715 in Germany, presumed based on a lost contemporary portrait.[22]

In Paris Bruno enjoyed the protection of his powerful French patrons. During this period, he published several works on mnemonics, including De umbris idearum (On the Shadows of Ideas, 1582), Ars Memoriae (The Art of Memory, 1582), and Cantus Circaeus (Circe’s Song, 1582). All of these were based on his mnemonic models of organised knowledge and experience, as opposed to the simplistic logic-based mnemonic techniques of Petrus Ramus then becoming popular. Bruno also published a comedy summarizing some of his philosophical positions, titled Il Candelaio (The Torchbearer, 1582). In the 16th century dedications were, as a rule, approved beforehand, and hence were a way of placing a work under the protection of an individual. Given that Bruno dedicated various works to the likes of King Henry III, Sir Philip Sidney, Michel de Castelnau (French Ambassador to England), and possibly Pope Pius V, it is apparent that this wanderer had risen sharply in status and moved in powerful circles.

In 1579 he arrived in Geneva. As D.W. Singer, a Bruno biographer, notes, “The question has sometimes been raised as to whether Bruno became a Protestant, but it is intrinsically most unlikely that he accepted membership in Calvin’s communion”[23] During his Venetian trial he told inquisitors that while in Geneva he told the Marchese de Vico of Naples, who was notable for helping Italian refugees in Geneva, “I did not intend to adopt the religion of the city. I desired to stay there only that I might live at liberty and in security.” Bruno had a pair of breeches made for himself, and the Marchese and others apparently made Bruno a gift of a sword, hat, cape and other necessities for dressing himself; in such clothing Bruno could no longer be recognized as a priest. Things apparently went well for Bruno for a time, as he entered his 23.1.3 England, 1583–1585 name in the Rector’s Book of the University of Geneva in May 1579. But in keeping with his personality he In April 1583, Bruno went to England with letters of reccould not long remain silent. In August he published an ommendation from Henry III as a guest of the French


23.1. LIFE

267 guage lost him the support of his friends. John Bossy has advanced the theory that, while staying in the French Embassy in London, Bruno was also spying on Catholic conspirators, under the pseudonym 'Henry Fagot', for Sir Francis Walsingham, Queen Elizabeth's Secretary of State.[26] Bruno is sometimes cited as being the first to propose that the universe is infinite, which he did during his time in England, but an English scientist, Thomas Digges, put forth this idea in a published work in 1576, some eight years earlier than Bruno.[27]

23.1.4 Last years of wandering, 1585–1592 In October 1585, after the French embassy in London was attacked by a mob, Bruno returned to Paris with Castelnau, finding a tense political situation. Moreover, his 120 theses against Aristotelian natural science and his pamphlets against the mathematician Fabrizio Mordente soon put him in ill favor. In 1586, following a violent quarrel about Mordente’s invention, the differential compass, he left France for Germany.

Woodcut illustration of one of Giordano Bruno’s less complex mnemonic devices

ambassador, Michel de Castelnau. There he became acquainted with the poet Philip Sidney (to whom he dedicated two books) and other members of the Hermetic circle around John Dee, though there is no evidence that Bruno ever met Dee himself. He also lectured at Oxford, and unsuccessfully sought a teaching position there. His views were controversial, notably with John Underhill, Rector of Lincoln College and subsequently bishop of Oxford, and George Abbot, who later became Archbishop of Canterbury. Abbot mocked Bruno for supporting “the opinion of Copernicus that the earth did go round, and the heavens did stand still; whereas in truth it was his own head which rather did run round, and his brains did not stand still”,[25] and reports accusations that Woodcut from “Articuli centum et sexaginta adversus huius temBruno plagiarized Ficino's work. pestatis mathematicos atque philosophos,” Prague 1588 Nevertheless, his stay in England was fruitful. During that time Bruno completed and published some of his most important works, the six “Italian Dialogues,” including the cosmological tracts La Cena de le Ceneri (The Ash Wednesday Supper, 1584), De la Causa, Principio et Uno (On Cause, Principle and Unity, 1584), De l'Infinito, Universo e Mondi (On the Infinite, Universe and Worlds, 1584) as well as Lo Spaccio de la Bestia Trionfante (The Expulsion of the Triumphant Beast, 1584) and De gl' Heroici Furori (On the Heroic Frenzies, 1585). Some of these were printed by John Charlewood. Some of the works that Bruno published in London, notably The Ash Wednesday Supper, appear to have given offense. Once again, Bruno’s controversial views and tactless lan-

In Germany he failed to obtain a teaching position at Marburg, but was granted permission to teach at Wittenberg, where he lectured on Aristotle for two years. However, with a change of intellectual climate there, he was no longer welcome, and went in 1588 to Prague, where he obtained 300 taler from Rudolf II, but no teaching position. He went on to serve briefly as a professor in Helmstedt, but had to flee again when he was excommunicated by the Lutherans. During this period he produced several Latin works, dictated to his friend and secretary Girolamo Besler, including De Magia (On Magic), Theses De Magia (Theses On Magic) and De Vinculis In Genere (A General Account


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of Bonding). All these were apparently transcribed or recorded by Besler (or Bisler) between 1589 and 1590.[28] He also published De Imaginum, Signorum, Et Idearum Compositione (On The Composition of Images, Signs and Ideas, 1591).

• holding opinions contrary to the Catholic faith pertaining to Jesus as Christ;

In 1591 he was in Frankfurt. Apparently, during the Frankfurt Book Fair, he received an invitation to Venice from the patrician Giovanni Mocenigo, who wished to be instructed in the art of memory, and also heard of a vacant chair in mathematics at the University of Padua. At the time the Inquisition seemed to be losing some of its strictness, and because Venice was the most liberal state in Italy, Bruno was lulled into making the fatal mistake of returning to Italy.[29]

• holding opinions contrary to the Catholic faith about both Transubstantiation and Mass;

He went first to Padua, where he taught briefly, and applied unsuccessfully for the chair of mathematics, which was given instead to Galileo Galilei one year later. Bruno accepted Mocenigo’s invitation and moved to Venice in March 1592. For about two months he served as an inhouse tutor to Mocenigo. When Bruno announced his plan to leave Venice to his host, the latter, who was unhappy with the teachings he had received and had apparently come to dislike Bruno, denounced him to the Venetian Inquisition, which had Bruno arrested on 22 May 1592. Among the numerous charges of blasphemy and heresy brought against him in Venice, based on Mocenigo’s denunciation, was his belief in the plurality of worlds, as well as accusations of personal misconduct. Bruno defended himself skillfully, stressing the philosophical character of some of his positions, denying others and admitting that he had had doubts on some matters of dogma. The Roman Inquisition, however, asked for his transfer to Rome. After several months of argument, the Venetian authorities reluctantly consented and Bruno was sent to Rome in February 1593.

23.1.5

Imprisonment, trial and execution, 1593–1600

During the seven years of his trial in Rome, Bruno was held in confinement, lastly in the Tower of Nona. Some important documents about the trial are lost, but others have been preserved, among them a summary of the proceedings that was rediscovered in 1940.[30] The numerous charges against Bruno, based on some of his books as well as on witness accounts, included blasphemy, immoral conduct, and heresy in matters of dogmatic theology, and involved some of the basic doctrines of his philosophy and cosmology. Luigi Firpo lists these charges made against Bruno by the Roman Inquisition:[31]

• holding opinions contrary to the Catholic faith regarding the virginity of Mary, mother of Jesus;

• claiming the existence of a plurality of worlds and their eternity; • believing in metempsychosis and in transmigration of the human soul into brutes;

the

• dealing in magics and divination.

The trial of Giordano Bruno by the Roman Inquisition. Bronze relief by Ettore Ferrari, Campo de' Fiori, Rome.

Bruno defended himself as he had in Venice, insisting that he accepted the Church’s dogmatic teachings, but trying to preserve the basis of his philosophy. In particular, he held firm to his belief in the plurality of worlds, although he was admonished to abandon it. His trial was overseen by the Inquisitor Cardinal Bellarmine, who demanded a full recantation, which Bruno eventually refused. On 20 January 1600, Pope Clement VIII declared Bruno a heretic and the Inquisition issued a sentence of death. According to the correspondence of Gaspar Schopp of Breslau, he is said to have made a threatening gesture towards his judges and to have replied: Maiori forsan cum timore sententiam in me fertis quam ego accipiam (“Perhaps you pronounce this sentence against me with greater fear than I receive it”).[32]

He was turned over to the secular authorities. On 17 February 1600, in the Campo de' Fiori (a central Roman market square), with his “tongue imprisoned because of his wicked words”, he was burned at the stake.[33] His ashes were thrown into the Tiber river. All of Bruno’s works were placed on the Index Librorum Prohibitorum in 1603. Inquisition cardinals who judged Giordano Bruno were: Cardinal Bellarmino (Bellarmine), Cardinal • holding opinions contrary to the Catholic faith and Madruzzo (Madruzzi), Cardinal Camillo Borghese (later Pope Paul V), Domenico Cardinal Pinelli, Pompeio Carspeaking against it and its ministers; dinal Arrigoni, Cardinal Sfondrati, Pedro Cardinal De • holding opinions contrary to the Catholic faith about Deza Manuel, Cardinal Santorio (Archbishop of Santa the Trinity, divinity of Christ, and Incarnation; Severina, Cardinal-Bishop of Palestrina).


23.2. COSMOLOGY

23.1.6

Physical appearance

269 center, but it was the Sun rather than the Earth. Copernicus also argued the Earth was a planet orbiting the Sun once every year. However he maintained the Ptolemaic hypothesis that the orbits of the planets were composed of perfect circles—deferents and epicycles—and that the stars were fixed on a stationary outer sphere.

The earliest likeness of Bruno is an engraving published in 1715[34] and cited by Salvestrini as “the only known portrait of Bruno”. Salvestrini suggests that it is a reengraving made from a now lost original.[22] This engraving has provided the source for later images. Despite the widespread publication of Copernicus’ work The records of Bruno’s imprisonment by the Venetian in- De revolutionibus orbium coelestium, during Bruno’s time quisition in May 1592 describe him as a man “of average most educated Catholics subscribed to the Aristotelian height, with a hazel-coloured beard and the appearance geocentric view that the earth was the center of the uniof being about forty years of age”. Alternately, a pas- verse, and that all heavenly bodies revolved around it.[37] sage in a work by George Abbot indicates that Bruno was The ultimate limit of the universe was the primum moof diminutive stature: “When that Italian Didapper, who bile, whose diurnal rotation was conferred upon it by a intituled himselfe Philotheus Iordanus Brunus Nolanus, transcendental God, not part of the universe (although, magis elaborata Theologia Doctor, &c with a name longer as the kingdom of heaven, adjacent to it[38] ), a motionthan his body...”.[35] The word “didapper” used by Abbot less prime mover and first cause. The fixed stars were is the derisive term which at the time meant “a small div- part of this celestial sphere, all at the same fixed distance from the immobile earth at the center of the sphere. ing waterfowl”.[36] Ptolemy had numbered these at 1,022, grouped into 48 constellations. The planets were each fixed to a transparent sphere. 23.2 Cosmology Few astronomers of Bruno’s time accepted Copernicus’s 23.2.1 Contemporary cosmological beliefs heliocentric model. Among those who did were the Germans Michael Maestlin (1550–1631), Christoph Rothmann, Johannes Kepler (1571–1630), the Englishman See also: Celestial spheres § History Thomas Digges, author of A Perfit Description of the CaeIn the first half of the 15th century, Nicholas of lestial Orbes, and the Italian Galileo Galilei (1564–1642).

23.2.2 Bruno’s cosmological claims In 1584, Bruno published two important philosophical dialogues (La Cena de le Ceneri and De l'infinito universo et mondi) in which he argued against the planetary spheres (Christoph Rothmann did the same in 1586 as did Tycho Brahe in 1587) and affirmed the Copernican principle.

Illuminated illustration of the Ptolemaic geocentric conception of the universe. The outermost text reads “The heavenly empire, dwelling of God and all the selected”

Cusa challenged the then widely accepted philosophies of Aristotelianism, envisioning instead an infinite universe whose center was everywhere and circumference nowhere, and moreover teeming with countless stars. He also predicted that neither were the rotational orbits circular nor were their movements uniform. In the second half of the 16th century, the theories of Copernicus (1473–1543) began diffusing through Europe. Copernicus conserved the idea of planets fixed to solid spheres, but considered the apparent motion of the stars to be an illusion caused by the rotation of the Earth on its axis; he also preserved the notion of an immobile

In particular, to support the Copernican view and oppose the objection according to which the motion of the Earth would be perceived by means of the motion of winds, clouds etc., in La Cena de le Ceneri Bruno anticipates some of the arguments of Galilei on the relativity principle.[39] Note that he also uses the example now known as Galileo’s ship. Theophilus - [...] air through which the clouds and winds move are parts of the Earth, [...] to mean under the name of Earth the whole machinery and the entire animated part, which consists of dissimilar parts; so that the rivers, the rocks, the seas, the whole vaporous and turbulent air, which is enclosed within the highest mountains, should belong to the Earth as its members, just as the air [does] in the lungs and in other cavities of animals by which they breathe, widen their arteries, and other similar effects necessary for life are performed. The clouds, too, move through accidents in the


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CHAPTER 23. GIORDANO BRUNO body of the earth and are in its bowels as are the waters. [...] With the Earth move [...] all things that are on the Earth. If, therefore, from a point outside the Earth something were thrown upon the Earth, it would lose, because of the latter’s motion, its straightness as would be seen on the ship [...] moving along a river, if someone on point C of the riverbank were to throw a stone along a straight line, and would see the stone miss its target by the amount of the velocity of the ship’s motion. But if someone were placed high on the mast of that ship, move as it may however fast, he would not miss his target at all, so that the stone or some other heavy thing thrown downward would not come along a straight line from the point E which is at the top of the mast, or cage, to the point D which is at the bottom of the mast, or at some point in the bowels and body of the ship. Thus, if from the point D to the point E someone who is inside the ship would throw a stone straight up, it would return to the bottom along the same line however far the ship moved, provided it was not subject to any pitch and roll.”[40]

Bruno’s overall contribution to the birth of modern science is still controversial. Some scholars follow Frances Yates stressing the importance of Bruno’s ideas about the universe being infinite and lacking geocentric structure as a crucial crosspoint between the old and the new. Others see in Bruno’s idea of multiple worlds instantiating the infinite possibilities of a pristine, indivisible One,[45] a forerunner of Everett's many-worlds interpretation of quantum mechanics.[46] While most academics note Bruno’s theological position as pantheism, physicist and philosopher Max Bernhard Weinstein in his Welt- und Lebensanschauungen, Hervorgegangen aus Religion, Philosophie und Naturerkenntnis (“World and Life Views, Emerging From Religion, Philosophy and Nature”), wrote that the theological model of pandeism was strongly expressed in the teachings of Bruno, especially with respect to the vision of a deity which had no particular relation to one part of the infinite universe more than any other, and was immanent, as present on Earth as in the Heavens, subsuming in itself the multiplicity of existence.[47]

23.3 Retrospective views of Bruno

Bruno’s infinite universe was filled with a substance—a “pure air,” aether, or spiritus—that offered no resistance to the heavenly bodies which, in Bruno’s view, rather than being fixed, moved under their own impetus (momentum). Most dramatically, he completely abandoned the idea of a hierarchical universe. The universe is then one, infinite, immobile.... It is not capable of comprehension and therefore is endless and limitless, and to that extent infinite and indeterminable, and consequently immobile.[41] Bruno’s cosmology distinguishes between “suns” which produce their own light and heat, and have other bodies moving around them; and “earths” which move around suns and receive light and heat from them.[42] Bruno suggested that some, if not all, of the objects classically known as fixed stars are in fact suns.[42] According to astrophysicist Steven Soter, he was the first person to grasp that “stars are other suns with their own planets.”[43]

The monument to Bruno in the place he was executed, Campo de' Fiori in Rome. 41°53′44.16″N 12°28′19.80″E / 41.8956000°N 12.4721667°E

23.3.1 Late Vatican position

The Vatican has published few official statements about Bruno wrote that other worlds “have no less virtue nor Bruno’s trial and execution. In 1942, Cardinal Giovanni a nature different to that of our earth” and, like Earth, Mercati, who discovered a number of lost documents re“contain animals and inhabitants”.[44] lating to Bruno’s trial, stated that the Church was perfectly During the late 16th century, and throughout the 17th justified in condemning him. On the 400th anniversary century, Bruno’s ideas were held up for ridicule, debate, of Bruno’s death, in 2000, Cardinal Angelo Sodano deor inspiration. Margaret Cavendish, for example, wrote clared Bruno’s death to be a “sad episode” but, despite an entire series of poems against “atoms” and “infinite his regret, he defended Bruno’s prosecutors, maintaining worlds” in Poems and Fancies in 1664. Bruno’s true, if that the Inquisitors “had the desire to serve freedom and partial, vindication would have to wait for the implica- promote the common good and did everything possible tions and impact of Newtonian cosmology. to save his life.”[48] In the same year, Pope John Paul II


23.4. ARTISTIC DEPICTIONS

271

made a general apology for “the use of violence that some sued Bruno early in his life on the basis of his ophave committed in the service of truth”.[49] position to Aristotle, interest in Arianism, reading of Erasmus, and possession of banned texts.[59] White considers that Bruno’s later heresy was “multifaceted” and 23.3.2 A martyr of science may have rested on his conception of infinite worlds. “This was perhaps the most dangerous notion of all... If Some authors have characterized Bruno as a “martyr other worlds existed with intelligent beings living there, of science,” suggesting parallels with the Galileo affair did they too have their visitations? The idea was quite which began around 1610.[50] They assert that, even unthinkable.”[59] though Bruno’s theological beliefs, or perceptions of them by others, were an important factor in his heresy Frances Yates rejects what she describes as the “legend trial, his Copernicanism and cosmological beliefs played that Bruno was prosecuted as a philosophical thinker, was burned for his daring views on innumerable worlds or on a significant role in the outcome. the movement of the earth.” Yates however writes that “It should not be supposed”, writes A. M. Pater- “the Church was... perfectly within its rights if it included son of Bruno and his “heliocentric solar system,” that philosophical points in its condemnation of Bruno’s herehe “reached his conclusions via some mystical revela- sies” because “the philosophical points were quite inseption....His work is an essential part of the scientific and arable from the heresies.”[60] philosophical developments that he initiated.”[51] Paterson echoes Hegel in writing that Bruno “ushers in a According to the Stanford Encyclopedia of Philosophy, modern theory of knowledge that understands all natural “in 1600 there was no official Catholic position on the things in the universe to be known by the human mind Copernican system, and it was certainly not a heresy. When [...] Bruno [...] was burned at the stake as a heretic, through the mind’s dialectical structure.”[52] it had nothing to do with his writings in support of CoperIngegno writes that Bruno embraced the philosophy of nican cosmology.”[61] Similarly, the Catholic EncyclopeLucretius, “aimed at liberating man from the fear of death dia (1908) asserts that and the gods.”[53] Characters in Bruno’s Cause, Principle and Unity desire “to improve speculative science and “Bruno was not condemned for his defence knowledge of natural things,” and to achieve a philosophy of the Copernican system of astronomy, nor “which brings about the perfection of the human intellect for his doctrine of the plurality of inhabited most easily and eminently, and most closely corresponds worlds, but for his theological errors, among [54] to the truth of nature” which were the following: that Christ was not Other scholars oppose such views, and claim Bruno’s God but merely an unusually skillful magician, martyrdom to science to be exaggerated, or outright that the Holy Ghost is the soul of the world, false. For Yates, while “nineteenth century liberals” that the Devil will be saved, etc.”[62] were thrown “into ecstasies” over Bruno’s Copernicanism, “Bruno pushes Copernicus’ scientific work back into The website of the Vatican Secret Archives, discussing a prescientific stage, back into Hermetism, interpreta summary of legal proceedings against Bruno in Rome, ing the Copernican diagram as a hieroglyph of divine states: mysteries.”[55]

23.3.3

Theological heresy

In his Lectures on the History of Philosophy Hegel writes that Bruno’s life represented “a bold rejection of all Catholic beliefs resting on mere authority.”[56]

“In the same rooms where Giordano Bruno was questioned, for the same important reasons of the relationship between science and faith, at the dawning of the new astronomy and at the decline of Aristotle’s philosophy, sixteen years later, Cardinal Bellarmino, who then contested Bruno’s heretical theses, summoned Galileo Galilei, who also faced a famous inquisitorial trial, which, luckily for him, ended with a simple abjuration.”[63]

Alfonso Ingegno states that Bruno’s philosophy “challenges the developments of the Reformation, calls into question the truth-value of the whole of Christianity, and claims that Christ perpetrated a deceit on mankind... Bruno suggests that we can now recognize the universal law which controls the perpetual becoming of all things in an infinite universe.”[57] A. M. Paterson says that, while 23.4 Artistic depictions we no longer have a copy of the official papal condemnation of Bruno, his heresies included “the doctrine of Following the 1870 Capture of Rome by the newly crethe infinite universe and the innumerable worlds” and his ated Kingdom of Italy and the end of the Church’s beliefs “on the movement of the earth”.[58] temporal power over the city, the erection of a monument Michael White notes that the Inquisition may have pur- to Bruno on the site of his execution became feasible. The


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monument was sharply opposed by the clerical party, but Bruno Giordano features as the hero in a series of historwas finally erected by the Rome Municipality and inau- ical crime novels by S.J. Parris (pseudonym of Stephanie gurated in 1889.[64] Merritt). A statue of a stretched human figure standing on its head, designed by Alexander Polzin and depicting Bruno’s death at the stake, was placed in Potsdamer Platz station 52°30′35.4″N 13°22′33.5″E / 52.509833°N 13.375972°E in Berlin on 2 March 2008.[65] [66]

Bertold Brecht wrote one of his “Calendar Stories” (Kalendergeschichten) on Bruno Giordano. In “The heretic’s coat” (Der Mantel des Ketzers) Brecht extolls Bruno’s unwavering honesty and selfless concern for justice.[74]

Retrospective iconography of Bruno shows him with a Dominican cowl but not tonsured. Edward Gosselin has suggested that it is likely Bruno kept his tonsure at least until 1579, and it is possible that he wore it again thereafter.

The Last Confession by Morris West (posthumously published) is a fictional autobiography of Bruno, ostensibly written shortly before his execution.

In 1973 the biographical drama Giordano Bruno was released, an Italian/French movie directed by Giuliano An idealized animated version of Bruno appears in the Montaldo, starring Gian Maria Volontè as Bruno. first episode of the 2014 television series Cosmos: A The computer game In Memoriam features a lead charSpacetime Odyssey. In this depiction, Bruno is shown with acter who claims to be Bruno, returned from the dead to a more modern look, without tonsure and wearing clerical seek vengeance. robes and without his hood. Cosmos presents Bruno as an impoverished philosopher who was ultimately executed Bruno features as a main character in the historical segdue to his refusal to recant his belief in other worlds, a ments of John Crowley's mystical Ægypt tetralogy of portrayal that was criticized by some as simplistic or his- novels. The story covers his education as a Dominican and his investigation for heresy, and presents multiple torically inaccurate.[67][68][69] versions of his execution on the Campo de' Fiori.

23.5 References in poetry

Bruno plays a small but significant role in Martin Seay’s 2016 novel The Mirror Thief.

His name appears and he is recognized in several novels, Algernon Charles Swinburne wrote a poem honouring including Giordano Bruno in 1889, when the statue of Bruno was constructed in Rome.[70] • Children of God by Mary Doria Russell. Poet Heather McHugh in the year 2000 depicts Bruno as the principal of a story told (at dinner, by an “underestimated” travel guide) to a group of contemporary American poets in Rome. The poem (originally published in McHugh’s collection of poems Hinge & Sign, nominee for the National Book Award, and subsequently reprinted widely) channels the very question of ars poetica, or metameaning itself, through the embedded narrative of the suppression of Bruno’s words, silenced towards the end of his life both literally and literarily.[71]

23.6 Appearances in fiction Bruno and his theory of 'the coincidence of contraries’ (coincidentia oppositorum) play an important role in James Joyce's novel Finnegans Wake. Joyce wrote in a letter to his patroness, Harriet Shaw Weaver, 'His philosophy is a kind of dualism – every power in nature must evolve an opposite in order to realise itself and opposition brings reunion'.[72] Amongst his numerous allusions to Bruno in his novel, including his trial and torture, Joyce plays upon Bruno’s notion of coincidentia oppositorum through applying his name to word puns such as “Browne and Nolan” (name of Dublin printers) and '"brownesberrow in nolandsland”.[73]

• The Accidental Time Machine by Joe Haldeman. • The Picture of Dorian Gray by Oscar Wilde • White Fire by Douglas Preston and Lincoln Child.[75] • He is cited and quoted in Pauline Hunter Blair's last adult novel, Jacob’s Ladder (Church Farmhouse Books, Bottisham, 2003).

23.7 Giordano Bruno Foundation Main article: Giordano Bruno Foundation The Giordano Bruno Foundation (German: Giordano Bruno Stiftung) is a non-profit foundation based in Germany that pursues the “Support of Evolutionary Humanism”. It was founded by entrepreneur Herbert Steffen in 2004. The Giordano Bruno Foundation is considered critical of religion, which it characterizes as detrimental to cultural evolution.


23.11. WORKS

273

23.8 Giordano Bruno Memorial Award The SETI League makes an annual award honoring the memory of Giordano Bruno to a deserving person or persons who have made a significant contribution to the practice of SETI (the search for extraterrestrial intelligence). The award was proposed by sociologist Donald Tarter in 1995 on the 395th anniversary of Bruno’s death. The trophy presented is called a Bruno.

• Spaccio de la Bestia Trionfante (The Expulsion of the Triumphant Beast, London, 1584) • Cabala del cavallo Pegaseo (Cabal of the Horse Pegasus, 1585) • De gli heroici furori (The Heroic Frenzies, 1585) [81] • Figuratio Aristotelici Physici auditus (Figures From Aristotle’s Physics, 1585) • Dialogi duo de Fabricii Mordentis Salernitani (Two Dialogues of Fabricii Mordentis Salernitani, 1586)

23.9 Astronomical objects named after Bruno

• Idiota triumphans (The Triumphant Idiot, 1586) [82]

The 22 km impact crater Giordano Bruno on the far side of the Moon is named in his honor, as are the main belt asteroids 5148 Giordano and 13223 Cenaceneri; the latter is named after his philosophical dialogue La Cena de le Ceneri (“The Ash Wednesday Supper”) (see above).

• Animadversiones circa lampadem lullianam (Amendments regarding Lull’s Lantern, 1586) [83]

• De somni interpretatione (Dream Interpretation, 1586) [83]

• Lampas triginta statuarum (The Lantern of Thirty Statues, 1586) [84] • Centum et viginti articuli de natura et mundo adversus peripateticos (One Hundred and Twenty Articles on Nature and the World Against the Peripatetics, 1586)

23.10 Other remembrances

[85]

Broadcasting station 2GB in Sydney, Australia is named for Bruno. The two letters “GB” in the call sign were chosen to honour Bruno who was much admired by Theosophists.[76]

23.11 Works • De umbris idearum (The Shadows of Ideas, Paris, 1582) • Cantus Circaeus (The Incantation of Circe, 1582) [77] • De compendiosa architectura et complento artis Lulli (A Compendium of Architecture and Lulli’s Art, 1582) [78]

• De Lampade combinatoria Lulliana (The Lamp of Combinations according to Lull, 1587) [86] • De progressu et lampade venatoria logicorum (Progress and the Hunter’s Lamp of Logical Methods, 1587) [87] • Oratio valedictoria (Valedictory Oration, 1588) [88] • Camoeracensis Acrotismus (The Pleasure of Dispute, 1588) [89] • De specierum scrutinio (Of Bonds in General, 1588) [90]

• Candelaio (The Torchbearer or The Candle Bearer, 1582; play)

• Articuli centum et sexaginta adversus huius tempestatis mathematicos atque Philosophos (One Hundred and Sixty Theses Against Mathematicians and Philosophers, 1588) [91]

• Ars reminiscendi (The Art of Memory, 1583)

• Oratio consolatoria (Consolation Oration, 1589) [91]

• Explicatio triginta sigillorum (Explanation of Thirty Seals, 1583) [79]

• De vinculis in genere (Of Bonds in General, 1591)

• Sigillus sigillorum (The Seal of Seals, 1583)

[80]

• La Cena de le Ceneri (The Ash Wednesday Supper, 1584) • De la causa, principio, et uno (Concerning Cause, Principle, and Unity, 1584) • De l'infinito universo et mondi (On the Infinite Universe and Worlds, 1584)

[90]

• De triplici minimo et mensura (On the Threefold Minimum and Measure, 1591) [14] • De monade numero et figura (On the Monad, Number, and Figure, Frankfurt, 1591) [92] • De innumerabilibus, immenso, et infigurabili (Of Innumerable Things, Vastness and the Unrepresentable, 1591)


274 • De imaginum, signorum et idearum compositione (On the Composition of Images, Signs and Ideas, 1591) • Summa terminorum metaphysicorum (Handbook of Metaphysical Terms, 1595) [93][94] • Artificium perorandi (The Art of Communicating, 1612)

23.12 Collections • Jordani Bruni Nolani opera latine conscripta (Giordano Bruno the Nolan’s Works Written in Latin), Dritter Band (1962) / curantibus F. Tocco et H. Vitelli

23.13 See also • Fermi paradox • List of Roman Catholic scientist-clerics • Saints of Ecclesia Gnostica Catholica

23.14 Notes [1] Leo Catana (2005). The Concept of Contraction in Giordano Bruno’s Philosophy. Ashgate Pub. ISBN 9780754652618. When Bruno states in De la causa that matter provides the extension of particulars, he follows Averroes. [2] Bouvet, Molière ; avec une notice sur le théâtre au XVIIe siècle, une biographie chronologique de Molière, une étude générale de son oeuvre, une analyse méthodique du “Malade”, des notes, des questions par Alphonse (1973). Le malade imaginaire ; L'amour médecin. Paris: Bordas. p. 23. ISBN 2-04-006776-0. [3] Bruno was a mathematician and philosopher, but is not considered an astronomer by the modern astronomical community, as there is no record of him carrying out physical observations, as was the case with Brahe, Kepler, and Galileo. Pogge, Richard W. http://www.astronomy. ohio-state.edu/~{}pogge/Essays/Bruno.html 1999. [4] Birx, Jams H.. “Giordano Bruno”. The Harbinger, Mobile, AL, 11 November 1997. “Bruno was burned to death at the stake for his pantheistic stance and cosmic perspective.” [5] Arturo Labriola, Giordano Bruno: Martyrs of free thought no. 1 [6] Frances Yates, Giordano Bruno and the Hermetic Tradition, Routledge and Kegan Paul, 1964, p. 450

CHAPTER 23. GIORDANO BRUNO

[7] Michael J. Crowe, The Extraterrestrial Life Debate 1750– 1900, Cambridge University Press, 1986, p. 10, "[Bruno’s] sources... seem to have been more numerous than his followers, at least until the eighteenth- and nineteenth-century revival of interest in Bruno as a supposed 'martyr for science.' It is true that he was burned at the stake in Rome in 1600, but the church authorities guilty of this action were almost certainly more distressed at his denial of Christ’s divinity and alleged diabolism than at his cosmological doctrines.” [8] Adam Frank, The Constant Fire: Beyond the Science vs. Religion Debate, University of California Press, 2009, p. 24, “Though Bruno may have been a brilliant thinker whose work stands as a bridge between ancient and modern thought, his persecution cannot be seen solely in light of the war between science and religion.” [9] White, Michael. The Pope and the Heretic: The True Story of Giordano Bruno, the Man who Dared to Defy the Roman Inquisition, p. 7. Perennial, New York, 2002. “This was perhaps the most dangerous notion of all... If other worlds existed with intelligent beings living there, did they too have their visitations? The idea was quite unthinkable.” [10] Shackelford, Joel (2009). “Myth 7 That Giordano Bruno was the first martyr of modern science”. In Numbers, Ronald L. Galileo goes to jail and other myths about science and religion. Cambridge, Mass: Havard University Press. p. 66. “Yet the fact remains that cosmological matters, notably the plurality of worlds, were an identifiable concern all along and appear in the summary document: Bruno was repeatedly questioned on these matters, and he apparently refused to recant them at the end.14 So, Bruno probably was burned alive for resolutely maintaining a series of heresies, among which his teaching of the plurality of worlds was prominent but by no means singular.” [11] Gatti, Hilary (2002). Giordano Bruno and Renaissance Science: Broken Lives and Organizational Power. Ithaca, New York: Cornell University Press. pp. 18–19. Retrieved 21 March 2014. For Bruno was claiming for the philosopher a principle of free thought and inquiry which implied an entirely new concept of authority: that of the individual intellect in its serious and continuing pursuit of an autonomous inquiry… It is impossible to understand the issue involved and to evaluate justly the stand made by Bruno with his life without appreciating the question of free thought and liberty of expression. His insistence on placing this issue at the center of both his work and of his defense is why Bruno remains so much a figure of the modern world. If there is, as many have argued, an intrinsic link between science and liberty of inquiry, then Bruno was among those who guaranteed the future of the newly emerging sciences, as well as claiming in wider terms a general principle of free thought and expression. [12] Montano, Aniello (24 November 2007). Antonio Gargano, ed. Le deposizioni davanti al tribunale dell'Inquisizione. Napoli: La Città del Sole. p. 71. In Rome, Bruno was imprisoned for seven years and subjected to a difficult trial that analyzed, minutely, all his philosophical ideas. Bruno, who in Venice had been willing to recant some theses, become increasingly resolute


23.14. NOTES

and declared on 21 December 1599 that he 'did not wish to repent of having too little to repent, and in fact did not know what to repent.' Declared an unrepentant heretic and excommunicated, he was burned alive in the Campo dei Fiori in Rome on 17 February 1600. On the stake, along with Bruno, burned the hopes of many, including philosophers and scientists of good faith like Galileo, who thought they could reconcile religious faith and scientific research, while belonging to an ecclesiastical organization declaring itself to be the custodian of absolute truth and maintaining a cultural militancy requiring continual commitment and suspicion. [13] Birx, James (11 November 1997). “Giordano Bruno”. Mobile Alabama Harbinger. Retrieved 28 April 2014. To me, Bruno is the supreme martyr for both free thought and critical inquiry… Bruno’s critical writings, which pointed out the hypocrisy and bigotry within the Church, along with his tempestuous personality and undisciplined behavior, easily made him a victim of the religious and philosophical intolerance of the 16th century. Bruno was excommunicated by the Catholic, Lutheran and Calvinist Churches for his heretical beliefs. The Catholic hierarchy found him guilty of infidelity and many errors, as well as serious crimes of heresy… Bruno was burned to death at the stake for his pantheistic stance and cosmic perspective. [14] “Giordano Bruno”. Encyclopedia Britannica. [15] The primary work on the relationship between Bruno and Hermeticism is Frances Yates, Giordano Bruno and The Hermetic Tradition, 1964; for an alternative assessment, placing more emphasis on the Kabbalah, and less on Hermeticism, see Karen Silvia De Leon-Jones, Giordano Bruno and the Kabbalah, Yale, 1997; for a return to emphasis on Bruno’s role in the development of Science, and criticism of Yates’ emphasis on magical and Hermetic themes, see Hillary Gatti, Giordano Bruno and Renaissance Science, Cornell, 1999 [16] Alessandro G. Farinella and Carole Preston, “Giordano Bruno: Neoplatonism and the Wheel of Memory in the 'De Umbris Idearum'", in Renaissance Quarterly, Vol. 55, No. 2, (Summer, 2002), pp. 596–624; Arielle Saiber, Giordano Bruno and the Geometry of Language, Ashgate, 2005 [17] Dorothea Waley Singer, Giordano Bruno, His Life and Thought, New York, 1950. [18] This is recorded in the diary of one Guillaume Cotin, librarian of the Abbey of St. Victor, who recorded recollections of a number of personal conversations he had with Bruno. Bruno also mentions this dedication in the Dedicatory Epistle of The Cabala of Pegasus (Cabala del Cavallo Pegaseo, 1585). [19] Gargano (2007), p. 11 [20] Gosselin has argued that Bruno’s report that he returned to Dominican garb in Padua suggests that he kept his tonsure at least until his arrival in Geneva in 1579. He also suggests it is likely that Bruno kept the tonsure even after this point, showing a continued and deep religious attachment contrary to the way in which Bruno has been

275

portrayed as a martyr for modern science. Instead, Gosselin argues, Bruno should be understood in the context of reformist Catholic dissenters. Edward A. Gosselin, “A Dominican Head in Layman’s Garb? A Correction to the Scientific Iconography of Giordano Bruno”, in The Sixteenth Century Journal, Vol. 27, No. 3 (Autumn, 1996), pp. 673–78. [21] Dorothea Waley Singer, Giordano Bruno, His Life and Thought, New York, 1950 “Following the northern route back through Brescia, Bruno came to Bergamo where he resumed the monastic habit. He perhaps visited Milan, and then leaving Italy he crossed the Alps by the Mont Cenis pass, and came to Chambéry. He describes his hospitable reception there by the Dominican Convent, but again he received no encouragement to remain, and he journeyed on to Lyons. Bruno’s next movements are obscure. In 1579 he reached Geneva.” [22] Virgilio Salvestrini, Bibliografia di Giordano Bruno, Firenze, 1958 [23] Dorothea Waley Singer, Giordano Bruno, His Life and Thought, New York, 1950; Singer points out in a footnote that Bruno’s name appears in a list, compiled one hundred years later, of Italian refugees who had belonged to the Protestant church of Geneva. However, she does not find this evidence convincing. [24] William Boulting, Giordano Bruno: His Life, Thought, and Martyrdom, 1916, p. 58 [25] Weiner, Andrew D. (1980). “Expelling the Beast: Bruno’s Adventures in England”. Modern Philology. 78 (1): 1–13. doi:10.1086/391002. JSTOR 437245. [26] Bossy, John (1991). Giordano Bruno and the Embassy Affair. New Haven: Yale University Press. ISBN 0-30004993-5. [27] John Gribbin (2009), In Search of the Multiverse: Parallel Worlds, Hidden Dimensions, and the Ultimate Quest for the Frontiers of Reality, ISBN 9780470613528. p. 88 [28] Giordano Bruno, Cause Principle and Unity, and Essays on Magic, Edited by Richard J. Blackwell and Robert de Lucca, Cambridge, 1998, xxxvi [29] “Giordano Bruno”. Encyclopedia Britannica. Retrieved 8 May 2014. At the time such a move did not seem to be too much of a risk: Venice was by far the most liberal of the Italian states; the European tension had been temporarily eased after the death of the intransigent pope Sixtus V in 1590; the Protestant Henry of Bourbon was now on the throne of France, and a religious pacification seemed to be imminent. [30] “II Sommario del Processo di Giordano Bruno, con appendice di Documenti sull'eresia e l'inquisizione a Modena nel secolo XVI”, edited by Angelo Mercati, in Studi e Testi, vol. 101. [31] Luigi Firpo, Il processo di Giordano Bruno, 1993. [32] This is discussed in Dorothea Waley Singer, Giordano Bruno, His Life and Thought, New York, 1950, ch. 7, “A gloating account of the whole ritual is given in a letter


276

CHAPTER 23. GIORDANO BRUNO

written on the very day by a youth named Gaspar Schopp of Breslau, a recent convert to Catholicism to whom Pope Clement VIII had shown great favour, creating him Knight of St. Peter and Count of the Sacred Palace. Schopp was addressing Conrad Rittershausen. He recounts that because of his heresy Bruno had been publicly burned that day in the Square of Flowers in front of the Theatre of Pompey. He makes merry over the belief of the Italians that every heretic is a Lutheran. It is evident that he had been present at the interrogations, for he relates in detail the life of Bruno and the works and doctrines for which he had been arraigned, and he gives a vivid account of Bruno’s final appearance before his judges on 8th February. To Schopp we owe the knowledge of Bruno’s bearing under judgement. When the verdict had been declared, records Schopp, Bruno with a threatening gesture addressed his judges: “Perchance you who pronounce my sentence are in greater fear than I who receive it.” Thus he was dismissed to the prison, gloats the convert, “and was given eight days to recant, but in vain. So today he was led to the funeral pyre. When the image of our Saviour was shown to him before his death he angrily rejected it with averted face. Thus my dear Rittershausen is it our custom to proceed against such men or rather indeed such monsters.” [33] “Il Sommario del Processo di Giordano Bruno, con appendice di Documenti sull'eresia e l'inquisizione a Modena nel secolo XVI”, edited by Angelo Mercati, in Studi e Testi, vol. 101; the precise terminology for the tool used to silence Bruno before burning is recorded as una morsa di legno, or “a vise of wood”, and not an iron spike as sometimes claimed by other sources. [34] Edward A. Gosselin, “A Dominican Head in Layman’s Garb? A Correction to the Scientific Iconography of Giordano Bruno”, in The Sixteenth Century Journal, Vol. 27, No. 3 (Autumn, 1996), p. 674 [35] Robert McNulty, “Bruno at Oxford”, in Renaissance News, 1960 (XIII), pp. 300–305 [36] The apparent contradiction is possibly due to different perceptions of “average height” between Oxford and Venice. [37] Blackwell, Richard (1991). Galileo, Bellarmine, and the Bible. Notre Dame: University of Notre Dame Press. p. 25. ISBN 0268010242. [38] See e.g. Cosmography by Peter Apian, Antwerp 1539 and its outer sphere

[42] Bruno, Giordano. “Third Dialogue”. On the infinite universe and worlds. [43] Soter, Steven (March 13, 2014). “The cosmos of Giordano Bruno”. Discover. Retrieved July 14, 2015. [44] “Giordano Bruno: On the Infinite Universe and Worlds (De l'Infinito Universo et Mondi) Introductory Epistle: Argument of the Third Dialogue”. Retrieved 4 October 2014. [45] Hetherington, Norriss S., ed. (April 2014) [1993]. Encyclopedia of Cosmology (Routledge Revivals): Historical, Philosophical, and Scientific Foundations of Modern Cosmology. Routledge. p. 419. ISBN 9781317677666. Retrieved 29 March 2015. Bruno (from the mouth of his character Philotheo) in his De l'infinito universo et mondi (1584) claims that “innumerable celestial bodies, stars, globes, suns and earths may be sensibly perceived therein by us and an infinite number of them may be inferred by our own reason.” [46] Max Tegmark, Parallel Universes, 2003 [47] Max Bernhard Weinsten, Welt- und Lebensanschauungen, Hervorgegangen aus Religion, Philosophie und Naturerkenntnis (“World and Life Views, Emerging From Religion, Philosophy and Nature”) (1910), p. 321: “Also darf man vielleicht glauben, daß das ganze System eine Erhebung des Physischen aus seiner Natur in das Göttliche ist oder eine Durchstrahlung des Physischen durch das Göttliche; beides eine Art Pandeismus. Und so zeigt sich auch der Begriff Gottes von dem des Universums nicht getrennt; Gott ist naturierende Natur, Weltseele, Weltkraft. Da Bruno durchaus ablehnt, gegen die Religion zu lehren, so hat man solche Angaben wohl umgekehrt zu verstehen: Weltkraft, Weltseele, naturierende Natur, Universum sind in Gott. Gott ist Kraft der Weltkraft, Seele der Weltseele, Natur der Natur, Eins des Universums. Bruno spricht ja auch von mehreren Teilen der universellen Vernunft, des Urvermögens und der Urwirklichkeit. Und damit hängt zusammen, daß für ihn die Welt unendlich ist und ohne Anfang und Ende; sie ist in demselben Sinne allumfassend wie Gott. Aber nicht ganz wie Gott. Gott sei in allem und im einzelnen allumfassend, die Welt jedoch wohl in allem, aber nicht im einzelnen, da sie ja Teile in sich zuläßt.” [48] Seife, Charles (1 March 2000). “Vatican Regrets Burning Cosmologist”. Science Now. Retrieved 24 June 2012. [49] Robinson, B A (7 March 2000), Apologies by Pope John Paul II, Ontario Consultants. Retrieved 27 December 2013

[39] Alessandro De Angelis and Catarina Espirito Santo (2015), “The contribution of Giordano Bruno to the principle of relativity” (PDF), Journal of Astronomical History and Heritage, 18 (3): 241–248, arXiv:1504.01604 , Bibcode:2015JAHH...18..241D

[50] “Giordano Bruno and Galileo Galilei,” The Popular Science Monthly, Supplement, 1878.

[40] Giordano Bruno, Teofilo, in La Cena de le Ceneri, “Third Dialogue,” (1584), ed. and trans. by S.L. Jaki (1975).

[52] Paterson, p. 61.

[41] Giordano Bruno, Teofilo, in Cause, Principle, and Unity, “Fifth Dialogue,” (1588), ed. and trans. by Jack Lindsay (1962).

[51] Antoinette Mann Paterson (1970). The Infinite Worlds of Giordano Bruno. Charles C. Thomas, Springfield, Illinois, 1970, p. 16.

[53] Cause, Principle and Unity, by Giordano Bruno. Edited by R.J. Blackwell and Robert de Lucca, with an Introduction by Alfonso Ingegno. Cambridge University Press, 1998


23.14. NOTES

277

[54] Cause, Principle and Unity, by Giordano Bruno. Edited by R.J. Blackwell and Robert de Lucca, with an Introduction by Alfonso Ingegno. Cambridge University Press, 1998, p. 63. [55] Giordano Bruno and the Hermetic Tradition, by Frances Yates. Routledge and Kegan Paul, London, 1964, p. 225 [56] Hegel’s lectures on the history of philosophy, translated by E.S. Haldane and F.H. Simson, in three volumes. Volume III, p. 119. The Humanities Press, 1974, New York. [57] Cause, Principle and Unity, by Giordano Bruno. Edited by R.J. Blackwell and Robert de Lucca, with an Introduction by Alfonso Ingegno. p.x. Cambridge University Press, 1998. [58] Paterson, p. 198. [59] White, Michael. The Pope and the Heretic: The True Story of Giordano Bruno, the Man who Dared to Defy the Roman Inquisition, p. 7. Perennial, New York, 2002. [60] Yates, Frances, Bruno and the Hermetic Tradition, pp. 354–356. Routledge and Kegan Paul, London, 1964. [61] Sheila Rabin, “Nicolaus Copernicus” in the Stanford Encyclopedia of Philosophy (online, accessed 19 November 2005). [62] Herbermann, Charles, ed. (1913). "Giordano Bruno". Catholic Encyclopedia. New York: Robert Appleton Company. [63] “Summary of the trial against Giordano Bruno: Rome, 1597”. Vatican Secret Archives. Archived from the original on 9 June 2010. Retrieved 18 September 2010. [64] Paula Findlen, “A Hungry Mind: Giordano Bruno, Philosopher and Heretic”, The Nation, September 10, 2008. “Campo de' Fiori was festooned with flags bearing Masonic symbols. Fiery speeches were made by politicians, scholars and atheists about the importance of commemorating Bruno as one of the most original and oppressed freethinkers of his age.” Accessed on 19 September 2008 [65] Bhattacharjee, Yudhiijit (13 March “Think About It”. Science. 319: doi:10.1126/science.319.5869.1467b.

2008). 1467.

[71] “Tom Hunley’s “Epiphanic Structure in Heather McHugh’s Ars Poetica, 'What He Thought'" - Voltage Poetry”. Voltage Poetry. [72] James Joyce, Letter to Harriet Shaw Weaver, 27 January 1925, Selected Letters, p. 307 [73] McHugh, Roland. Annotations to Finnegans Wake. Baltimore: Johns Hopkins UP, 1980. Print, xv. [74] Brecht, Bertold. Kalendergeschichten. Hamburg: Rowohlt Taschenbuch Verlag, 1978, pp. 38-46. [75] p. 542 of White Fire by Douglas Preston and Lincoln Child. [76] Kohn, Rachael (15 November 2006). “Theosophy Today”. The Spirit of Things (Transcript) “Erica Patient: She came into contact with theosophy through 2GB, Station 2GB when it was owned by the Theosophical Society. Rachael Kohn: GB stands for Giordano Bruno. Erica Patient: It does. Actually we wanted to have AB for Annie Besant, but it sounded too like ABC. So they said they wouldn't have it.”. Australian Broadcasting Corporation. Retrieved 12 January 2009. [77] Esoteric Archives, bruno/circaeus.htm

http://www.esotericarchives.com/

[78] “A PERSPECTIVE ON BRUNO'S “DE COMPENDIOSA ARCHITECTURA ET COMPLEMENTO ARTIS LULLII"". [79] “Thirty dangerous seals - Lines of thought”. [80] "'Meanings of “contractio” in Giordano Bruno’s Sigillus sigillorum' - Staff”. [81] Esoteric Archives, bruno/furori.htm

http://www.esotericarchives.com/

[82] Quora, https://www.quora.com/ What-was-Giordano-Brunos-exact-argument-about-the-compass-How-did-t [83] “All About Heaven - Sources returnpage”. [84] “Anima Mundi: The Rise of the World Soul Theory in Modern German Philosophy”. [85] “Giordano Bruno”. [86] “Giordano Bruno”.

[66] Dr. Michael Schmidt-Salomon (26 February 2008). “giordano bruno denkmal”. [67] Powell, Corey S. (10 March 2014). “Did Cosmos Pick the Wrong Hero?". Discover. Kalmbach Publishing. Retrieved 16 March 2014. [68] Rosenau, Josh. “Why Did Cosmos Focus on Giordano Bruno?". National Center for Science Education. Retrieved 14 April 2014. [69] Sessions, David (3 March 2014). “How 'Cosmos’ Bungles the History of Religion and Science”. The Daily Beast. Retrieved 8 May 2014. [70] Swinburne, Algernon Charles. “The Monument of Giordano Bruno”. Retrieved July 13, 2015.

[87] “Progress and the Hunter’s Lamp of Logical Methods”. galileo. [88] “Giordano Bruno”. [89] “Full text of “THE PLEASURE OF THE DISPUTE"". [90] “Eros and Magic in the Renaissance”. [91] “Giordano Bruno”. [92] “De monade, numero et figura liber”. Encyclopedia Britannica. [93] “Summa Terminorum metaphysicorum”. [94] “Giordano Bruno”.


278

23.15 References • Blackwell, Richard J.; de Lucca, Robert (1998). Cause, Principle and Unity: And Essays on Magic by Giordano Bruno. Cambridge University Press. ISBN 0-521-59658-0. • Blum, Paul Richard (1999). Giordano Bruno. Munich: Beck Verlag. ISBN 3-406-41951-8. • Blum, Paul Richard (2012). Giordano Bruno: An Introduction. Amsterdam/New York, NY: Rodopi. ISBN 978-90-420-3555-3. • Bombassaro, Luiz Carlos (2002). Im Schatten der Diana. Die Jagdmetapher im Werk von Giordano Bruno. Frankfurt am Main: Peter Lang Verlag. • Culianu, Ioan P. (1987). Eros and Magic in the Renaissance. University of Chicago Press. ISBN 0226-12315-4. • Aquilecchia, Giovanni; montano, aniello; bertrando, spaventa (2007). Gargano, Antonio, ed. Le deposizioni davanti al tribunale dell'Inquisizione. La Citta del Sol. • Gatti, Hilary (2002). Giordano Bruno and Renaissance Science. Cornell University Press. ISBN 08014-8785-4.

CHAPTER 23. GIORDANO BRUNO • Michel, Paul Henri (1962) The Cosmology of Giordano Bruno. Translated by R.E.W. Maddison. Paris: Hermann; London: Methuen; Ithaca, New York: Cornell. ISBN 0-8014-0509-2 • The Cabala of Pegasus by Giordano Bruno, ISBN 0-300-09217-2 • Giordano Bruno, Paul Oskar Kristeller, Collier’s Encyclopedia, Vol 4, 1987 ed., p. 634 • Il processo di Giordano Bruno, Luigi Firpo, 1993 • Giordano Bruno,Il primo libro della Clavis Magna, ovvero, Il trattato sull'intelligenza artificiale, a cura di Claudio D'Antonio, Di Renzo Editore. • Giordano Bruno,Il secondo libro della Clavis Magna, ovvero, Il Sigillo dei Sigilli, a cura di Claudio D'Antonio, Di Renzo Editore. • Giordano Bruno, Il terzo libro della Clavis Magna, ovvero, La logica per immagini, a cura di Claudio D'Antonio, Di Renzo Editore • Giordano Bruno, Il quarto libro della Clavis Magna, ovvero, L'arte di inventare con Trenta Statue, a cura di Claudio D'Antonio, Di Renzo Editore • Giordano Bruno L'incantesimo di Circe, a cura di Claudio D'Antonio, Di Renzo Editore

• Kessler, John (1900). Giordano Bruno: The Forgotten Philosopher. Rationalist Association.

• Guido del Giudice, WWW Giordano Bruno, Marotta & Cafiero Editori, 2001 ISBN 88-88234-01-2

• McIntyre, J. Lewis (1997). Giordano Bruno. Kessinger Publishing. ISBN 1-56459-141-7.

• Giordano Bruno, De Umbris Idearum, a cura di Claudio D'Antonio, Di Renzo Editore

• Mendoza, Ramon G. (1995). The Acentric Labyrinth. Giordano Bruno’s Prelude to Contemporary Cosmology. Element Books Ltd. ISBN 185230-640-8.

• Guido del Giudice, La coincidenza degli opposti, Di Renzo Editore, ISBN 88-8323-110-4, 2005 (seconda edizione accresciuta con il saggio Bruno, Rabelais e Apollonio di Tiana, Di Renzo Editore, Roma 2006 ISBN 88-8323-148-1)

• Rowland, Ingrid D. (2008). Giordano Bruno: Philosopher/Heretic. Farrar, Straus, and Giroux. ISBN 0-8090-9524-6. • Saiber, Arielle (2005). Giordano Bruno and the Geometry of Language. Ashgate. ISBN 0-7546-33217. • Singer, Dorothea (1950). Giordano Bruno: His Life and Thought, With Annotated Translation of His Work – On the Infinite Universe and Worlds. Schuman. ISBN 1-117-31419-7. • White, Michael (2002). The Pope & the Heretic. New York: William Morrow. ISBN 0-06-0186267. • Yates, Frances (1964). Giordano Bruno and the Hermetic Tradition. University of Chicago Press. ISBN 0-226-95007-7.

• Giordano Bruno, Due Orazioni: Oratio Valedictoria – Oratio Consolatoria, a cura di Guido del Giudice, Di Renzo Editore, 2007 ISBN 88-8323-174-0 • Giordano Bruno, La disputa di Cambrai. Camoeracensis Acrotismus, a cura di Guido del Giudice, Di Renzo Editore, 2008 ISBN 88-8323-199-6 • Somma dei termini metafisici, a cura di Guido del Giudice, Di Renzo Editore, Roma, 2010

23.16 External links • Bruno’s works: text, concordances and frequency list • Writings of Giordano Bruno


23.16. EXTERNAL LINKS • Giordano Bruno Library of the World’s Best Literature Ancient and Modern Charles Dudley Warner Editor • Bruno’s Latin and Italian works online: Biblioteca Ideale di Giordano Bruno • Complete works of Bruno as well as main biographies and studies available for free download in PDF format from the Warburg Institute and the Centro Internazionale di Studi Bruniani Giovanni Aquilecchia • Online Galleries, History of Science Collections, University of Oklahoma Libraries High resolution images of works by and/or portraits of Giordano Bruno in .jpg and .tiff format. • Works by Giordano Bruno at Project Gutenberg • Works by or about Giordano Bruno at Internet Archive

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Chapter 24

Copernican heliocentrism mathematically ordered cosmos. Thus his heliocentric model retained several of the Ptolemaic elements causing the inaccuracies, such as the planets’ circular orbits, epicycles, and uniform speeds,[1] while at the same time re-introducing such innovations as, • Earth is one of several planets revolving around a stationary Sun in a determined order • Earth has three motions: daily rotation, annual revolution, and annual tilting of its axis • Retrograde motion of the planets is explained by Earth’s motion • Distance from Earth to the Sun is small compared to the distance from the Sun to the stars.

Heliocentric model from Nicolaus Copernicus’ De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres)

Copernican heliocentrism is the name given to the astronomical model developed by Nicolaus Copernicus and published in 1543. It positioned the Sun near the center of the Universe, motionless, with Earth and the other planets rotating around it in circular paths modified by epicycles and at uniform speeds. The Copernican model departed from the Ptolemaic system that prevailed in Western culture for centuries, placing Earth at the center of the Universe, and is often regarded as the launching point to modern astronomy and the Scientific Revolution.[1] Copernicus was aware that the ancient Greek Aristarchus had already proposed a heliocentric theory, and cited him as a proponent of it in a reference that was deleted before publication, but there is no evidence that Copernicus had knowledge of, or access to, the specific details of Aristarchus’ theory.[2] Although he had circulated an outline of his own heliocentric theory to colleagues sometime before 1514, he did not decide to publish it until he was urged to do so late in his life by his pupil Rheticus. Copernicus’s challenge was to present a practical alternative to the Ptolemaic model by more elegantly and accurately determining the length of a solar year while preserving the metaphysical implications of a

24.1 Earlier theories Earth in motion

with

the

Main article: Heliocentrism Philolaus (4th century BCE) was one of the first to hypothesize movement of the Earth, probably inspired by Pythagoras' theories about a spherical, moving globe. Aristarchus of Samos in the 3rd century BCE had developed some theories of Heraclides Ponticus (speaking of a revolution by Earth on its axis) to propose what was, so far as is known, the first serious model of a heliocentric solar system. Though his original text has been lost, a reference in Archimedes' book The Sand Reckoner (Archimedis Syracusani Arenarius & Dimensio Circuli) describes a work by Aristarchus in which he advanced the heliocentric model. Archimedes wrote:

280

You (King Gelon) are aware the 'universe' is the name given by most astronomers to the sphere the center of which is the center of the Earth, while its radius is equal to the straight


24.2. ANTICIPATIONS OF COPERNICUS’S MODELS FOR PLANETARY ORBITS line between the center of the Sun and the center of the Earth. This is the common account as you have heard from astronomers. But Aristarchus has brought out a book consisting of certain hypotheses, wherein it appears, as a consequence of the assumptions made, that the universe is many times greater than the 'universe' just mentioned. His hypotheses are that the fixed stars and the Sun remain unmoved, that the Earth revolves about the Sun on the circumference of a circle, the Sun lying in the middle of the Floor, and that the sphere of the fixed stars, situated about the same center as the Sun, is so great that the circle in which he supposes the Earth to revolve bears such a proportion to the distance of the fixed stars as the center of the sphere bears to its surface.[3] — The Sand Reckoner

281

etary positions, but not real or physical. Al-Btiruji’s alternative system spread through most of Europe during the 13th century.[13] Copernicus cited Aristarchus and Philolaus in an early manuscript of his book which survives, stating: “Philolaus believed in the mobility of the earth, and some even say that Aristarchus of Samos was of that opinion.”[14] For reasons unknown (although possibly out of reluctance to quote pre-Christian sources), he did not include this passage in the publication of his book. Inspiration came to Copernicus not from observation of the planets, but from reading two authors. In Cicero he found an account of the theory of Hicetas. Plutarch provided an account of the Pythagoreans Heraclides Ponticus, Philolaus, and Ecphantes. These authors had proposed a moving Earth, which did not, however, revolve around a central sun. When Copernicus’ book was published, it contained an unauthorized preface by the Lutheran theologian Andreas Osiander. This cleric stated that Copernicus wrote his heliocentric account of the Earth’s movement as a mere mathematical hypothesis, not as an account that contained truth or even probability. Since Copernicus’ hypothesis was believed to contradict the Old Testament account of the Sun’s movement around the Earth (Joshua 10:12-13), this was apparently written to soften any religious backlash against the book. However, there is no evidence that Copernicus himself considered the heliocentric model as merely mathematically convenient, separate from reality.

It is a common idea that the heliocentric view was rejected by the contemporaries of Aristarchus. This is due to Gilles Ménage's translation of a passage from Plutarch's On the Apparent Face in the Orb of the Moon. Plutarch reported that Cleanthes (a contemporary of Aristarchus and head of the Stoics) as a worshipper of the Sun and opponent to the heliocentric model, was jokingly told by Aristarchus that he should be charged with impiety. Gilles Ménage, shortly after the trials of Galileo and Giordano Bruno, amended an accusative (identifying the object of the verb) with a nominative (the subject of 24.2 Anticipations of Copernicus’s the sentence), and vice versa, so that the impiety accumodels for planetary orbits sation fell over the heliocentric sustainer. The resulting misconception of an isolated and persecuted Aristarchus is still transmitted today.[4][5] Mathematical techniques developed in the 13th to Several Islamic astronomers questioned the Earth’s 14th centuries by the Arab and Persian astronomers apparent immobility,[6][7] and centrality within the Mo'ayyeduddin al-Urdi, Nasir al-Din al-Tusi, and Ibn aluniverse.[8] Some accepted that the earth rotates around Shatir for geocentric models of planetary motions closely its axis, such as Abu Sa'id al-Sijzi (d. circa 1020).[9][10] resemble some of those used later by Copernicus in his [15] Copernicus used what is now who invented an astrolabe based on a belief held by some heliocentric models. known as the Urdi lemma and the Tusi couple in the of his contemporaries “that the motion we see is due to [10][11] same planetary models as found in Arabic sources.[16] the Earth’s movement and not to that of the sky.” The prevalence of this view is further confirmed by a ref- Furthermore, the exact replacement of the equant by two erence from an Arabic work in the 13th century which epicycles used by Copernicus in the Commentariolus was found in an earlier work by Ibn al-Shatir (d. c. 1375) of states: Damascus.[17] Ibn al-Shatir’s lunar and Mercury models are also identical to those of Copernicus.[18] This has led According to the geometers [or engineers] some scholars to argue that Copernicus must have had ac(muhandisīn), the earth is in constant circular cess to some yet to be identified work on the ideas of those motion, and what appears to be the motion of earlier astronomers.[19] However, no likely candidate for the heavens is actually due to the motion of the this conjectured work has yet come to light, and other earth and not the stars.[10] scholars have argued that Copernicus could well have developed these ideas independently of the late Islamic In the 12th century, Nur ad-Din al-Bitruji proposed a tradition.[20] Nevertheless, Copernicus cited some of the complete alternative to the Ptolemaic system (although Islamic astronomers whose theories and observations he not heliocentric).[12][13] He declared the Ptolemaic sys- used in De Revolutionibus, namely al-Battani, Thabit ibn tem as an imaginary model, successful at predicting plan- Qurra, al-Zarqali, Averroes, and al-Bitruji.[21]


282

24.3 The Ptolemaic system

CHAPTER 24. COPERNICAN HELIOCENTRISM cosmology—namely, that the motions of the planets should be explained in terms of uniform circular motion, and was considered a serious defect by many medieval astronomers.[24] In Copernicus’s day, the most up-to-date version of the Ptolemaic system was that of Peurbach (1423–1461) and Regiomontanus (1436–1476).

24.4 Copernican theory Further information: Nicolaus Copernicus Copernicus’ major work, De revolutionibus orbium

Line art drawing of Ptolemaic system

Main article: Geocentric model The prevailing astronomical model of the cosmos in Europe in the 1,400 years leading up to the 16th century was that created by the Roman citizen Claudius Ptolemy in his Almagest, dating from about 150 A.D. Throughout the Middle Ages it was spoken of as the authoritative text on astronomy, although its author remained a little understood figure frequently mistaken as one of the Ptolemaic rulers of Egypt.[22] The Ptolemaic system drew on many previous theories that viewed Earth as a stationary center of the universe. Stars were embedded in a large outer sphere which rotated relatively rapidly, while the planets dwelt in smaller spheres between—a separate one for each planet. To account for apparent anomalies in this view, such as the apparent retrograde motion of the planets, a system of deferents and epicycles was used. The planet was said to revolve in a small circle (the epicycle) about a center, which itself revolved in a larger circle (the deferent) about a center on or near the Earth.[23] Nicolai Copernicito Torinensis De Revolutionibus Orbium A complementary theory to Ptolemy’s employed homocentric spheres: the spheres within which the planets rotated could themselves rotate somewhat. This theory predated Ptolemy (it was first devised by Eudoxus of Cnidus; by the time of Copernicus it was associated with Averroes). Also popular with astronomers were variations such as eccentrics—by which the rotational axis was offset and not completely at the center. Ptolemy’s unique contribution to this theory was the equant—a point about which the center of a planet’s epicycle moved with uniform angular velocity, but which was offset from the center of its deferent. This violated one of the fundamental principles of Aristotelian

Coelestium, Libri VI (On the Revolutions of the Heavenly Spheres, in six books) (title page of 2nd edition, Basel, 1566)

coelestium - On the Revolutions of the Heavenly Spheres (first edition 1543 in Nuremberg, second edition 1566 in Basel[25] ), was published during the year of his death, though he had arrived at his theory several decades earlier. The book marks the beginning of the shift away from a geocentric (and anthropocentric) universe with the Earth at its center. Copernicus held that the Earth is another planet revolving around the fixed sun once a year, and turning on its axis once a day. But while Copernicus put the Sun at the center of the celestial spheres, he did not put it at the exact center of the universe, but near it.


24.5. ACCEPTANCE OF COPERNICAN HELIOCENTRISM Copernicus’ system used only uniform circular motions, correcting what was seen by many as the chief inelegance in Ptolemy’s system. The Copernican model replaced Ptolemy's equant circles with more epicycles.[26] This is the main reason that Copernicus’ system had even more epicycles than Ptolemy’s. The Copernican system can be summarized in several propositions, as Copernicus himself did in his early Commentariolus that he handed only to friends probably in the 1510s. The “little commentary” was never printed. Its existence was only known indirectly until a copy was discovered in Stockholm around 1880, and another in Vienna a few years later.[27] The major features of Copernican theory are: 1. Heavenly motions are uniform, eternal, and circular or compounded of several circles (epicycles). 2. The center of the universe is near the Sun.

283 1. General vision of the heliocentric theory, and a summarized exposition of his idea of the World. 2. Mainly theoretical, presents the principles of spherical astronomy and a list of stars (as a basis for the arguments developed in the subsequent books). 3. Mainly dedicated to the apparent motions of the Sun and to related phenomena. 4. Description of the Moon and its orbital motions. 5. Concrete exposition of the new system including planetary longitude. 6. Further concrete exposition of the new system including planetary latitude.

24.5 Acceptance of Copernican heliocentrism

3. Around the Sun, in order, are Mercury, Venus, Earth and Moon, Mars, Jupiter, Saturn, and the fixed Main article: Copernican Revolution stars. From publication until about 1700, few astronomers 4. The Earth has three motions: daily rotation, annual revolution, and annual tilting of its axis. 5. Retrograde motion of the planets is explained by the Earth’s motion. 6. The distance from the Earth to the Sun is small compared to the distance to the stars.

24.4.1 De revolutionibus orbium coelestium Main article: De revolutionibus orbium coelestium It opened with an originally anonymous preface by Andreas Osiander, a theologian friend of Copernicus, who urged that the theory, which was considered a tool that allows simpler and more accurate calculations, did not necessarily have implications outside the limited realm of astronomy.[28] Copernicus’ actual book began with a letter from his (by then deceased) friend Nikolaus von Schönberg, Cardinal Archbishop of Capua, urging Copernicus to publish his theory.[29] Then, in a lengthy introduction, Copernicus dedicated the book to Pope Paul III, explaining his ostensible motive in writing the book as relating to the inability of earlier astronomers to agree on an adequate theory of the planets, and noting that if his system increased the accuracy of astronomical predictions it would allow the Church to develop a more accurate calendar. At that time, a reform of the Julian Calendar was considered necessary and was one of the major reasons for the Church’s interest in astronomy. The work itself was then divided into six books:[30]

Statue of Copernicus next to Cracow University's Collegium Novum

were convinced by the Copernican system, though the book was relatively widely circulated (around 500 copies of the first and second editions have survived,[31] which is a large number by the scientific standards of the time). Few of Copernicus’ contemporaries were ready to concede that the Earth actually moved, although Erasmus Reinhold used Copernicus’ parameters to produce the


284 Prutenic Tables. However, these tables translated Copernicus’ mathematical methods back into a geocentric system, rejecting heliocentric cosmology on physical and theological grounds.[32] The Prutenic tables came to be preferred by Prussian and German astronomers. The degree of improved accuracy of these tables remains an open question, but their usage of Copernican ideas led to more serious consideration of a heliocentric model. However, even forty-five years after the publication of De Revolutionibus, the astronomer Tycho Brahe went so far as to construct a cosmology precisely equivalent to that of Copernicus, but with the Earth held fixed in the center of the celestial sphere instead of the Sun.[33] It was another generation before a community of practicing astronomers appeared who accepted heliocentric cosmology.

CHAPTER 24. COPERNICAN HELIOCENTRISM system of Ptolemy. On no point does it offend the principle of mathematics. Yet it ascribes to the Earth, that hulking, lazy body, unfit for motion, a motion as quick as that of the aethereal torches, and a triple motion at that.”[36] Likewise, Tycho took issue with the vast distances to the stars that Copernicus had assumed in order to explain why the Earth’s motion produced no visible changes in the appearance of the fixed stars (known as annual stellar parallax). Tycho had measured the apparent sizes of stars (now known to be illusory – see stellar magnitude), and used geometry to calculate that in order to both have those apparent sizes and be as far away as heliocentrism required, stars would have to be huge (the size of Earth’s orbit or larger, and thus much larger than the sun). Regarding this Tycho wrote, “Deduce these things geometrically if you like, and you will see how many absurdities (not to mention others) accompany this assumption [of the motion of the earth] by inference.”[37] He said his Tychonic system, which incorporated Copernican features into a geocentric system, “offended neither the principles of physics nor Holy Scripture”.[38] Thus many astronomers accepted some aspects of Copernicus’s theory at the expense of others. His model did have a large influence on later scientists such as Galileo and Johannes Kepler, who adopted, championed and (especially in Kepler’s case) sought to improve it. However, in the years following publication of de Revolutionibus, for leading astronomers such as Erasmus Reinhold, the key attraction of Copernicus’s ideas was that they reinstated the idea of uniform circular motion for the planets.[39]

From a modern point of view, the Copernican model has a number of advantages. It accurately predicts the relative distances of the planets from the Sun, although this meant abandoning the cherished Aristotelian idea that there is no empty space between the planetary spheres. Copernicus also gave a clear account of the cause of the seasons: that the Earth’s axis is not perpendicular to the plane of its orbit. In addition, Copernicus’s theory provided a strikingly simple explanation for the apparent retrograde motions of the planets—namely as parallactic displacements resulting from the Earth’s motion around the Sun— an important consideration in Johannes Kepler's conviction that the theory was substantially correct.[34] In the heliocentric model the planets’ apparent retrograde motions’ occurring at opposition to the Sun are a natural consequence of their heliocentric orbits. In the geocentic During the 17th century, several further discoveries evenmodel, however, these are explained by the ad hoc use tually led to the wider acceptance of heliocentrism: of epicycles, whose revolutions are mysteriously tied to that of the Sun’s.[35] • Using the newly invented telescope, Galileo discovered the four large moons of Jupiter (evidence that However, for his contemporaries, the ideas presented by the solar system contained bodies that did not orbit Copernicus were not markedly easier to use than the geoEarth), the phases of Venus (the first observational centric theory and did not produce more accurate preevidence not properly explained by the Ptolemaic dictions of planetary positions. Copernicus was aware of theory) and the rotation of the Sun about a fixed this and could not present any observational “proof”, reaxis[40] as indicated by the apparent annual variation lying instead on arguments about what would be a more in the motion of sunspots; complete and elegant system. The Copernican model appeared to be contrary to common sense and to contradict the Bible. Tycho Brahe’s arguments against Copernicus are illustrative of the physical, theological, and even astronomical grounds on which heliocentric cosmology was rejected. Tycho, arguably the most accomplished astronomer of his time, appreciated the elegance of the Copernican system, but objected to the idea of a moving Earth on the basis of physics, astronomy, and religion. The Aristotelian physics of the time (modern Newtonian physics was still a century away) offered no physical explanation for the motion of a massive body like Earth, but could easily explain the motion of heavenly bodies by postulating that they were made of a different sort of substance called aether that moved naturally. So Tycho said that the Copernican system “... expertly and completely circumvents all that is superfluous or discordant in the

• With a telescope, Giovanni Zupi saw the phases of Mercury in 1639; • Kepler in 1609 introduced the idea that the orbits of the planets were elliptical rather than circular, while retaining the heliocentric concept. • Isaac Newton in 1687 proposed universal gravity and the inverse-square law of gravitational attraction to explain Kepler’s elliptical planetary orbits. In 1725, James Bradley discovered stellar aberration, an apparent annual motion of stars around small ellipses, and attributed it to the finite speed of light and the motion of Earth in its orbit around the Sun.[41] In 1838, Friedrich Bessel made the first successful measurements of annual parallax for the star 61 Cygni, of


24.8. NOTES 0.314 arcseconds; which indicated that the star was 10.3 ly away, close to the currently accepted value of 11.4 ly. He narrowly beat Friedrich Georg Wilhelm Struve and Thomas Henderson, who measured the parallaxes of Vega and Alpha Centauri in the same year.

24.6 Modern opinion

285

[8] Adi Setia (2004), “Fakhr Al-Din Al-Razi on Physics and the Nature of the Physical World: A Preliminary Survey”, Islam & Science, 2, retrieved 2010-03-02 [9] Alessandro Bausani (1973). “Cosmology and Religion in Islam”. Scientia/Rivista di Scienza. 108 (67): 762. [10] Young, M. J. L., ed. (2006-11-02). Religion, Learning and Science in the 'Abbasid Period. Cambridge University Press. p. 413. ISBN 9780521028875.

Whether Copernicus’ propositions were “revolutionary” [11] Nasr, Seyyed Hossein (1993-01-01). An Introduction to Islamic Cosmological Doctrines. SUNY Press. p. 135. or “conservative” was a topic of debate in the late twentiISBN 9781438414195. eth century. Thomas Kuhn argued that Copernicus only transferred “some properties to the Sun’s many astronom- [12] Samsó, Julio (2007). “Biṭrūjī: Nūr al‐Dīn Abū Isḥāq [Abū ical functions previously attributed to the earth.” Other Jaʿfar] Ibrāhīm ibn Yūsuf al‐Biṭrūjī". In Thomas Hockey; historians have since argued that Kuhn underestimated et al. The Biographical Encyclopedia of Astronomers. what was “revolutionary” about Copernicus’ work, and New York: Springer. pp. 133–4. ISBN 978-0-38731022-0. (PDF version) emphasized the difficulty Copernicus would have had in putting forward a new astronomical theory relying alone on simplicity in geometry, given that he had no experi- [13] Samsó, Julio (1970–80). “Al-Bitruji Al-Ishbili, Abu Ishaq”. Dictionary of Scientific Biography. New York: mental evidence. Charles Scribner’s Sons. ISBN 0-684-10114-9.

In his book The Sleepwalkers: A History of Man’s Changing Vision of the Universe, Arthur Koestler puts Coper- [14] Gingerich, O. “Did Copernicus Owe a Debt to Aristarchus?" Journal for the History of Astronomy, nicus in a different light to what many authors seem to Vol.16, NO.1/FEB, P. 37, 1985 suggest, portraying him as a coward who was reluctant to publish his work due to a crippling fear of ridicule. [15] Esposito 1999, p. 289

24.7 See also • Copernican principle • Heliocentrism • Nicolaus Copernicus

24.8 Notes [1] Kuhn 1985 [2] Gingerich, O. “Did Copernicus Owe a Debt to Aristarchus?" Journal for the History of Astronomy, Vol.16, NO.1/FEB, pp.37, 39, 1985 [3] Heath (1913), p. 302.

[16] Saliba, George (1995-07-01). A History of Arabic Astronomy: Planetary Theories During the Golden Age of Islam. NYU Press. ISBN 9780814780237. [17] Swerdlow, Noel M. (1973-12-31). “The Derivation and First Draft of Copernicus’s Planetary Theory: A Translation of the Commentariolus with Commentary”. Proceedings of the American Philosophical Society. 117 (6): 424. ISSN 0003-049X. JSTOR 986461. [18] King, David A. (2007). “Ibn al‐Shāṭir: ʿAlāʾ al‐Dīn ʿAlī ibn Ibrāhīm”. In Thomas Hockey; et al. The Biographical Encyclopedia of Astronomers. New York: Springer. pp. 569–70. ISBN 978-0-387-31022-0. (PDF version) [19] Linton (2004, pp.124,137–38), Saliba (2009, pp.160– 65). [20] Goddu (2010, pp.261–69, 476–86), Huff (2010, pp.263– 64), di Bono (1995), Veselovsky (1973).

[4] Lucio Russo, Silvio M. Medaglia, Sulla presunta accusa di empietà ad Aristarco di Samo, in “Quaderni urbinati di cultura classica”, n.s. 53 (82) (1996), pp. 113–121

[21] Freely, John (2015-03-30). Light from the East: How the Science of Medieval Islam Helped to Shape the Western World. I.B.Tauris. p. 179. ISBN 9781784531386.

[5] Lucio Russo, The forgotten revolution, Springer (2004)

[22] McCluskey (1998), pp. 27

[6] Ragep, F. Jamil (2001a), “Tusi and Copernicus: The Earth’s Motion in Context”, Science in Context, Cambridge University Press, 14 (1–2): 145–163, doi:10.1017/s0269889701000060

[23] Koestler (1989), pp. 69-72

[7] Ragep, F. Jamil; Al-Qushji, Ali (2001b), “Freeing Astronomy from Philosophy: An Aspect of Islamic Influence on Science”, Osiris, 2nd Series, 16 (Science in Theistic Contexts: Cognitive Dimensions): 49–64 & 66–71, Bibcode:2001Osir...16...49R, doi:10.1086/649338

[24] Gingerich (2004), p. 53 [25] Koestler (1989), p.194 [26] Koestler (1989), pp. 579-80 [27] Gingerich (2004), pp.31–32 [28] Gingerich (2004), p.139


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[31] Gingerich (2004), p.248

• Gingerich, Owen (June 2011), “Galileo, the Impact of the Telescope, and the Birth of Modern Astronomy” (PDF), Proceedings of the American Philosophical Society, Philadelphia PA, 155 (2): 134–141

[32] Hanne Andersen, Peter Barker, and Xiang Chen. The Cognitive Structure of Scientific Revolutions. New York: Cambridge University Press, 2006. pp 138-148

• Goddu, André (2010). Copernicus and the Aristotelian tradition. Leiden, Netherlands: Brill. ISBN 978-90-04-18107-6.

[33] Kuhn 1985, pp. 200–202

• Huff, Toby E (2010). Intellectual Curiosity and the Scientific Revolution: A Global Perspective. Cambridge: Cambridge University Press. ISBN 978-0521-17052-9.

[29] Koestler (1989), p.196 [30] Stanford Encyclopedia of Philosophy

[34] Linton (2004, pp.138, 169), Crowe (2001, pp.90–92), Kuhn 1985, pp. 165–167 [35] Gingerich 2011, pp. 134–135 [36] Owen Gingerich, The eye of heaven: Ptolemy, Copernicus, Kepler, New York: American Institute of Physics, 1993, 181, ISBN 0-88318-863-5 [37] Blair, Ann (1990). “Tycho Brahe’s critique of Copernicus and the Copernican system”. Journal of the History of Ideas. 51 (3): 355–377 [p. 364]. JSTOR 2709620. [38] Gingerich, O. & Voelkel, J. R., J. Hist. Astron., Vol. 29, 1998, page 1 [39] Gingerich (2004), pp.23, 55 [40] Fixed, that is, in the Copernican system. In a geostatic system the apparent annual variation in the motion of sunspots could only be explained as the result of an implausibly complicated precession of the Sun’s axis of rotation (Linton, 2004, p.212; Sharratt, 1994, p.166; Drake, 1970, pp.191–196) [41] Hirschfeld, Alan (2001). Parallax:The Race to Measure the Cosmos. New York: Henry Holt. ISBN 0-8050-71334.

24.9 Bibliography • Crowe, Michael J. (2001). Theories of the World from Antiquity to the Copernican Revolution. Mineola, New York: Dover Publications, Inc. ISBN 0-486-41444-2. • di Bono, Mario (1995). “Copernicus, Amico, Fracastoro and Ṭūsï's Device: Observations on the Use and Transmission of a Model”. Journal for the History of Astronomy. xxvi: 133–54. Bibcode:1995JHA....26..133D. • Drake, Stillman (1970). Galileo Studies. Ann Arbor: The University of Michigan Press. ISBN 0472-08283-3.

• Koestler, Arthur (1989). The Sleepwalkers. Arkana. ISBN 978-0-14-019246-9. • Kuhn, Thomas S. (1985). The Copernican Revolution—Planetary Astronomy in the Development of Western Thought. Cambridge, Mississippi: Harvard University Press. ISBN 978-0-674-171039. • Linton, Christopher M. (2004). From Eudoxus to Einstein—A History of Mathematical Astronomy. Cambridge: Cambridge University Press. ISBN 978-0-521-82750-8. • McCluskey, S. C. (1998). Astronomies and Cultures in Early Medieval Europe. Cambridge: CUP. • Raju, C. K. (2007). Cultural foundations of mathematics: the nature of mathematical proof and the transmission of the calculus from India to Europe in the 16th c. CE. Pearson Education India. ISBN 97881-317-0871-2. • Saliba, George (2009). “Islamic reception of Greek astronomy”. in Valls-Gabaud & Boskenberg (2009). pp. 149–65 • Sharratt, Michael (1994). Galileo: Decisive Innovator. Cambridge: Cambridge University Press. ISBN 0-521-56671-1. • Valls-Gabaud, D.; Boskenberg, A., eds. (2009). The Role of Astronomy in Society and Culture. Proceedings IAU Symposium No. 260. • Veselovsky, I.N. (1973). “Copernicus and Naṣīr alDīn al-Ṭūsī". Journal for the History of Astronomy. iv: 128–30. Bibcode:1973JHA.....4..128V.

24.10 Further reading

• Esposito, John L. (1999). The Oxford history of Islam. Oxford University Press. ISBN 978-0-19510799-9.

• Hannam, James (2007). “Deconstructing Copernicus”. Medieval Science and Philosophy. Retrieved 2007-08-17. Analyses the varieties of argument used by Copernicus in De revolutionibus.

• Gingerich, Owen (2004). The Book Nobody Read. London: William Heinemann. ISBN 0-434-013153.

• Goldstone, Lawrence (2010). The Astronomer: A Novel of Suspense. New York: Walker and Company. ISBN 0-8027-1986-4.


24.11. EXTERNAL LINKS

24.11 External links • Heliocentric Pantheon

287


Chapter 25

Aristarchus of Samos Aristarchus of Samos (/ˌærəˈstɑːrkəs/; Greek: Ἀρίσταρχος Aristarkhos; c. 310 – c. 230 BC) was an ancient Greek astronomer and mathematician who presented the first known model that placed the Sun at the center of the known universe with the Earth revolving around it (see Solar system). He was influenced by Philolaus of Croton, but he identified the “central fire” with the Sun, and put the other planets in their correct order of distance around the Sun.[1] Like Anaxagoras before him, he suspected that the stars were just other bodies like the Sun. His astronomical ideas were often rejected in favor of the incorrect geocentric theories of Aristotle and Ptolemy.

25.1 Heliocentrism See also: Heliocentrism Though the original text has been lost, a reference in Archimedes' book The Sand Reckoner (Archimedis Syracusani Arenarius & Dimensio Circuli) describes a work by Aristarchus in which he advanced the heliocentric model as an alternative hypothesis to geocentrism. Archimedes wrote: You (King Gelon) are aware the 'universe' is the name given by most astronomers to the sphere the center of which is the center of the Earth, while its radius is equal to the straight line between the center of the Sun and the center of the Earth. This is the common account as you have heard from astronomers. But Aristarchus has brought out a book consisting of certain hypotheses, wherein it appears, as a consequence of the assumptions made, that the universe is many times greater than the 'universe' just mentioned. His hypotheses are that the fixed stars and the Sun remain unmoved, that the Earth revolves about the Sun on the circumference of a circle, the Sun lying in the middle of the Floor, and that the sphere of the fixed stars, situated about the same center as the Sun, is so great that the circle in which he supposes the Earth to

revolve bears such a proportion to the distance of the fixed stars as the center of the sphere bears to its surface.[2] — The Sand Reckoner Aristarchus suspected the stars were other suns[3] that are very far away, and that in consequence there was no observable parallax, that is, a movement of the stars relative to each other as the Earth moves around the Sun. Since stellar parallax is only detectable with telescopes, his accurate speculation was unprovable at the time. It is a common misconception that the heliocentric view was rejected by the contemporaries of Aristarchus. This is due to Gilles Ménage's translation of a passage from Plutarch's On the Apparent Face in the Orb of the Moon. Plutarch reported that Cleanthes (a contemporary of Aristarchus and head of the Stoics) as a worshipper of the Sun and opponent to the heliocentric model, was jokingly told by Aristarchus that he should be charged with impiety. Gilles Ménage, shortly after the trials of Galileo and Giordano Bruno, amended an accusative (identifying the object of the verb) with a nominative (the subject of the sentence), and vice versa, so that the impiety accusation fell over the heliocentric sustainer. The resulting misconception of an isolated and persecuted Aristarchus is still transmitted today.[4][5] Some facts suggest that Aristarchus’ heliocentric model was an accepted theory for some centuries. It is known that a demonstration of the model was given by Seleucus of Seleucia, a Hellenistic astronomer who lived a century after Aristarchus,[6] but no full record has been found. Pliny the Elder[7] and Seneca[8] referred to planets’ retrograde motion as an apparent (and not real) phenomenon, which is an implication of heliocentrism rather than geocentrism. Still, no stellar parallax was observed, and Ptolemy later preferred the geocentric model, which was held as true throughout the Middle Ages. The heliocentric theory was successfully revived by Copernicus, after which Johannes Kepler described planetary motions with greater accuracy with his three laws. Isaac Newton later gave a theoretical explanation based on laws of gravitational attraction and dynamics.

288


25.3. SEE ALSO

289

25.2 Distance to the Sun (lunar di- 25.3 See also chotomy)

• Aristarchus’ inequality • Belief Perseverance

25.4 Notes [1] Draper, John William, "History of the Conflict Between Religion and Science" in Joshi, S. T. (2007) [1874]. The Agnostic Reader. Prometheus. pp. 172–173. ISBN 9781-59102-533-7. [2] Heath (1913), p. 302. [3] Louis Strous. “Who discovered that the Sun was a star?". solar-center.stanford.edu. Retrieved 2014-07-13.

Aristarchus’s 3rd-century BC calculations on the relative sizes of (from left) the Sun, Earth and Moon, from a 10th-century AD Greek copy

[4] Lucio Russo, Silvio M. Medaglia, Sulla presunta accusa di empietà ad Aristarco di Samo, in “Quaderni urbinati di cultura classica”, n.s. 53 (82) (1996), pp. 113–121 [5] Lucio Russo, The forgotten revolution, Springer (2004) [6] Plutarch, Platonicae quaestiones, VIII, i [7] Naturalis historia, II, 70

Main article: Aristarchus On the Sizes and Distances

[8] Naturales quaestiones, VII, xxv, 6–7 [9] http://www.dioi.org/vols/we0.pdf

The only surviving work usually attributed to Aristarchus, On the Sizes and Distances of the Sun and Moon, is based on a geocentric world view. It has historically been read as stating that the angle subtended by the Sun’s diameter is 2 degrees, but Archimedes states in The Sand Reckoner that Aristarchus had a value of ½ degree, which is much closer to the actual average value of 32' or 0.53 degrees. The discrepancy may come from a misinterpretation of what unit of measure was meant by a certain Greek term in Aristarchus’ text.[9] Aristarchus claimed that at half moon (first or last quarter moon), the angle between the Sun and Moon was 87°.[10] He might have proposed 87° as a lower bound, since gauging the lunar terminator's deviation from linearity to 1° accuracy is beyond the unaided human ocular limit (that limit being about 3° accuracy). Aristarchus is known to have also studied light and vision.[11] Using correct geometry, but the insufficiently accurate 87° datum, Aristarchus concluded that the Sun was between 18 and 20 times farther away than the Moon.[12] (The true value of this angle is close to 89° 50', and the Sun’s distance is actually about 400 times the Moon’s.) The implicit false solar parallax of slightly under 3° was used by astronomers up to and including Tycho Brahe, c. AD 1600. Aristarchus pointed out that the Moon and Sun have nearly equal apparent angular sizes, and therefore their diameters must be in proportion to their distances from Earth; thus, the diameter of the Sun was calculated to be between 18 and 20 times the diameter of the Moon.[13]

[10] Greek Mathematical Works, Loeb Classical Library, Harvard University, 1939–1941, edited by Ivor Thomas, volume 2 (1941), pages 6–7 [11] Heath, 1913, pp. 299–300; Thomas, 1942, pp. 2–3. [12] A video on reconstruction of Aristarchus’ method [13] Kragh, Helge (2007). Conceptions of cosmos: from myths to the accelerating universe: a history of cosmology. Oxford University Press. p. 26. ISBN 0-19-920916-2.

25.5 References • Heath, Sir Thomas (1913). Aristarchus of Samos, the ancient Copernicus; a history of Greek astronomy to Aristarchus, together with Aristarchus’s Treatise on the sizes and distances of the sun and moon : a new Greek text with translation and notes. London: Oxford University Press.

25.6 Further reading • Gomez, A. G. (2013). Aristarchos of Samos, the Polymath. AuthorHouse. ISBN 9781496994233. • Stahl, William (1970). “Aristarchus of Samos”. Dictionary of Scientific Biography. 1. New York: Charles Scribner’s Sons. pp. 246–250. ISBN 0684-10114-9.


290

25.7 External links • Biography: JRASC, 75 (1981) 29 • First estimate of the Moon’s distance and First estimate of the Sun’s distance from educational website From Stargazers to Starships • Heath, T. L. (1913) Aristarchus of Samos, the Ancient Copernicus: A history of Greek astronomy to Aristarchus together with Aristarchus’ treatise on the sizes and distances of the sun and moon, a new Greek text with translation and notes, Oxford, Clarendon Press (PDF). • O'Connor, John J.; Robertson, Edmund F., “Aristarchus of Samos”, MacTutor History of Mathematics archive, University of St Andrews. • Online Galleries, History of Science Collections, University of Oklahoma Libraries High resolution images of works by Aristarchus of Samos in .jpg and .tiff format.

CHAPTER 25. ARISTARCHUS OF SAMOS


Chapter 26

Ellipse This article is about the geometric figure. For other uses, see Ellipse (disambiguation). “Elliptical” redirects here. For the exercise machine, see Elliptical trainer. Not to be confused with Ellipsis. In mathematics, an ellipse is a curve in a plane surround-

points such that the ratio of the distance of each point on the curve from a given point (called a focus or focal point) to the distance from that same point on the curve to a given line (called the directrix) is a constant. This ratio is called the eccentricity of the ellipse. Ellipses are common in physics, astronomy and engineering. For example, the orbit of each planet in our solar system is approximately an ellipse with the barycenter of the planet-Sun pair at one of the focal points. The same is true for moons orbiting planets and all other systems having two astronomical bodies. The shapes of planets and stars are often well described by ellipsoids. Ellipses also arise as images of a circle under parallel projection and the bounded cases of perspective projection, which are simply intersections of the projective cone with the plane of projection. It is also the simplest Lissajous figure formed when the horizontal and vertical motions are sinusoids with the same frequency. A similar effect leads to elliptical polarization of light in optics. The name, ἔλλειψις (élleipsis, “omission”), was given by Apollonius of Perga in his Conics, emphasizing the connection of the curve with “application of areas”.

An ellipse obtained as the intersection of a cone with an inclined plane.

ing two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. As such, it is a generalization of a circle, which is a special type of an ellipse having both focal points at the same location. The shape of an ellipse (how 'elongated' it is) is represented by its eccentricity, which for an ellipse can be any number from 0 (the limiting case of a circle) to arbitrarily close to but less than 1.

26.1 Elements of an ellipse See also: Features of conic sections Ellipses have two perpendicular axes about which the PF1+PF2 = 2a

b

e=f÷a

P

−a

−f F1

C

f F2

a

d

Ellipses are the closed type of conic section: a plane curve resulting from the intersection of a cone by a plane. D P e = PF ÷PD 0<e<1 (See figure to the right.) Ellipses have many similarities 2 −b with the other two forms of conic sections: parabolas and hyperbolas, both of which are open and unbounded. The The ellipse and some of its mathematical properties. cross section of a cylinder is an ellipse, unless the section is parallel to the axis of the cylinder. ellipse is symmetric. Due to this symmetry, these axes Analytically, an ellipse may also be defined as the set of intersect at the center of the ellipse (C). The larger of 291


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CHAPTER 26. ELLIPSE

The distance traveled from one focus to another, via some point on the ellipse, is the same regardless of the point selected.

these two axes, which corresponds to the larger distance between antipodal points on the ellipse, is called the major axis (in the figure to the right it is represented by the line segment between the point labeled −a and the point labeled a). The smaller of these two axes, and the smaller Ellipse Reflection distance between antipodal points on the ellipse, is called the minor axis.[1] (in the figure to the right it is represented by the line segment between the point labeled −b e, is the ratio of the distance between the two foci, to the to the point labeled b). length of the major axis or e = 2f/2a = f/a. For an ellipse The semi-major axis (denoted by a in the figure) and the eccentricity is between 0 and 1 (0 < e < 1). When the the semi-minor axis (denoted by b in the figure) are one eccentricity is 0 the foci coincide with the center point half of the major and minor axes, respectively. These and the figure is a circle. As the eccentricity tends toare sometimes called (especially in technical fields) the ward 1, the ellipse gets a more elongated shape. It tends major and minor semi-axes,[2][3] the major and mi- towards a line segment (see below) if the two foci remain nor semiaxes,[4][5] or major radius and minor ra- a finite distance apart and a parabola if one focus is kept fixed as the other is allowed to move arbitrarily far away. dius.[6][7][8][9] The eccentricity is also equal to the ratio of the distance The four points where these axes cross the ellipse are the (such as the (blue) line PF2 ) from any particular point vertices and are marked as a, −a, b, and −b. In addition on an ellipse to one of the foci to the perpendicular disto being at the largest and smallest distance from the cen- tance to the directrix from the same point (line PD), e = ter, these points are where the curvature of the ellipse is PF2 /PD. maximum and minimum.[10] The two foci or focal points of an ellipse are two special points F1 and F2 on the ellipse’s major axis that are equidistant from the center point. The sum of the distances from any point P on the ellipse to those two foci is constant and equal to the major axis (PF1 + PF2 = 2a) (in the figure to the right this corresponds to the sum of the two green lines equaling the length of the major axis that goes from −a to a).

26.2 Drawing ellipses

The distance to the focal point from the center of the ellipse is sometimes called the linear eccentricity, f, of the ellipse. Here it is denoted by f, but it is often denoted by c. Due to the Pythagorean theorem and the definition of the ellipse explained in the previous paragraph: f 2 = a2 −b2 . A second equivalent method of constructing an ellipse using a directrix is shown on the plot as the three blue lines. (See the Directrix section of this article for more information about this method). The dashed blue line is the directrix of the ellipse shown. Drawing an ellipse with two pins, a loop, and a pen The eccentricity of an ellipse, usually denoted by ε or


26.2. DRAWING ELLIPSES

293

26.2.2 The gardener’s ellipse: worked example Create an ellipse 3.0m by 1.5m Tools required: • 5 pegs and a mallet to drive them • a ball of non-stretchy cotton string or bricklayers line • a calculator Method: 1. Place center peg at C (the center of the ellipse)

Trammel of Archimedes (ellipsograph) animation

2. Determine the orientation of the long (major) axis and, if desired, place a long line (longer than the major axis) along that axis passing through C 3. Write down the major radius (a) and minor radius (b), that is, half of the full major/minor axes: a = 1500 b = 750 4. Calculate √ the positions of the foci (F1 ) and (F2 ) f = 15002 − 7502 Note: This is the distance = 1299 CF. The distance F1 F2 = 2598 5. Place pegs accordingly at F1 and F2 on the orientation line you affixed at step 2. 6. Cut the string to the length of the major axis, 2a (allowing for the knot and tail ends) 2a = 3000 7. Place the string on the ground around the pegs F1 and F2 , pull taut and then moving around the periphery, mark as desired on the ground. It doesn't matter where you start/stop.

Ellipse construction applying the parallelogram method

26.2.3 Trammel method 26.2.1

Pins-and-string method

The characterization of an ellipse as the locus of points so that sum of the distances to the foci is constant leads to a method of drawing one using two drawing pins, a length of string, and a pencil.[11] In this method, pins are pushed into the paper at two points, which become the ellipse’s foci. A string tied at each end to the two pins and the tip of a pen pulls the loop taut to form a triangle. The tip of the pen then traces an ellipse if it is moved while keeping the string taut. Using two pegs and a rope, gardeners use this procedure to outline an elliptical flower bed—thus it is called the gardener’s ellipse.[12]

An ellipse can also be drawn using a ruler, a set square, and a pencil: Draw two perpendicular lines M,N on the paper; these are the major (M) and minor (N) axes of the ellipse. Mark three points A, B, C on the ruler. A->C being the length of the semi-major axis and B->C the length of the semi-minor axis. With one hand, move the ruler on the paper, turning and sliding it so as to keep point A always on line N, and B on line M. With the other hand, keep the pencil’s tip on the paper, following point C of the ruler. The tip traces out an ellipse.


294

CHAPTER 26. ELLIPSE

The trammel of Archimedes, or ellipsograph, is a mechanical device that implements this principle. The ruler is replaced by a rod with a pencil holder (point C) at one end, and two adjustable side pins (points A and B) that slide into two perpendicular slots cut into a metal plate.[13] The mechanism can be used with a router to cut ellipses from board material. The mechanism is also used in a toy called the “nothing grinder”.

26.2.4

Focus The distance from the center C to either focus is f = ae, which can be expressed in terms of the major and minor radii:

Parallelogram method

In the parallelogram method, an ellipse is constructed point by point using equally spaced points on two horizontal lines and equally spaced points on two vertical lines. It is based on Steiner’s theorem on the generation of conic sections. Similar methods exist for the parabola and hyperbola.

26.3 Mathematical definitions and properties 26.3.1

is equivalent to (1). Substituting a cos t for x and b sin t for y in (1) yields the basic trigonometric identity cos2 t+ sin2 t = 1.

In Euclidean geometry

Definition In Euclidean geometry, the ellipse is usually defined as the bounded case of a conic section, or as the set of points such that the sum of the distances to two fixed points (the foci) is constant. The ellipse can also be defined as the set of points such that the distance from any point in that set to a given point in the plane (a focus) is a constant positive fraction less than 1 (the eccentricity) of the perpendicular distance of the point in the set to a given line (called the directrix). Yet another equivalent definition of the ellipse is that it is the set of points that are equidistant from one point in the plane (a focus) and a particular circle, the directrix circle (whose center is the other focus).

f=

a2 − b2 .

The sum of the distances from any point P = P(x,y) on the ellipse to those two foci is constant and equal to the major axis length:

P F1 +P F2 =

√ (x + f )2 + y 2 + (x − f )2 + y 2 = 2a.

This is just a mathematical formulation of the definition in the first sentence of this article. Eccentricity The eccentricity of the ellipse (commonly denoted as either e or ε ) is √ e=ε=

a2 − b2 = a2

( )2 b 1− = f /a a

(where again a and b are one-half of the ellipse’s major and minor axes respectively, and f is the focal distance) or, as expressed √ in terms using the flattening factor g = 1 − ab = 1 − 1 − e2 ,

√ The equivalence of these definitions can be proved using e = g(2 − g). the Dandelin spheres. Other formulas for the eccentricity of an ellipse are listed in the article on eccentricity of conic sections. Formulas Equations for the eccentricity of an ellipse that is expressed in the more general quadratic form are described in the article The equation of an ellipse whose major axis is the x axis dedicated to conic sections. and minor axis is the y axis is Directrix Each focus F of the ellipse is associated with a line paralThis equation is a direct consequence of the definition lel to the minor axis called a directrix. Refer to the illusfrom the two focal points.[14] This equation means an eltration on the right, in which the ellipse is centered at the lipse is a unit circle scaled by a factor of a in the x direcorigin. The distance from any point P on the ellipse to tion and a factor of b in the y direction. the focus F is a constant fraction of that point’s perpenThe trigonometric parametric formula dicular distance to the directrix, resulting in the equality e = PF/PD. The ratio of these two distances is the eccentricity of the ellipse. This property (which can be proved


26.3. MATHEMATICAL DEFINITIONS AND PROPERTIES

295

Area

0<e<1

The area Aellipse enclosed by an ellipse is C

f

a

d

Aellipse = πab where a and b are the lengths of the semi-major and semiminor axes, respectively. The area formula πab is intuitive: start with a circle of radius b (so its area is πb2 ) and stretch it by a factor a/b to make an ellipse. This scales the area by the same factor: πb2 (a/b) = πab. It is also easy to rigorously prove the area formula using using the Dandelin spheres) can be taken as another defintegration √as follows. Equation (1) can be rewritten as inition of the ellipse. y(x) = b 1 − x2 /a2 . For x ∈ [−a, a], this curve is the Besides the well-known ratio e = f/a, where f is the top half of the ellipse. So twice the integral of y(x) over distance from the center to the focus and a is the disthe interval [−a, a] will be the area of the ellipse: tance from the center to the farthest vertices (most sharply curved points of the ellipse), it is also true that e = a/d, ∫ a √ where d is the distance from the center to the directrix. Aellipse = 2b 1 − x2 /a2 dx −a ∫ b a √ 2 2 a − x2 dx. = Circular directrix a −a P e = PF÷PD

D

The ellipse can also be defined as the set of points that The second integral is the area of a circle of radius a, that 2 are equidistant from one focus and a circle, the directrix is, πa . So circle, that is centered on the other focus. The radius of the directrix circle equals the ellipse’s major axis, so the focus and the entire ellipse are inside the directrix circle. Aellipse = b πa2 = πab. a Ellipse as hypotrochoid

2 2 An ellipse defined √ implicitly by Ax + Bxy + Cy = 1 2 has area 2π/ 4AC − B .

Circumference The circumference C of an ellipse is:

C = 4aE(e) where again a is√ the length of the semi-major axis, e is the eccentricity 1 − b2 /a2 , and the function E is the complete elliptic integral of the second kind, ∫ E(e) =

π/2

√ 1 − e2 sin2 θ dθ,

0

which calculates the circumference of the ellipse in the first quadrant alone, and the formula for the circumference of an ellipse can thus be written An ellipse (in red) as a special case of the hypotrochoid with R = 2r.

The arc length of an ellipse, in general, has no closedThe ellipse is a special case of the hypotrochoid when R form solution in terms of elementary functions. Elliptic = 2r, as shown in the image to the right. integrals were motivated by this problem. Equation (3)


296

CHAPTER 26. ELLIPSE

√ √ √ may be evaluated directly using the Carlson symmetric 4 a2 + b2 ≤ C ≤ 2π a2 + b2 . form.[15] This gives a succinct and quadratically converging iterative method for evaluating the circumference us- Here the upper bound 2πa is the circumference of a circumscribed concentric circle passing through the ending the arithmetic-geometric mean.[16] points √ of the ellipse’s major axis, and the lower bound The exact infinite series is: 4 a2 + b2 is the perimeter of an inscribed rhombus with vertices at the endpoints of the major and minor axes. [ ] ( )2 ( )2 4 ( )2 6 1 1·3 e 1·3·5 e 2 C = 2πa 1 − e − − − ··· Chords 2 2·4 3 2·4·6 5 The midpoints of a set of parallel chords of an ellipse are collinear.[21]:p.147

or [ C = 2πa 1 −

)2 ∞ ( ∑ (2n − 1)!!

] e2n , 2n − 1

Latus rectum The chords of an ellipse that are perpendicular to the major axis and pass through one of its foci are called the latera recta of the ellipse. The length where n!! is the double factorial. Unfortunately, this se- of each latus rectum is 2b2 /a. ries converges rather slowly; however, by expanding in terms of h = (a − b)2 /(a + b)2 , Ivory[17] and Bessel[18] derived an expression that converges much more rapidly, Curvature 2n n!

n=1

[ C = π(a + b) 1 +

)2 ∞ ( ∑ (2n − 1)!! n=1

2n n!

]

hn . (2n − 1)2

The curvature is given by κ =

1 a2 b2

(

x2 a4

+

y2 b4

)− 23

.

Angle bisection property Ramanujan gives two good approximations for the circumference in §16 of “Modular Equations and Approxi- A local normal (perpendicular) to the ellipse at any point mations to π ";[19] they are P on the ellipse bisects the angle ∠F1 P F2 to the foci. This is evident graphically in the parallelogram method of√construction, and can]be proven analytically, for exam[ ] [ √ using the 2parametric form in canonical position, as C ≈ π 3(a + b) − (3a + b)(a + 3b) = π 3(a + b) −ple by 10ab + 3(a + b2 ) given below. and ( C ≈ π (a + b) 1 +

3h √ 4 − 3h

Reflexive property

) .

When a ray of light originating from one focus reflects off the inner surface of an ellipse, it always passes through The errors in these approximations, which were obtained the other focus. A ray of light coming from outside the empirically, are of order h3 and h5 , respectively. ellipse toward a focus reflects off the ellipse directly away [22]:pp. 36ff. More generally, the arc length of a portion of the circum- from the other focus. ference, as a function of the angle subtended, is given by an incomplete elliptic integral. Tangent property 10 +

See also: Meridian arc § Meridian distance on the The angle containing part of the ellipse, formed at a point ellipsoid on the major axis by a tangent line to the ellipse and the major axis, has measure less than 45°.[22]:p. 26. The inverse function, the angle subtended as a function of the arc length, is given by the elliptic functions. Some lower and upper bounds on the circumference of 26.3.2 In projective geometry the canonical ellipse x2 /a2 + y 2 /b2 = 1 with a ≥ b In a projective geometry defined over a field, a conic secare[20] tion can be defined as the set of all points of intersection between corresponding lines of two pencils of lines in a plane that are related by a projective, but not perspective, C ≤ 2πa, map (see Steiner’s theorem). By projective duality, a π(a + b) ≤ C ≤ 4(a + b), conic section can also be defined as the envelope of all


26.3. MATHEMATICAL DEFINITIONS AND PROPERTIES

297

lines that connect corresponding points of two lines re- The general equation’s coefficients can be obtained from lated by a projective, but not perspective, map. known semi-major axis a , semi-minor axis b , center coordinates (xc , yc ) and rotation angle Θ using the followIn a pappian projective plane (one defined over a field), all ing formulae: conic sections are equivalent to each other, and the different types of conic sections are determined by how they intersect the line at infinity, denoted by Ω. An ellipse is a conic section that does not intersect this line. A parabola is a conic section that is tangent to Ω, and a hyperbola is one that crosses Ω twice.[23] Since an ellipse does not intersect the line at infinity, it properly belongs to the affine plane determined by removing the line at infinity and all of its points from the projective plane.

A = a2 (sin Θ)2 + b2 (cos Θ)2 B = 2(b2 − a2 ) sin Θ cos Θ C = a2 (cos Θ)2 + b2 (sin Θ)2 D = −2Axc − Byc E = −Bxc − 2Cyc F = Ax2c + Bxc yc + Cyc2 − a2 b2

Affine space

These expressions can be derived from the canonical equation (see next section) by substituting the coordinates An ellipse is also the result of projecting a circle, sphere, with expressions for rotation and translation of the cooror ellipse in a three dimensional affine space onto a plane dinate system: (flat), by parallel lines. This is a special case of conical (perspective) projection of any of those geometric objects 2 in the affine space from a point O onto a plane P, when the x2can ycan + =1 point O lies in the plane at infinity of the affine space. In a2 b2 the setting of pappian projective planes, the image of an ellipse by any affine map (a projective map that leaves the xcan = (x − xc ) cos Θ + (y − yc ) sin Θ line at infinity invariant) is an ellipse, and, more generally, ycan = −(x − xc ) sin Θ + (y − yc ) cos Θ the image of an ellipse by any projective map M such that the line M −1 (Ω) does not touch or cross the ellipse is an Canonical form ellipse.

26.3.3

In analytic geometry

Let a > b . Through change of coordinates (a rotation of axes and a translation of axes) the general ellipse can be described by the canonical implicit equation

General ellipse 2 2 In analytic geometry, the ellipse is defined as the set x + y = 1 b2 of points (X, Y ) of the Cartesian plane that, in non- a2 [24][25] degenerate cases, satisfy the implicit equation Here (x, y) are the point coordinates in the canonical system, whose origin is the center (Xc , Yc ) of the ellipse, whose x -axis is the unit vector (Xa , Ya ) coincidAX 2 + BXY + CY 2 + DX + EY + F = 0 ing with the major axis, and whose y -axis is the perpendicular vector (−Ya , Xa ) coinciding with the minor provided B 2 − 4AC < 0. axis. That is, x = Xa (X − Xc ) + Ya (Y − Yc ) and To distinguish the degenerate cases from the non- y = −Ya (X − Xc ) + Xa (Y − Yc ) . degenerate case, let ∆ be the determinant In this system, the center is the origin (0, 0) and the foci are (−ea, 0) and (+ea, 0) .

A Any ellipse can be obtained by rotation and translation of B/2 D/2

B/2

a canonical ellipse with the proper semi-diameters. The C E/2 ;

D/2 E/2

expression of an ellipse centered at (Xc , Yc ) is F

that is,

∆=

) ( BED CD2 AE 2 B2 F+ − − . AC − 4 4 4 4

(y − Yc )2 (x − Xc )2 + =1 a2 b2 Moreover, any canonical ellipse can be obtained by scaling the unit circle of R2 , defined by the equation

Then the ellipse is a non-degenerate real ellipse if and only if C∆ < 0. If C∆ > 0, we have an imaginary ellipse, X2 + Y 2 = 1 and if ∆ = 0, we have a point ellipse.[26]:p.63


298

CHAPTER 26. ELLIPSE

by factors a and b along the two axes. For an ellipse in canonical form, we have

Y = ±b

√ √ 1 − (X/a)2 = ± (a2 − X 2 )(1 − e2 )

The distances from a point (X, Y ) on the ellipse to the left and right foci are a + eX and a − eX , respectively. The canonical form coefficients can be obtained from the general form coefficients using the following equations: √ ( )( ) √ − 2 AE 2 + CD2 − BDE + (B 2 − 4AC)F A + C ± (A − C)2 + B 2 a, b = 2CD − BE Xc = 2 B − 4AC 2AE − BD Yc = 2 B − 4AC    0 Θ = 90◦ √   arctan C−A− (A−C)2 +B 2 B

B 2 − 4AC Parametric equation for the ellipse (red) in canonical position. The eccentric anomaly t is the angle of the blue line with the Xaxis.

forB = 0, A < C Parametric form in canonical position forB = 0, A > C forB ̸= 0

For an ellipse in canonical position (center at origin, major axis along the X-axis), the equation simplifies to

where Θ is the angle from the positive horizontal axis to the ellipse’s major axis. X(t) = a cos t Line segment as a type of degenerate ellipse A line segment is a degenerate ellipse with semi-minor axis = 0 and eccentricity = 1, and with the focal points at the ends.[27] It arises when the sum of the distances of a point on the ellipse to the foci is required to equal the distance between the foci. Although the eccentricity is 1 this is not a parabola. A radial elliptic trajectory is a nontrivial special case of an elliptic orbit, where the ellipse is a line segment.

26.3.4

In trigonometry

General parametric form An ellipse in general position can be expressed parametrically as the path of a point (X(t), Y (t)) , where

Y (t) = b sin t The parameter t (called the eccentric anomaly in astronomy) is not the angle of (X(t), Y (t)) with the X-axis (see diagram at right). For a given point on an ellipse, formulae connecting the tangential angle ϕ , the polar angle from the ellipse center θ , and the parametric angle t [28] are:[29][30][31][32]

− cot ϕ =

tan θ tan θ a tan t = = , 2 b (1 − g) 1 − e2

− tan t =

√ b − tan θ a cot ϕ = 1 − e2 cot ϕ = (1−g) cot ϕ = √ = − tan a b 1 − e2

Polar form relative to center X(t) = Xc + a cos t cos φ − b sin t sin φ Y (t) = Yc + a cos t sin φ + b sin t cos φ

In polar coordinates, with the origin at the center of the ellipse and with the angular coordinate θ measured from the major axis, the ellipse’s equation is[26]:p. 75

as the parameter t varies from 0 to 2π. Here (Xc , Yc ) is ab the center of the ellipse, and φ is the angle between the r(θ) = √ X -axis and the major axis of the ellipse. (b cos θ)2 + (a sin θ)2


26.3. MATHEMATICAL DEFINITIONS AND PROPERTIES

299

P r θ

C

d1

F2

B

Major axis

d2

Minor axis

A F1

Semi-latus rectum

Semi-latus rectum. Polar coordinates centered at the center.

General polar form

P r A F1

C

θ

d1

F2

B

The following equation on the polar coordinates (r, θ) describes a general ellipse with semidiameters a and b, centered at a point (r0 , θ0 ), with the a axis rotated by φ relative to the polar axis:

d2 r(θ) =

P (θ) + Q(θ) R(θ)

where r is the radius or central distance, and Polar coordinates centered at focus.

P (θ) = r0

[(

) ( ) ] b2 − a2 cos (θ + θ0 − 2φ) + a2 + b2 cos (θ − θ0 )

√ √ Q(θ) = 2ab R(θ) − 2r02 sin2 (θ − θ0 ) If instead we use polar coordinates with the origin at one ( 2 ) 2 2 2 focus, with the angular coordinate θ = 0 still measured R(θ) = b − a cos(2θ − 2φ) + a + b from the major axis, the ellipse’s equation is Polar form relative to focus

Angular eccentricity r(θ) =

a(1 − e2 ) 1 ± e cos θ

The angular eccentricity α is the angle whose sine is the eccentricity e; that is,

where the sign in the denominator is negative if the refer(√ ) ( ) ence direction θ = 0 points towards the center (as illusb a−b = 2 arctan . trated on the right), and positive if that direction points α = arcsin(e) = arccos a a+b away from the center. In the slightly more general case of an ellipse with one focus at the origin and the other focus at angular coordinate 26.3.5 ϕ , the polar form is

As a parametric rational polynomial

An ellipse can be parameterized as a rational quadratic polynomial, in other words described by the equations a(1 − e ) r= . x(t) = p(t)/r(t) and y(t) = q(t)/r(t) where p(t), q(t), 1 − e cos(θ − ϕ) and r(t) are quadratic polynomials in t. The tangent halfidentities angle The angle θ in these formulas is called the true anomaly 2 of the point. The numerator a(1 − e ) of these formulas is the semi-latus rectum of the ellipse, usually denoted l . It is the distance from a focus of the ellipse to the ellipse u = tan(t/2) = sin t/(1 + cos t) = (1 − cos t)/ sin t itself, measured along a line perpendicular to the major axis. imply u2 = (1 − cos t)/(1 + cos t) and this implies 2


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CHAPTER 26. ELLIPSE

curve has such a property, it can be used as an alternative definition of an ellipse. (In the special case of a circos t = (1 − u2 )/(u2 + 1). cle with a source at its center all light would be reflected back to the center.) If the ellipse is rotated along its maSubstituting this equation for cos t into the first tangent jor axis to produce an ellipsoidal mirror (specifically, a half-angle identity yields prolate spheroid), this property holds for all rays out of the source. Alternatively, a cylindrical mirror with elliptical cross-section can be used to focus light from a linear sin t = u(1 + cos t) = 2u/(u2 + 1). fluorescent lamp along a line of the paper; such mirrors are used in some document scanners. Substituting these values for sin t and cos t into the Sound waves are reflected in a similar way, so in a large trigonometric parameterization above yields elliptical room a person standing at one focus can hear a person standing at the other focus remarkably well. The effect is even more evident under a vaulted roof shaped x(u) = a(1 − u2 )/(u2 + 1) . as a section of a prolate spheroid. Such a room is called a y(u) = 2bu/(u2 + 1) whisper chamber. The same effect can be demonstrated For u ∈ [0, 1], this formula represents the quarter ellipse with two reflectors shaped like the end caps of such a centered at the origin with radii a and b moving counter- spheroid, placed facing each other at the proper distance. clockwise with increasing u. It is easy to test this by com- Examples are the National Statuary Hall at the United puting (x(0), y(0)) = (a, 0) and (x(1), y(1)) = (0, b). States Capitol (where John Quincy Adams is said to have used this property for eavesdropping on political matters); the Mormon Tabernacle at Temple Square in Salt Lake City, Utah; at an exhibit on sound at the Museum of Sci26.3.6 Degrees of freedom ence and Industry in Chicago; in front of the University An ellipse in the plane has five degrees of freedom (the of Illinois at Urbana-Champaign Foellinger Auditorium; same as a general conic section), defining its vertical and and also at a side chamber of the Palace of Charles V, in horizontal position, orientation, shape, and scale. In com- the Alhambra. parison, circles have only three degrees of freedom (horizontal position, vertical position and scale), while parabolae have four. Said another way, the set of all ellipses in Planetary orbits the plane, with any natural metric (such as the Hausdorff distance) is a five-dimensional manifold. Main article: Elliptic orbit The five degrees of freedom can be identified with, for example, the coefficients A,B,C,D,E of the implicit equation, or with the coefficients X , Y , φ, a, b of the general parametric form. Thus an ellipse is uniquely determined by any five points lying on it.

26.4 Applications 26.4.1

Ellipses in physics

Elliptical reflectors and acoustics See also: Fresnel zone If the water’s surface is disturbed at one focus of an elliptical water tank, the circular waves of that disturbance, after reflecting off the walls, converge simultaneously to a single point: the second focus. This is a consequence of the total travel length being the same along any wallbouncing path between the two foci.

In the 17th century, Johannes Kepler discovered that the orbits along which the planets travel around the Sun are ellipses with the Sun [approximately] at one focus, in his first law of planetary motion. Later, Isaac Newton explained this as a corollary of his law of universal gravitation. More generally, in the gravitational two-body problem, if the two bodies are bound to each other (that is, the total energy is negative), their orbits are similar ellipses with the common barycenter being one of the foci of each ellipse. The other focus of either ellipse has no known physical significance. Interestingly, the orbit of either body in the reference frame of the other is also an ellipse, with the other body at the same focus.

Keplerian elliptical orbits are the result of any radially directed attraction force whose strength is inversely proportional to the square of the distance. Thus, in principle, the motion of two oppositely charged particles in empty space would also be an ellipse. (However, this conclusion ignores losses due to electromagnetic radiation and Similarly, if a light source is placed at one focus of an quantum effects, which become significant when the parelliptic mirror, all light rays on the plane of the ellipse ticles are moving at high speed.) are reflected to the second focus. Since no other smooth For elliptical orbits, useful relations involving the eccen-


26.4. APPLICATIONS tricity e are:

e=

ra − rp ra − rp = ra + rp 2a

ra = (1 + e)a rp = (1 − e)a where • ra is the radius at apoapsis (the farthest distance) • rp is the radius at periapsis (the closest distance) • a is the length of the semi-major axis

301 chainring may be elliptical, or an ovoid similar to an ellipse in form. Such elliptical gears may be used in mechanical equipment to produce variable angular speed or torque from a constant rotation of the driving axle, or in the case of a bicycle to allow a varying crank rotation speed with inversely varying mechanical advantage. Elliptical bicycle gears make it easier for the chain to slide off the cog when changing gears.[33] An example gear application would be a device that winds thread onto a conical bobbin on a spinning machine. The bobbin would need to wind faster when the thread is near the apex than when it is near the base.[34] Optics

Also, in terms of ra and rp , the semi-major axis a is their arithmetic mean, the semi-minor axis b is their geometric mean, and the semi-latus rectum l is their harmonic mean. In other words,

• In a material that is optically anisotropic (birefringent), the refractive index depends on the direction of the light. The dependency can be described by an index ellipsoid. (If the material is optically isotropic, this ellipsoid is a sphere.)

ra + rp 2 √ b = ra · rp 2 2ra rp l= 1 1 = r +r + a p ra rp

• In lamp-pumped solid-state lasers, elliptical cylinder-shaped reflectors have been used to direct light from the pump lamp (coaxial with one ellipse focal axis) to the active medium rod (coaxial with the second focal axis).[35]

a=

Harmonic oscillators The general solution for a harmonic oscillator in two or more dimensions is also an ellipse. Such is the case, for instance, of a long pendulum that is free to move in two dimensions; of a mass attached to a fixed point by a perfectly elastic spring; or of any object that moves under influence of an attractive force that is directly proportional to its distance from a fixed attractor. Unlike Keplerian orbits, however, these “harmonic orbits” have the center of attraction at the geometric center of the ellipse, and have fairly simple equations of motion.

• In laser-plasma produced EUV light sources used in microchip lithography, EUV light is generated by plasma positioned in the primary focus of an ellipsoid mirror and is collected in the secondary focus at the input of the lithography machine.[36]

26.4.2 Ellipses in statistics and finance

In statistics, a bivariate random vector (X, Y) is jointly elliptically distributed if its iso-density contours — loci of equal values of the density function — are ellipses. The concept extends to an arbitrary number of elements of the random vector, in which case in general the iso-density contours are ellipsoids. A special case is the multivariate normal distribution. The elliptical distributions are imPhase visualization portant in finance because if rates of return on assets are In electronics, the relative phase of two sinusoidal sig- jointly elliptically distributed then all portfolios can be nals can be compared by feeding them to the vertical and characterized completely by their mean and variance — horizontal inputs of an oscilloscope. If the display is an that is, any two portfolios with identical mean and variellipse, rather than a straight line, the two signals are out ance of portfolio return have identical distributions of portfolio return.[37][38] of phase. Elliptical gears

26.4.3 Ellipses in computer graphics

Two non-circular gears with the same elliptical outline, each pivoting around one focus and positioned at the proper angle, turn smoothly while maintaining contact at all times. Alternatively, they can be connected by a link chain or timing belt, or in the case of a bicycle the main

Drawing an ellipse as a graphics primitive is common in standard display libraries, such as the MacIntosh QuickDraw API, and Direct2D on Windows. Jack Bresenham at IBM is most famous for the invention of 2D drawing primitives, including line and circle drawing,


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using only fast integer operations such as addition and branch on carry bit. M. L. V. Pitteway extended Bresenham’s algorithm for lines to conics in 1967.[39] Another efficient generalization to draw ellipses was invented in 1984 by Jerry Van Aken.[40] In 1970 Danny Cohen presented at the “Computer Graphics 1970” conference in England a linear algorithm for drawing ellipses and circles. In 1971, L. B. Smith published similar algorithms for all conic sections and proved them to have good properties.[41] These algorithms need only a few multiplications and additions to calculate each vector. It is beneficial to use a parametric formulation in computer graphics because the density of points is greatest where there is the most curvature. Thus, the change in slope between each successive point is small, reducing the apparent “jaggedness” of the approximation.

• Elliptic coordinates, an orthogonal coordinate system based on families of ellipses and hyperbolae • Elliptic partial differential equation • Elliptical distribution, in statistics • Geodesics on an ellipsoid • Great ellipse • Hyperbola • Kepler’s laws of planetary motion • Matrix representation of conic sections • n-ellipse, a generalization of the ellipse for n foci • Oval • Parabola

Drawing with Bézier paths Composite Bézier curves may also be used to draw an ellipse to sufficient accuracy, since any ellipse may be construed as an affine transformation of a circle. The spline methods used to draw a circle may be used to draw an ellipse, since the constituent Bézier curves behave appropriately under such transformations. Drawing with three points of a parallelogram Rytz’s construction can be used to find the minor and major axes and their angle of an ellipse from conjugate diameters (which can be seen as three points of a parallelogram). The method uses the conjugate diameters of an ellipse to map the ellipse to an unit circle under affine transformation and calculate the ellipse parameters from that.

26.4.4

Ellipses in optimization theory

It is sometimes useful to find the minimum bounding ellipse on a set of points. The ellipsoid method is quite useful for attacking this problem.

26.5 See also • Apollonius of Perga, the classical authority • Cartesian oval, a generalization of the ellipse • Circumconic and inconic • Conic section • Ellipse fitting • Ellipsoid, a higher dimensional analog of an ellipse

• Rytz’s construction, a method for finding the ellipse axes from conjugate diameters or a parallelogram • Spheroid, the ellipsoid obtained by rotating an ellipse about its major or minor axis • Steiner circumellipse, the unique ellipse circumscribing a triangle and sharing its centroid • Steiner inellipse, the unique ellipse inscribed in a triangle with tangencies at the sides’ midpoints • Superellipse, a generalization of an ellipse that can look more rectangular or more “pointy” • True, eccentric, and mean anomaly

26.6 Notes [1] The “major axis” and “minor axis” are sometimes called the “transverse diameter” and “conjugate diameter"; see Haswell, Charles Haynes (1920). Mechanics’ and Engineers’ Pocket-book of Tables, Rules, and Formulas. Harper & Brothers. This usage is now rare [2] Herschel, Sir John Frederick William (1842). A treatise on astronomy. Lea & Blanchard. p. 256. [3] Lankford, John (1997). History of Astronomy: An Encyclopedia. Taylor & Francis. p. 194. ISBN 978-0-81530322-0. [4] Prasolov, Viktor Vasilʹevich; Tikhomirov, Vladimir Mikhaĭlovich (2001). Geometry. American Mathematical Society. p. 80. ISBN 978-0-8218-2038-4. [5] Fenna, Donald (2007). Cartographic Science: A Compendium of Map Projections, With Derivations. CRC Press. p. 24. ISBN 978-0-8493-8169-0. [6] AutoCAD release 13 command reference. Autodesk, Inc. 1994. p. 216.


26.6. NOTES

[7] Salomon, David (2006). Curves And Surfaces for Computer Graphics. Birkhäuser. p. 365. ISBN 978-0-38724196-8.

303

[22] Downs, J.W., Practical Conic Sections, Dover, 2003 (orig. 1993). [23] Meserve 1983, p. 159

[8] Kreith, Frank; Goswami, D. Yogi (2005). The CRC Handbook Of Mechanical Engineering. CRC Press. pp. 11–8. ISBN 978-0-8493-0866-6. Circles and Ellipses (11.3.2)

[24] Larson, Ron; Hostetler, Robert P.; Falvo, David C. (2006). “Chapter 10”. Precalculus with Limits. Cengage Learning. p. 767. ISBN 0-618-66089-5.

[9] The Mathematical Association of America (1976), The American Mathematical Monthly, vol. 83, page 207

[25] Young, Cynthia Y. (2010). “Chapter 9”. Precalculus. John Wiley and Sons. p. 831. ISBN 0-471-75684-9.

[10] Gibson, C. G. (2001), Elementary Geometry of Differentiable Curves: An Undergraduate Introduction, Cambridge University Press, p. 127, ISBN 9780521011075.

[26] Lawrence, J. Dennis, A Catalog of Special Plane Curves, Dover Publ., 1972.

[11] Besant 1907, p. 57 [12] Armengaud, Aîné (1853). “Ovals, Ellipses, Parabolas, Volutes, etc. §53”. The Practical Draughtsman’s Book of Industrial Design. Longman, Brown, Green, and Longmans. p. 16. [13] Brown, Henry T. (1881). Five Hundred and Seven Mechanical Movements: Embracing All Those which are Most Important in Dynamics, Hydraulics, Hydrostatics, Pneumatics, Steam Engines, Mill and Other Gearing, Presses, Horology, and Miscellaneous Machinery; and Including Many Movements Never Before Published, and Several which Have Only Recently Come Into Use. Brown & Brown. pp. 40–41 section 152. [14] “Derivation of standard equation for ellipse from the locus definition of an ellipse” (PDF). nebula.deanza.edu. Retrieved 18 July 2016. [15] Carlson, B. C. (1995). “Numerical computation of real or complex elliptic integrals”. Numerical Algorithms. 10 (1): 13–98. arXiv:math/9409227 . Bibcode:1995NuAlg..10...13C. doi:10.1007/BF02198293. [16] Python code for the circumference of an ellipse in terms of the complete elliptic integral of the second kind, retrieved 2013-12-28 [17] Ivory, J. (1798). “A new series for the rectification of the ellipsis”. Transactions of the Royal Society of Edinburgh. 4: 177–190. doi:10.1017/s0080456800030817.

[27] Seligman, Courtney (1993–2010). “Orbital Motions Ellipses and Other Conic Sections”. Online Astronomy eText. [28] If the ellipse is illustrated as a meridional one for the earth, the tangential angle is equal to geodetic latitude, the angle θ is the geocentric latitude, and parametric angle t is a parametric (or reduced) latitude of auxiliary circle [29] Ellipse at MathWorld, derived from formula (58) and (60) [30] clarifies problems with MathWorld formula (60) [31] Auxiliary circle and various ellipse formulas [32] Meeus, J. (1991). “Ch. 10: The Earth’s Globe”. Astronomical Algorithms. Willmann-Bell. p. 78. ISBN 0943396-35-2. [33] David Drew. “Elliptical Gears”. [34] Grant, George B. (1906). A treatise on gear wheels. Philadelphia Gear Works. p. 72. [35] http://www.rp-photonics.com/lamp_pumped_lasers. html [36] http://www.cymer.com/plasma_chamber_detail/ [37] Chamberlain, G. (February 1983). “A characterization of the distributions that imply mean—Variance utility functions”. Journal of Economic Theory. 29 (1): 185–201. doi:10.1016/0022-0531(83)90129-1.

[18] Bessel, F. W. (2010). “The calculation of longitude and latitude from geodesic measurements (1825)". Astron. Nachr. 331 (8): 852–861. arXiv:0908.1824 . doi:10.1002/asna.201011352. English translation of Astron. Nachr. 4, 241–254 (1825).

[38] Owen, J.; Rabinovitch, R. (June 1983). “On the class of elliptical distributions and their applications to the theory of portfolio choice”. Journal of Finance. 38: 745– 752. doi:10.1111/j.1540-6261.1983.tb02499.x. JSTOR 2328079.

[19] Ramanujan, Srinivasa, (1914). “Modular Equations and Approximations to π". Quart. J. Pure App. Math. 45: 350–372.

[39] Pitteway, M.L.V. (1967). “Algorithm for drawing ellipses or hyperbolae with a digital plotter”. The Computer Journal. 10 (3): 282–9. doi:10.1093/comjnl/10.3.282.

[20] Jameson, G.J.O. “inequalities for the perimeter of an ellipse”, Mathematical Gazette 98, July 2014, 227-234. doi: 10.2307/3621497

[40] Van Aken, J.R. (September 1984). “An Efficient EllipseDrawing Algorithm”. IEEE Computer Graphics and Applications. 4 (9): 24–35. doi:10.1109/MCG.1984.275994.

[21] Chakerian, G. D. “A Distorted View of Geometry.” Ch. 7 in Mathematical Plums (R. Honsberger, editor). Washington, DC: Mathematical Association of America, 1979.

[41] Smith, L.B. (1971). “Drawing ellipses, hyperbolae or parabolae with a fixed number of points”. The Computer Journal. 14 (1): 81–86. doi:10.1093/comjnl/14.1.81.


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26.7 References • Besant, W.H. (1907). “Chapter III. The Ellipse”. Conic Sections. London: George Bell and Sons. p. 50. • Coxeter, H.S.M. (1969). Introduction to Geometry (2nd ed.). New York: Wiley. pp. 115–9. • Meserve, Bruce E. (1983) [1959], Fundamental Concepts of Geometry, Dover, ISBN 0-486-63415-9 • Miller, Charles D.; Lial, Margaret L.; Schneider, David I. (1990). Fundamentals of College Algebra (3rd ed.). Scott Foresman/Little. p. 381. ISBN 0673-38638-4.

26.8 External links • Apollonius’ Derivation of the Ellipse at Convergence • The Shape and History of The Ellipse in Washington, D.C. by Clark Kimberling • Ellipse circumference calculator • Collection of animated ellipse demonstrations • Weisstein, Eric W. “Ellipse”. MathWorld. • Weisstein, Eric W. “Ellipse as special case of hypotrochoid”. MathWorld. • Ivanov, A.B. (2001), “Ellipse”, in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4

CHAPTER 26. ELLIPSE


Chapter 27

Elliptic orbit

A small body in space orbits a large one (like a planet around the sun) along an elliptical path, with the large body being located at one of the ellipse foci.

An elliptical orbit is depicted in the top-right quadrant of this diagram, where the gravitational potential well of the central mass shows potential energy, and the kinetic energy of the orbital speed is shown in red. The height of the kinetic energy decreases as the orbiting body’s speed decreases and distance increases according to Kepler’s laws.

In a gravitational two-body problem with negative energy both bodies follow similar elliptic orbits with the same orbital period around their common barycenter. Also the relative position of one body with respect to the other follows an elliptic orbit. Examples of elliptic orbits include: Hohmann transfer orbit, Molniya orbit and tundra orbit. Two bodies with similar mass orbiting around a common barycenter with elliptic orbits.

In astrodynamics or celestial mechanics an elliptic orbit is a Kepler orbit with the eccentricity less than 1; this includes the special case of a circular orbit, with eccentricity equal to zero. In a stricter sense, it is a Kepler orbit with the eccentricity greater than 0 and less than 1 (thus excluding the circular orbit). In a wider sense it is a Kepler orbit with negative energy. This includes the radial elliptic orbit, with eccentricity equal to 1.

27.1 Velocity Under standard assumptions the orbital speed ( v ) of a body traveling along an elliptic orbit can be computed from the Vis-viva equation as: √ ( ) 2 1 v= µ − r a

305


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CHAPTER 27. ELLIPTIC ORBIT • µ is the standard gravitational parameter.

where: • µ is the standard gravitational parameter,

Conclusions:

• r is the distance between the orbiting bodies. • a is the length of the semi-major axis.

• For a given semi-major axis the specific orbital energy is independent of the eccentricity.

The velocity equation for a hyperbolic trajectory has either + a1 , or it is the same with the convention that in that Using the virial theorem we find: case a is negative.

27.2 Orbital period

• the time-average of the specific potential energy is equal to −2ε • the time-average of r−1 is a−1

Under standard assumptions the orbital period ( T ) of a body traveling along an elliptic orbit can be computed as:

• the time-average of the specific kinetic energy is equal to ε

√ T = 2π

a3 µ

where: • µ is the standard gravitational parameter, • a is the length of the semi-major axis.

27.4 Flight path angle The flight path angle is the angle between the orbiting body’s velocity vector (= the vector tangent to the instantaneous orbit) and the local horizontal. Under standard assumptions of the conservation of angular momentum the flight path angle ϕ satisfies the equation:

Conclusions: • The orbital period is equal to that for a circular orbit h = r v cos ϕ with the orbital radius equal to the semi-major axis where: ( a ), • For a given semi-major axis the orbital period does not depend on the eccentricity (See also: Kepler’s third law).

• h is the specific relative angular momentum of the orbit, • v is the orbital speed of the orbiting body,

27.3 Energy Under standard assumptions, specific orbital energy ( ϵ ) of elliptic orbit is negative and the orbital energy conservation equation (the Vis-viva equation) for this orbit can take the form:

µ µ v2 − =− =ϵ<0 2 r 2a where: • v is the orbital speed of the orbiting body, • r is the distance of the orbiting body from the central body, • a is the length of the semi-major axis,

• r is the radial distance of the orbiting body from the central body, • ϕ is the flight path angle The angular momentum is related to the vector cross product of position and velocity, which is proportional to the sine of the angle between these two vectors. Here ϕ is defined as the angle which differs by 90 degrees from this, so the cosine appears in place of the sine.

27.5 Equation of motion Main article: orbit equation


27.9. HISTORY

27.6 Orbital parameters

307 dropping an object (neglecting air resistance). See also Free fall#Inverse-square law gravitational field.

The state of an orbiting body at any given time is defined by the orbiting body’s position and velocity with respect to the central body, which can be represented by the threedimensional Cartesian coordinates (position of the orbiting body represented by x, y, and z) and the similar Cartesian components of the orbiting body’s velocity. This set of six variables, together with time, are called the orbital state vectors. Given the masses of the two bodies they determine the full orbit. The two most general cases with these 6 degrees of freedom are the elliptic and the hyperbolic orbit. Special cases with fewer degrees of freedom are the circular and parabolic orbit.

27.9 History The Babylonians were the first to realize that the Sun’s motion along the ecliptic was not uniform, though they were unaware of why this was; it is today known that this is due to the Earth moving in an elliptic orbit around the Sun, with the Earth moving faster when it is nearer to the Sun at perihelion and moving slower when it is farther away at aphelion.[1]

Because at least six variables are absolutely required to completely represent an elliptic orbit with this set of parameters, then six variables are required to represent an orbit with any set of parameters. Another set of six parameters that are commonly used are the orbital elements.

In the 17th century, Johannes Kepler discovered that the orbits along which the planets travel around the Sun are ellipses with the Sun at one focus, and described this in his first law of planetary motion. Later, Isaac Newton explained this as a corollary of his law of universal gravitation.

27.7 Solar System

27.10 See also

In the Solar System, planets, asteroids, most comets and some pieces of space debris have approximately elliptical orbits around the Sun. Strictly speaking, both bodies revolve around the same focus of the ellipse, the one closer to the more massive body, but when one body is significantly more massive, such as the sun in relation to the earth, the focus may be contained within the larger massing body, and thus the smaller is said to revolve around it. The following chart of the perihelion and aphelion of the planets, dwarf planets and Halley’s Comet demonstrates the variation of the eccentricity of their elliptical orbits. For similar distances from the sun, wider bars denote greater eccentricity. Note the almost-zero eccentricity of Earth and Venus compared to the enormous eccentricity of Halley’s Comet and Eris.

• Characteristic energy • Ellipse • List of orbits • Orbital eccentricity • Orbit equation • Parabolic trajectory

27.11 References [1] David Leverington (2003), Babylon to Voyager and beyond: a history of planetary astronomy, Cambridge University Press, pp. 6–7, ISBN 0-521-80840-5

27.8 Radial elliptic trajectory 27.12 Further reading A radial trajectory can be a double line segment, which is a degenerate ellipse with semi-minor axis = 0 and eccentricity = 1. Although the eccentricity is 1, this is not a parabolic orbit. Most properties and formulas of elliptic orbits apply. However, the orbit cannot be closed. It is an open orbit corresponding to the part of the degenerate ellipse from the moment the bodies touch each other and move away from each other until they touch each other again. In the case of point masses one full orbit is possible, starting and ending with a singularity. The velocities at the start and end are infinite in opposite directions and the potential energy is equal to minus infinity. The radial elliptic trajectory is the solution of a two-body problem with at some instant zero speed, as in the case of

• D’Eliseo, MM (2007). “The first-order orbital equation”. American Journal of Physics. 75 (4): 352–355. Bibcode:2007AmJPh..75..352D. doi:10.1119/1.2432126. • D’Eliseo, MM; Mironov, Sergey V. (2009). “The gravitational ellipse”. Journal of Mathematical Physics. 50: 022901–022901. arXiv:0802.2435 . Bibcode:2009JMP....50a2901M. doi:10.1063/1.3078419. • Curtis, Howard (2009). Orbital Mechanics for Engineering Students. Butterworth-Heinemann. ISBN 978-0123747785.


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27.13 External links • JAVA applet animating the orbit of a satellite in an elliptic Kepler orbit around the Earth with any value for semi-major axis and eccentricity. • Apogee - Perigee Lunar photographic comparison • Aphelion - Perihelion Solar photographic comparison • http://www.castor2.ca

CHAPTER 27. ELLIPTIC ORBIT


Chapter 28

Astronomia nova the movement of free floating bodies as opposed to objects on rotating spheres. It is recognized as one of the most important works of the Scientific Revolution.[2]

28.1 Background Prior to Kepler, Nicolaus Copernicus proposed in 1543 that the Earth and other planets orbit the Sun. The Copernican model of the solar system was regarded as a device to explain the observed positions of the planets rather than a physical description. Kepler sought for and proposed physical causes for planetary motion. His work is primarily based on the research of his mentor, Tycho Brahe. The two, though close in their work, had a tumultuous relationship. Regardless, on his deathbed, Brahe asked Kepler to make sure that he did not “die in vain,” and to continue the development of his Tychonic system. Kepler would instead write the Astronomia nova, in which he rejects the Tychonic system, as well as the Ptolemaic system and the Copernican system. Some scholars have speculated that Kepler’s dislike for Brahe may have had a hand in his rejection of the Tychonic system and formation of a new one.[3]

28.2 Structure and Summary of the Astronomia nova Title Page of Kepler’s Astronomia nova (1609)

The Astronomia nova (full title in original Latin: Astronomia Nova ΑΙΤΙΟΛΟΓΗΤΟΣ seu physica coelestis, tradita commentariis de motibus stellae Martis ex observationibus G.V. Tychonis Brahe[1] ) is a book, published in 1609, that contains the results of the astronomer Johannes Kepler's ten-year-long investigation of the motion of Mars. One of the greatest books on astronomy, the Astronomia nova provided strong arguments for heliocentrism and contributed valuable insight into the movement of the planets, including the first mention of their elliptical path and the change of their movement to

In English, the full title of his work is the New Astronomy, Based upon Causes, or Celestial Physics, Treated by Means of Commentaries on the Motions of the Star Mars, from the Observations of Tycho Brahe, Gent. For over 650 pages, Kepler walks his readers, step by step, through his process of discovery so as to dispel any impression of “cultivating novelty,” he says. The Astronomia nova's introduction, specifically the discussion of scripture, was the most widely distributed of Kepler’s works in the seventeenth century.[4] The introduction outlines the four steps Kepler took during his research. The first is his claim that the sun itself and not any imaginary point near the sun (as in the Copernican system) is the point where all the planes of the eccentrics

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CHAPTER 28. ASTRONOMIA NOVA Kepler discusses all his work at great length throughout the book. He addresses this length in the sixteenth chapter: If thou art bored with this wearisome method of calculation, take pity on me, who had to go through with at least seventy repetitions of it, at a very great loss of time.[5] Kepler, in a very important step, also questions the assumption that the planets move around the center of their orbit at a uniform rate. He finds that computing critical measurements based upon the Sun’s actual position in the sky, instead of the Sun’s “mean” position injects a significant degree of uncertainty into the models, opening the path for further investigations. The idea that the planets do not move at a uniform rate, but at a speed that varies as their distance from the Sun, was completely revolutionary and would become his second law (discovered before his first). Kepler, in his calculations leading to his second law, made multiple mathematical errors, which luckily cancelled each other out “as if by miracle.”[6] Given this second law, he puts forth in Chapter 33 that the sun is the engine that moves the planets. To describe the motion of the planets, he claims the sun emits a physical species, analogous to the light it also emits, which pushes the planets along. He also suggests a second force within every planet itself that pulls it toward then sun to keep it from spiraling off into space.

Diagrams of the three models of planetary motion prior to Kepler

of the planets intersect, or the center of the orbits of the planets. The second step consists of Kepler placing the sun as the center and mover of the other planets. This step also contains Kepler’s reply to objections against placing the sun at the center of the universe, including objections based on scripture. In reply to scripture, he argues that it is not meant to claim physical dogma, and the content should be taken spiritually. In the third step, he posits that the sun is the source of the motion of all planets, using Brahe’s proof based on comets that planets do not rotate on orbs. The fourth step consists of describing the path of planets as not a circle, but an oval.

Kepler then attempts to finally find the true path of the planets, which he determines is an ellipse. His initial attempt to define the orbit of Mars, far before he arrived at the ellipse shape, was off by only eight minutes of arc, yet this was enough for Kepler to require an entirely new system. Kepler tried a number of shapes before the ellipse, including an egg shape. What is more, he discovered the mathematical definition for the ellipse as the orbit, then rejected it, then adopted the ellipse without knowing that it was the same: ”I laid [the original equation] aside, and fell back on ellipses, believing that this was quite a different hypothesis, whereas the two, as I shall prove in the next chapter, are one in the same…Ah, what a foolish bird I have been!”[7]

As the Astronomia nova proper starts, Kepler demonstrates that the Tychonic, Ptolemaic, and Copernican systems are indistinguishable on the basis of observations alone. The three models predict the same positions for 28.3 Kepler’s laws the planets in the near term, although they diverge from historical observations, and fail in their ability to predict The Astronomia nova records the discovery of the first future planetary positions by a small, though absolutely two of the three principles known today as Kepler’s laws measurable amount. Kepler here introduces his famous of planetary motion, which are: diagram of the movement of Mars in relation to Earth if Earth remained unmoving at the center of its orbit. The 1. That the planets move in elliptical orbits with the sun diagram shows that Mars’s orbit would be completely imat one focus.[8] perfect and never follow along the same path.


28.5. KEPLER’S KNOWLEDGE OF GRAVITY 2. That the speed of the planet changes at each moment such that the time between two positions is always proportional to the area swept out on the orbit between these positions.[9]

311 a space proportional to the bulk [moles] of the other.... For it follows that if the earth’s power of attraction will be much more likely to extend to the moon and far beyond, and accordingly, that nothing that consists to any extent whatever of terrestrial material, carried up on high, ever escapes the grasp of this mighty power of attraction.”[11]

Kepler discovered the “second law” before the first. He presented his second law in two different forms: In Chapter 32 he states that the speed of the planet varies inversely based upon its distance from the Sun, and therefore he could measure changes in position of the planet Kepler discusses the moon’s gravitational effect upon the by adding up all the distance measures, or looking at the tides as follows:[12][13] area along an orbital arc. This is his so-called “distance law”. In Chapter 59, he states that a radius from the Sun The sphere of the attractive virtue which is to a planet sweeps out equal areas in equal times. This is in the moon extends as far as the earth, and enhis so-called “area law”. tices up the waters; but as the moon flies rapidly However, Kepler’s “area-time principle” did not facilitate across the zenith, and the waters cannot follow easy calculation of planetary positions. Kepler could diso quickly, a flow of the ocean is occasioned vide up the orbit into an arbitrary number of parts, comin the torrid zone towards the westward. If the pute the planet’s position for each one of these, and then attractive virtue of the moon extends as far as refer all questions to a table, but he could not determine the earth, it follows with greater reason that the the position of the planet at each and every individual moattractive virtue of the earth extends as far as ment because the speed of the planet was always changthe moon and much farther; and, in short, nothing. This paradox, referred to as the "Kepler problem,” ing which consists of earthly substance anyhow prompted the development of calculus. constituted although thrown up to any height, can ever escape the powerful operation of this attractive virtue.

28.4 The “third law” Kepler discovered his “third law” a decade after the publication of the Astronomia nova as a result of his investigations in the 1619 Harmonices Mundi (Harmonies of the world).[10] He found that the ratio of the cube of the length of the semi-major axis of each planet’s orbit, to the square of time of its orbital period, is the same for all planets.

28.5 Kepler’s knowledge of gravity

Johannes also clarifies the concept of lightness in terms of relative density, in opposition to the Aristotelian concept of the absolute nature or quality of lightness as follows. His argument could easily be applied today to something like the flight of a hot air balloon. Nothing which consists of corporeal matter is absolutely light, but that is comparatively lighter which is rarer, either by its own nature, or by accidental heat. And it is not to be thought that light bodies are escaping to the surface of the universe while they are carried upwards, or that they are not attracted by the earth. They are attracted, but in a less degree, and so are driven outwards by the heavy bodies; which being done, they stop, and are kept by the earth in their own place.[13]

In his introductory discussion of a moving earth, Kepler addressed the question of how the Earth could hold its parts together if it moved away from the center of the universe which, according to Aristotelian physics, was the place toward which all heavy bodies naturally moved. Kepler proposed an attractive force similar to magnetism, In reference to Kepler’s discussion relating to gravitation, which may have been known by Newton. Walter William Bryant makes the following statement in his book Kepler (1920). “Gravity is a mutual corporeal disposition among kindred bodies to unite or join together; thus the earth attracts a stone much more than the stone seeks the earth. (The magnetic faculty is another example of this sort).... If two stones were set near one another in some place in the world outside the sphere of influence of a third kindred body, these stones, like two magnetic bodies, would come together in an intermediate place, each approaching the other by

...the Introduction to Kepler’s “Commentaries on the Motion of Mars,” always regarded as his most valuable work, must have been known to Newton, so that no such incident as the fall of an apple was required to provide a necessary and sufficient explanation of the genesis of his Theory of Universal Gravitation. Kepler’s glimpse at such a theory could have


312

CHAPTER 28. ASTRONOMIA NOVA been no more than a glimpse, for he went no further with it. This seems a pity, as it is far less fanciful than many of his ideas, though not free from the “virtues” and “animal faculties,” that correspond to Gilbert’s “spirits and humours”.[13]

Kepler considered that this attraction was mutual and was proportional to the bulk of the bodies, but he considered it to have a limited range and he did not consider whether or how this force may have varied with distance. Furthermore, this attraction only acted between “kindred bodies”—bodies of a similar nature, a nature which he did not clearly define.[14][15] Kepler’s idea differed significantly from Newton’s later concept of gravitation and it can be “better thought of as an episode in the struggle for heliocentrism than as a step toward Universal gravitation.”[16]

28.6 Commemoration The 2009 International Year of Astronomy commemorates the 400th anniversary of the publication of this work.[17]

28.7 Notes [1] Here G.V. is a siglum for “Generositas Vestra”, see Winiarczyk, Marek (1995). Sigla Latina in libris impressis occurrentia: cum siglorum graecorum appendice (2nd ed.). OCLC 168613439. [2] Voelkel, James R. (2001). The composition of Kepler’s Astronomia nova. Princeton: Princeton University Press. p. 1. ISBN 0-691-00738-1. [3] Koestler, Arthur (1990). The Sleepwalkers: A history of man’s changing vision of the universe. London: Penguin Books. p. 1. ISBN 0-14-019246-8. [4] Kepler, Johannes; William H. Donahue (2004). Selections from Kepler’s Astronomia Nova. Santa Fe: Green Lion Press. p. 1. ISBN 1-888009-28-4. [5] Koestler, Arthur (1990). The Sleepwalkers: A history of man’s changing vision of the universe. London: Penguin Books. p. 325. ISBN 0-14-019246-8. [6] Koestler, Arthur (1990). The Sleepwalkers: A history of man’s changing vision of the universe. London: Penguin Books. p. 325. ISBN 0-14-019246-8. [7] Koestler, Arthur (1990). The Sleepwalkers: A history of man’s changing vision of the universe. London: Penguin Books. p. 338. ISBN 0-14-019246-8. [8] In his Astronomia nova, Kepler presented only a proof that Mars’ orbit is elliptical. Evidence that the other known planets’ orbits are elliptical was presented later. See: Johannes Kepler, Astronomia nova … (1609), p. 285. After

having rejected circular and oval orbits, Kepler concluded that Mars’ orbit must be elliptical. From the top of page 285: “Ergo ellipsis est Planetæ iter; … " (Thus, an ellipse is the planet’s [i.e., Mars’] path; … ) Later on the same page: " … ut sequenti capite patescet: ubi simul etiam demonstrabitur, nullam Planetæ relinqui figuram Orbitæ, præterquam perfecte ellipticam; … " ( … as will be revealed in the next chapter: where it will also then be proved that any figure of the planet’s orbit must be relinquished, except a perfect ellipse; … ) And then: “Caput LIX. Demonstratio, quod orbita Martis, … , fiat perfecta ellipsis: … " (Chapter 59. Proof that Mars’ orbit, … , be a perfect ellipse: … ) The geometric proof that Mars’ orbit is an ellipse appears as Protheorema XI on pages 289-290. Kepler stated that all planets travel in elliptical orbits having the Sun at one focus in: Johannes Kepler, Epitome Astronomiae Copernicanae [Summary of Copernican Astronomy] (Linz (“Lentiis ad Danubium”), (Austria): Johann Planck, 1622), book 5, part 1, III. De Figura Orbitæ (III. On the figure [i.e., shape] of orbits), pages 658-665. From p. 658: “Ellipsin fieri orbitam planetæ … " (Of an ellipse is made a planet’s orbit … ). From p. 659: " … Sole (Foco altero huius ellipsis) … " ( … the Sun (the other focus of this ellipse) … ). [9] In his Astronomia nova … (1609), Kepler did not present his second law in its modern form. He did that only in his Epitome of 1621. Furthermore, in 1609, he presented his second law in two different forms, which scholars call the “distance law” and the “area law”. • His “distance law” is presented in: “Caput XXXII. Virtutem quam Planetam movet in circulum attenuari cum discessu a fonte.” (Chapter 32. The force that moves a planet circularly weakens with distance from the source.) See: Johannes Kepler, Astronomia nova … (1609), pp. 165-167. On page 167, Kepler states: " … , quanto longior est αδ quam αε, tanto diutius moratur Planeta in certo aliquo arcui excentrici apud δ, quam in æquali arcu excentrici apud ε.” ( … , as αδ is longer than αε, so much longer will a planet remain on a certain arc of the eccentric near δ than on an equal arc of the eccentric near ε.) That is, the farther a planet is from the Sun (at the point α), the slower it moves along its orbit, so a radius from the Sun to a planet passes through equal areas in equal times. However, as Kepler presented it, his argument is accurate only for circles, not ellipses. • His “area law” is presented in: “Caput LIX. Demonstratio, quod orbita Martis, … , fiat perfecta ellipsis: … " (Chapter 59. Proof that Mars’ orbit, … , is a perfect ellipse: … ), Protheorema XIV and XV, pp. 291-295. On the top p. 294, it reads: “Arcum ellipseos, cujus moras metitur area AKN, debere terminari in LK, ut sit AM.” (The arc of the ellipse, of which the duration is delimited [i.e., measured] by the area AKM, should be terminated in LK, so that it [i.e., the arc] is AM.) In other words, the time that Mars requires to move along an arc AM of its elliptical orbit is measured by the area of the segment AMN of the ellipse (where N is the position of the Sun), which in turn is proportional to the section AKN of the circle that encircles the ellipse and


28.8. REFERENCES

that is tangent to it. Therefore, the area AMN that is swept out by a radius from the Sun to Mars as Mars moves along an arc AM of its elliptical orbit is proportional to the time that Mars requires to move along that arc. Thus, a radius from the Sun to Mars sweeps out equal areas in equal times. In 1621, Kepler restated his second law for any planet: Johannes Kepler, Epitome Astronomiae Copernicanae [Summary of Copernican Astronomy] (Linz (“Lentiis ad Danubium”), (Austria): Johann Planck, 1622), book 5, page 668. From page 668: “Dictum quidem est in superioribus, divisa orbita in particulas minutissimas æquales: accrescete iis moras planetæ per eas, in proportione intervallorum inter eas & Solem.” (It has been said above that, if the orbit of the planet is divided into the smallest equal parts, the times of the planet in them increase in the ratio of the distances between them and the sun.) That is, a planet’s speed along its orbit is inversely proportional to its distance from the Sun. (The remainder of the paragraph makes clear that Kepler was referring to what is now called angular velocity.) [10] Johannes Kepler, Harmonices Mundi [The Harmony of the World] (Linz, (Austria): Johann Planck, 1619), p. 189. From the bottom of p. 189: “Sed res est certissima exactissimaque quod proportio qua est inter binorum quorumcunque Planetarum tempora periodica, sit præcise sesquialtera proportionis mediarum distantiarum, … " (But it is absolutely certain and exact that the proportion between the periodic times of any two planets is precisely the sesquialternate proportion [i.e., the ratio of 3:2] of their mean distances, … ") An English translation of Kepler’s Harmonices Mundi is available as: Johannes Kepler with E.J. Aiton, A.M. Duncan, and J.V. Field, trans., The Harmony of the World (Philadelphia, Pennsylvania: American Philosophical Society, 1997); see especially p. 411. [11] Kepler, Johannes; William H. Donahue (2004). Selections from Kepler’s Astronomia Nova. Santa Fe: Green Lion Press. p. 1. ISBN 1-888009-28-4. [12] Johannes Kepler, Astronomia nova … (1609), p. 5 of the Introductio in hoc opus (Introduction to this work). From page 5: “Orbis virtutis tractoriæ, quæ est in Luna, porrigitur utque ad Terras, & prolectat aquas sub Zonam Torridam, … Celeriter vero Luna verticem transvolante, cum aquæ tam celeriter sequi non possint, fluxus quidem fit Oceani sub Torrida in Occidentem, … " (The sphere of the lifting power, which is [centered] in the moon, is extended as far as to the earth and attracts the waters under the torrid zone, … However the moon flies swiftly across the zenith ; because the waters cannot follow so quickly, the tide of the ocean under the torrid [zone] is indeed made to the west, … ) [13] Bryant, Walter William (1920), Kepler, Pioneers of Progress: Men of Science, London: Society for Promoting Christian Knowledge, p. 36 [14] Stephenson, Bruce (1994), Kepler’s Physical Astronomy, Princeton: Princeton University Press, pp. 4–6, ISBN 0691-03652-7

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[15] Koyré, Alexandre (1973), The astronomical revolution: Copernicus, Kepler, Borelli, Ithaca, NY: Cornell University Press, pp. 194–5, ISBN 0-8014-0504-1 [16] Stephenson, Bruce (1994), Kepler’s Physical Astronomy, Princeton: Princeton University Press, p. 5, ISBN 0-69103652-7 [17] “International Year of Astronomy and Johannes Kepler”. Kepler Mission. Archived from the original on September 8, 2008. Retrieved 9 January 2009.

28.8 References • Johannes Kepler, New Astronomy, translated by William H. Donahue, Cambridge: Cambridge Univ. Pr., 1992. ISBN 0-521-30131-9 • http://www.hao.ucar.edu/Public/education/bios/ kepler.3.html (dead link 18 feb 2016) • http://www.library.usyd.edu.au/libraries/rare/ modernity/kepler4.html

28.9 External links • Astronomia nova by Johannes Kepler, 1609, in Latin, full text scan • Origins of Modernity - Kepler: Astronomia nova


Chapter 29

Aristotelian physics Aristotelian physics is a form of natural science described in the works of the Greek philosopher Aristotle (384–322 BCE). In his work Physics, Aristotle intended to establish general principles of change that govern all natural bodies, both living and inanimate, celestial and terrestrial – including all motion, change with respect to place, change with respect to size or number, qualitative change of any kind; and “coming to be” (coming into existence, “generation”) and “passing away” (no longer existing, “corruption”).

(particularly in the analysis of local motion), and relied on such suspect explanatory principles as final causes and “occult” essences. Yet in his Physics Aristotle characterizes physics or the “science of nature” as pertaining to magnitudes (megethê), motion (or “process” or “gradual change” – kinêsis), and time (chronon) (Phys III.4 202b30–1). Indeed, the Physics is largely concerned with an analysis of motion, particularly local motion, and the other concepts that Aristotle believes are requisite to that analysis.[2] — Michael J. White, “Aristotle on the Infinite, Space, and Time” in Blackwell Companion to Aristotle

To Aristotle, “physics” was a broad field that included subjects such as the philosophy of mind, sensory experience, memory, anatomy and biology. It constitutes the foundation of the thought underlying many of his works.

29.1 Concepts 29.1.1 Terrestrial change

nature is everywhere the cause of order.[1] — Aristotle, Physics VIII.1

FIRE

While consistent with common human experience, Aristotle’s principles were not based on controlled, quantitative experiments, so, while they account for many broad features of nature, they do not describe our universe in the precise, quantitative way now expected of science. Contemporaries of Aristotle like Aristarchus rejected these principles in favor of heliocentrism, but their ideas were not widely accepted. Aristotle’s principles were difficult to disprove merely through casual everyday observation, but later development of the scientific method challenged his views with experiments and careful measurement, using increasingly advanced technology such as the telescope and vacuum pump.

hot

dry

AIR

EARTH

wet

cold

WATER

The four terrestrial elements

In claiming novelty for their doctrines, those natural philosophers who developed the “new science” of the seventeenth century frequently contrasted “Aristotelian” physics with their own. Physics of the former sort, so they claimed, emphasized the qualitative at the expense of the quantitative, neglected mathematics and its proper role in physics

Unlike the eternal and unchanging celestial aether, each of the four terrestrial elements are capable of changing into either of the two elements they share a property with: e.g. the cold and wet (water) can transform into the hot and wet (air) or the cold and dry (earth) and any apparent change into the hot and dry (fire) is actually a two-step process. These properties are predicated of an actual sub314


29.1. CONCEPTS

315

stance relative to the work it is able to do; that of heating composition.[5] or chilling and of desiccating or moistening. The four elements exist only with regard to this capacity and relative to some potential work. The celestial element is eternal and unchanging, so only the four terrestrial elements acAether count for “coming to be” and “passing away” – or, in the terms of Aristotle’s De Generatione et Corruptione (Περὶ γενέσεως καὶ φθορᾶς), “generation” and “corruption”. Main articles: Aether (classical element) and Dynamics of the celestial spheres

29.1.2

Elements

According to Aristotle, the elements which compose the terrestrial spheres are different from that constituting the celestial spheres.[3] He believed that four elements make up everything under the Moon, i.e. everything terrestrial: earth, air, fire and water.[a][4] He also held that the heavens are made of a special weightless and incorruptible (i.e. unchangeable) fifth element called "aether".[4] Aether also has the name “quintessence”, meaning, literally, “fifth being”.[5]

The Sun, Moon, planets and stars – are embedded in perfectly concentric "crystal spheres" that rotate eternally at fixed rates. Because the celestial spheres are incapable of any change except rotation, the terrestrial sphere of fire must account for the heat, starlight and occasional meteorites.[6] The lunar sphere is the only celestial sphere that actually comes in contact with the sublunary orb’s changeable, terrestrial matter, dragging the rarefied fire and air along underneath as it rotates.[7] Like Homer's æthere (αἰθήρ) – the “pure air” of Mount Olympus – was the divine counterpart of the air breathed by mortal beings (άήρ, aer). The celestial spheres are composed of the special element aether, eternal and unchanging, the sole capability of which is a uniform circular motion at a given rate (relative to the diurnal motion of the outermost sphere of fixed stars). The concentric, aetherial, cheek-by-jowl "crystal spheres" that carry the Sun, Moon and stars move eternally with unchanging circular motion. Spheres are embedded within spheres to account for the “wandering stars” (i.e. the planets, which, in comparison with the Sun, Moon and stars, appear to move erratically). Later, the belief that all spheres are concentric was forsaken in favor of Ptolemy's deferent and epicycle model. Aristotle submits to the calculations of astronomers regarding the total number of spheres and various accounts give a number in the neighborhood of fifty spheres. An unmoved mover is assumed for each sphere, including a “prime mover” for the sphere of fixed stars. The unmoved movers do not push the spheres (nor could they, being immaterial and dimensionless) but are the final cause of the spheres’ motion, i.e. they explain it in a way that’s similar to the explanation “the soul is moved by beauty”.

A page from an 1837 edition of the ancient Greek philosopher Aristotle's Physica, a book addressing a variety of subjects including the philosophy of nature and topics now part of its modern-day namesake: physics.

Aristotle considered heavy substances such as iron and other metals to consist primarily of the element earth, with a smaller amount of the other three terrestrial elements. Other, lighter objects, he believed, have less earth, relative to the other three elements in their

29.1.3 Four causes Main articles: Four causes and Teleology According to Aristotle, there are four ways to explain the aitia or causes of change. He writes that “we do not have knowledge of a thing until we have grasped its why, that is to say, its cause.”[8][9] Aristotle held that there were four kinds of causes.[9][10]


316 Material

CHAPTER 29. ARISTOTELIAN PHYSICS

a table is a carpenter, who knows the form of the table. In his Physics II, 194b29—32, Aristotle writes: “there is that The material cause of a thing is that of which it is made. which is the primary originator of the change and of its For a table, that might be wood; for a statue, that might cessation, such as the deliberator who is responsible [sc. be bronze or marble. for the action] and the father of the child, and in general the producer of the thing produced and the changer of the thing changed”. “In one way we say that the aition is that out of which. as existing, something comes to be, like the bronze for the statue, the Aristotle’s examples here are instructive: silver for the phial, and their genera” (194b2 one case of mental and one of physical cau3—6). By “genera,” Aristotle means more sation, followed by a perfectly general chargeneral ways of classifying the matter (e.g. acterization. But they conceal (or at any rate “metal”; “material”); and that will become fail to make patent) a crucial feature of Arisimportant. A little later on. he broadens the totle’s concept of efficient causation, and one range of the material cause to include letters which serves to distinguish it from most mod(of syllables), fire and the other elements (of ern homonyms. For Aristotle, any process rephysical bodies), parts (of wholes), and even quires a constantly operative efficient cause as premisses (of conclusions: Aristotle re-iterates long as it continues. This commitment appears this claim, in slightly different terms, in An. most starkly to modern eyes in Aristotle’s disPost II. 11).[11] cussion of projectile motion: what keeps the — R.J. Hankinson, “The Theory of the projectile moving after it leaves the Physics” in Blackwell Companion to Aristotle hand? “Impetus,” “momentum,” much less “inertia,” are not possible answers. There must be a mover, distinct (at least in some sense) from the thing moved, which is exercising its Formal motive capacity at every moment of the projectile’s flight (see Phys VIII. 10 266b29— The formal cause of a thing is the essential property that 267a11). Similarly, in every case of animal makes it the kind of thing it is. In Metaphysics Book generation, there is always some thing responΑ Aristotle emphasizes that form is closely related to sible for the continuity of that generation, alessence and definition. He says for example that the ratio though it may do so by way of some intervening 2:1, and number in general, is the cause of the octave. instrument (Phys II.3 194b35—195a3).[12] — R.J. Hankinson, “Causes” in Blackwell “Another [cause] is the form and the Companion to Aristotle exemplar: this is the formula (logos) of the essence (to ti en einai), and its genera, for instance the ratio 2:1 of the octave” (Phys 11.3 194b26—8)... Form is not just shape... Final We are asking (and this is the connection with essence, particularly in its canonical The final cause is that for the sake of which something Aristotelian formulation) what it is to be takes place, its aim or teleological purpose: for a germisome thing. And it is a feature of musical nating seed, it is the adult plant,[13] for a ball at the top of harmonics (first noted and wondered at by the a ramp, it is coming to rest at the bottom, for an eye, it is Pythagoreans) that intervals of this type do seeing, for a knife, it is cutting. indeed exhibit this ratio in some form in the instruments used to create them (the length Goals have an explanatory function: that of pipes, of strings, etc.). In some sense, the is a commonplace, at least in the context of ratio explains what all the intervals have in action-ascriptions. Less of a commonplace is common, why they turn out the same.[12] the view espoused by Aristotle, that finality — R.J. Hankinson, “Cause” in Blackwell and purpose are to be found throughout naCompanion to Aristotle ture. which is for him the realm of those things which contain within themselves principles of movement and rest (i.e. efficient causes); thus it makes sense to attribute Efficient purposes not only to natural things themselves, The efficient cause of a thing is the primary agency by but also to their parts: the parts of a natural which its matter took its form. For example, the efficient whole exist for the sake of the whole. As Ariscause of a baby is a parent of the same species and that of totle himself notes, “for the sake of” locutions


29.1. CONCEPTS are ambiguous: "A is for the sake of B" may mean that A exists or is undertaken in order to bring B about; or it may mean that A is for B’s benefit (An II.4 415b2—3, 20—1); but both types of finality have, he thinks. a crucial role to play in natural. as well as deliberative, contexts. Thus a man may exercise for the sake of his health: and so “health,” and not just the hope of achieving it, is the cause of his action (this distinction is not trivial). But the eyelids are for the sake of the eye (to protect it: PA II.1 3) and the eye for the sake of the animal as a whole (to help it function properly: cf. An II.7).[14] — R.J. Hankinson, “Causes” in Blackwell Companion to Aristotle

29.1.4

Biology

According to Aristotle, the science of living things proceeds by gathering observations about each natural kind of animal, organizing them into genera and species (the differentiae in History of Animals) and then going on to study the causes (in Parts of Animals and Generation of Animals, his three main biological works).[15] The four causes of animal generation can be summarized as follows. The mother and father represent the material and efficient causes, respectively. The mother provides the matter out of which the embryo is formed, while the father provides the agency that informs that material and triggers its development. The formal cause is the definition of the animal’s substantial being (GA I.1 715a4: ho logos tês ousias). The final cause is the adult form, which is the end for the sake of which development takes place.[15] — Devin M. Henry, “Generation of Animals” in Blackwell Companion to Aristotle

Organism and mechanism Main articles: Organism (philosophy) and Mechanism (philosophy) The four elements make up the uniform materials such as blood, flesh and bone, which are themselves the matter out of which are created the non-uniform organs of the body (e.g. the heart, liver and hands) “which in turn, as parts, are matter for the functioning body as a whole (PA II. 1 646a 13—24)".[11] [There] is a certain obvious conceptual economy about the view that in natural

317 processes naturally constituted things simply seek to realize in full actuality the potentials contained within them (indeed, this is what is for them to be natural); on the other hand, as the detractors of Aristotelianism from the seventeenth century on were not slow to point out, this economy is won at the expense of any serious empirical content. Mechanism, at least as practiced by Aristotle’s contemporaries and predecessors, may have been explanatorily inadequate — but at least it was an attempt at a general account given in reductive terms of the lawlike connections between things. Simply introducing what later reductionists were to scoff at as “occult qualities” does not explain — it merely, in the manner of Molière’s famous satirical joke, serves to re-describe the effect. Formal talk, or so it is said, is vacuous. Things are not however quite as bleak as this. For one thing, there’s no point in trying to engage in reductionist science if you don’t have the wherewithal, empirical and conceptual, to do so successfully: science shouldn't be simply unsubstantiated speculative metaphysics. But more than that. there is a point to describing the world in such teleologically loaded terms: it makes sense of things in a way that atomist speculations do not. And further. Aristotle’s talk of species-forms is not as empty as his opponents would insinuate. He doesn't simply say that things do what they do because that’s the sort of thing they do: the whole point of his classificatory biology, most clearly exemplified in PA, is to show what sorts of function go with what, which presuppose which and which are subservient to which. And in this sense, formal or functional biology is susceptible of a type of reductionism. We start, he tells us, with the basic animal kinds which we all pre-theoretically (although not indefeasibly) recognize (cf. PA I.4): but we then go on to show how their parts relate to one another: why it is, for instance that only blooded creatures have lungs, and how certain structures in one species are analogous or homologous to those in another (such as scales in fish, feathers in birds, hair in mammals). And the answers, for Aristotle, are to be found in the economy of functions, and how they all contribute to the overall well-being (the final cause in this sense) of the animal.[16] — R.J. Hankinson, “The Relations between the Causes” in Blackwell Companion to Aristotle

See also Organic Form.


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Psychology According to Aristotle, perception and thought are similar, though not exactly alike in that perception is concerned only with the external objects that are acting on our sense organs at any given time, whereas we can think about anything we choose. Thought is about universal forms, in so far as they've been successfully understood, based on our memory of having encountered instances of those forms directly.[17] Aristotle’s theory of cognition rests on two central pillars: his account of perception and his account of thought. Together, they make up a significant portion of his psychological writings, and his discussion of other mental states depends critically on them. These two activities, moreover, are conceived of in an analogous manner, at least with regard to their most basic forms. Each activity is triggered by its object – each, that is, is about the very thing that brings it about. This simple causal account explains the reliability of cognition: perception and thought are, in effect, transducers, bringing information about the world into our cognitive systems, because, at least in their most basic forms, they are infallibly about the causes that bring them about (An III.4 429a13–18). Other, more complex mental states are far from infallible. But they are still tethered to the world, in so far as they rest on the unambiguous and direct contact perception and thought enjoy with their objects.[17] — Victor Caston, “Phantasia and Thought” in Blackwell Companion to Aristotle

Arab polymath al-Hasan Ibn al-Haytham (Alhazen) in his Discourse on Place.[20]

29.1.6 Natural motion Terrestrial objects rise or fall, to a greater or lesser extent, according to the ratio of the four elements of which they are composed. For example, earth, the heaviest element, and water, fall toward the center of the cosmos; hence the Earth and for the most part its oceans, will have already come to rest there. At the opposite extreme, the lightest elements, air and especially fire, rise up and away from the center.[21] The elements are not proper substances in Aristotelian theory (or the modern sense of the word). Instead, they are abstractions used to explain the varying natures and behaviors of actual materials in terms of ratios between them. Motion and change are closely related in Aristotelian physics. Motion, according to Aristotle, involved a change from potentiality to actuality.[22] He gave example of four types of change.

Aristotle proposed that the speed at which two identically shaped objects sink or fall is directly proportional to their weights and inversely proportional to the density of the medium through which they move.[23] While describing their terminal velocity, Aristotle must stipulate that there would be no limit at which to compare the speed of atoms falling through a vacuum, (they could move indefinitely fast because there would be no particular place for them to come to rest in the void). Now however it is understood that at any time prior to achieving terminal velocity in a relatively resistance-free medium like air, two such objects are expected to have nearly identical speeds because both are experiencing a force of gravity proportional to their masses and have thus been accelerating at nearly the same rate. This became especially apparent 29.1.5 Natural place from the eighteenth century when partial vacuum experThe Aristotelian explanation of gravity is that all bodies iments began to be made, but some two hundred years move toward their natural place. For the elements earth earlier Galileo had already demonstrated that objects of and water, that place is the center of the (geocentric) different weights reach the ground in similar times.[24] universe;[18] the natural place of water is a concentric shell around the earth because earth is heavier; it sinks in water. The natural place of air is likewise a concentric 29.1.7 Unnatural motion shell surrounding that of water; bubbles rise in water. Finally, the natural place of fire is higher than that of air but Apart from the natural tendency of terrestrial exhalations below the innermost celestial sphere (carrying the Moon). to rise and objects to fall, unnatural or forced motion from side to side results from the turbulent collision and slidIn Book Delta of his Physics (IV.5), Aristotle defines ing of the objects as well as transmutation between the topos (place) in terms of two bodies, one of which con- elements (On Generation and Corruption). tains the other: a “place” is where the inner surface of the former (the containing body) touches the outer surface of the other (the contained body). This definition remained Chance dominant until the beginning of the 17th century, even though it had been questioned and debated by philoso- In his Physics Aristotle examines accidents phers since antiquity.[19] The most significant early cri- (συμβεβηκός, sumbebekos) that have no cause but tique was made in terms of geometry by the 11th-century chance. “Nor is there any definite cause for an accident,


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but only chance (τύχη, tukhe), namely an indefinite be temporary and self-expending, meaning that all mo(ἀόριστον) cause” (Metaphysics V, 1025a25). tion would tend toward the form of Aristotle’s natural motion. It is obvious that there are principles and causes which are generable and destructible apart from the actual processes of generation and destruction; for if this is not true, everything will be of necessity: that is, if there must necessarily be some cause, other than accidental, of that which is generated and destroyed. Will this be, or not? Yes, if this happens; otherwise not (Metaphysics VI, 1027a29).

29.1.8

Continuum and vacuum

In The Book of Healing (1027), the 11th-century Persian polymath Avicenna developed Philoponean theory into the first coherent alternative to Aristotelian theory. Inclinations in the Avicennan theory of motion were not self-consuming but permanent forces whose effects were dissipated only as a result of external agents such as air resistance, making him “the first to conceive such a permanent type of impressed virtue for non-natural motion”. Such a self-motion (mayl) is “almost the opposite of the Aristotelian conception of violent motion of the projectile type, and it is rather reminiscent of the principle of inertia, i.e. Newton’s first law of motion.”[27]

The eldest Banū Mūsā brother, Ja'far Muhammad ibn Mūsā ibn Shākir (800-873), wrote the Astral Motion and The Force of Attraction. The Persian physicist, Ibn al-Haytham (965-1039) discussed the theory of attraction between bodies. It seems that he was aware of the magnitude of acceleration due to gravity and he discovered that the heavenly bodies “were accountable to the laws of physics".[28] The Persian polymath Abū Rayhān al-Bīrūnī (973-1048) was the first to realize that acceleration is connected with non-uniform motion (as later expressed by Newton’s second law of motion).[29] During his debate with Avicenna, al-Biruni also criticized the Aristotelian theory of gravity firstly for denying the The "voids" of modern-day astronomy (such as the Local existence of levity or gravity in the celestial spheres; and, Void adjacent to our own galaxy) have the opposite effect: secondly, for its notion of circular motion being an innate [30] ultimately, bodies off-center are ejected from the void due property of the heavenly bodies. to the gravity of the material outside.[26] In 1121, al-Khazini, in The Book of the Balance of Wisdom, proposed that the gravity and gravitational potential energy of a body varies depending on its distance from 29.1.9 Speed, weight and resistance the centre of the Earth.[31] Hibat Allah Abu'l-Barakat alBaghdaadi (1080–1165) wrote al-Mu'tabar, a critique of The ideal speed of a terrestrial object is directly propor- Aristotelian physics where he negated Aristotle’s idea that tional to its weight. In nature however, vacuum does not a constant force produces uniform motion, as he realized occur, the matter obstructing an object’s path is a limiting that a force applied continuously produces acceleration, a factor that is inversely proportional to the viscosity of the fundamental law of classical mechanics and an early foremedium. shadowing of Newton’s second law of motion.[32] Like Newton, he described acceleration as the rate of change of speed.[33] Aristotle argues against the indivisibles of Democritus (which differ considerably from the historical and the modern use of the term "atom"). As a place without anything existing at or within it, Aristotle argued against the possibility of a vacuum or void. Because he believed that the speed of an object’s motion is proportional to the force being applied (or, in the case of natural motion, the object’s weight) and inversely proportional to the viscosity of the medium, he reasoned that objects moving in a void would move indefinitely fast – and thus any and all objects surrounding the void would immediately fill it. The void, therefore, could never form.[25]

29.2 Medieval commentary Main article: Theory of impetus The Aristotelian theory of motion came under criticism and modification during the Middle Ages. Modifications began with John Philoponus in the 6th century, who partly accepted Aristotle’s theory that “continuation of motion depends on continued action of a force” but modified it to include his idea that a hurled body also acquires an inclination (or “motive power”) for movement away from whatever caused it to move, an inclination that secures its continued motion. This impressed virtue would

In the 14th century, Jean Buridan developed the theory of impetus as an alternative to the Aristotelian theory of motion. The theory of impetus was a precursor to the concepts of inertia and momentum in classical mechanics.[34] Buridan and Albert of Saxony also refer to Abu'l-Barakat in explaining that the acceleration of a falling body is a result of its increasing impetus.[35] In the 16th century, Al-Birjandi discussed the possibility of the Earth’s rotation and, in his analysis of what might occur if the Earth were rotating, developed a hypothesis similar to Galileo's notion of “circular inertia”.[36] He described it in terms of the following observational test: “The small or large rock will fall to the


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CHAPTER 29. ARISTOTELIAN PHYSICS Earth along the path of a line that is perpendicular to the plane (sath) of the horizon; this is witnessed by experience (tajriba). And this perpendicular is away from the tangent point of the Earth’s sphere and the plane of the perceived (hissi) horizon. This point moves with the motion of the Earth and thus there will be no difference in place of fall of the two rocks.”[37]

jects revolving around a body other than the Earth – and noted the phases of Venus, which demonstrated that Venus (and, by implication, Mercury) traveled around the Sun, not the Earth.

29.3 Life and death of Aristotelian physics

In a relatively dense medium such as water, a heavier body falls faster than a lighter one. This led Aristotle to speculate that the rate of falling is proportional to the weight and inversely proportional to the density of the medium. From his experience with objects falling in water, he concluded that water is approximately ten times denser than air. By weighing a volume of compressed air, Galileo showed that this overestimates the density of air by a factor of forty.[39] From his experiments with inclined planes, he concluded that if friction is neglected, all bodies fall at the same rate (which is also not true, since not only friction but also density of the medium relative to density of the bodies has to be negligible. Aristotle correctly noticed that medium density is a factor but focused on body weight instead of density. Galileo neglected medium density which led him to correct conclusion for vacuum).

According to legend, Galileo dropped balls of various densities from the Tower of Pisa and found that lighter and heavier ones fell at almost the same speed. His experiments actually took place using balls rolling down inclined planes, a form of falling sufficiently slow to be measured without advanced instruments.

Galileo also advanced a theoretical argument to support his conclusion. He asked if two bodies of different weights and different rates of fall are tied by a string, does the combined system fall faster because it is now more massive, or does the lighter body in its slower fall hold back the heavier body? The only convincing answer is neither: all the systems fall at the same rate.[38] Aristotle depicted by Rembrandt.

The reign of Aristotelian physics, the earliest known speculative theory of physics, lasted almost two millennia. After the work of many pioneers such as Copernicus, Tycho Brahe, Galileo, Descartes and Newton, it became generally accepted that Aristotelian physics was neither correct nor viable.[5] Despite this, it survived as a scholastic pursuit well into the seventeenth century, until universities amended their curricula. In Europe, Aristotle’s theory was first convincingly discredited by Galileo’s studies. Using a telescope, Galileo observed that the Moon was not entirely smooth, but had craters and mountains, contradicting the Aristotelian idea of the incorruptibly perfect smooth Moon. Galileo also criticized this notion theoretically; a perfectly smooth Moon would reflect light unevenly like a shiny billiard ball, so that the edges of the moon’s disk would have a different brightness than the point where a tangent plane reflects sunlight directly to the eye. A rough moon reflects in all directions equally, leading to a disk of approximately equal brightness which is what is observed.[38] Galileo also observed that Jupiter has moons – i.e. ob-

Followers of Aristotle were aware that the motion of falling bodies was not uniform, but picked up speed with time. Since time is an abstract quantity, the peripatetics postulated that the speed was proportional to the distance. Galileo established experimentally that the speed is proportional to the time, but he also gave a theoretical argument that the speed could not possibly be proportional to the distance. In modern terms, if the rate of fall is proportional to the distance, the differential expression for the distance y travelled after time t is:

dy ∝y dt with the condition that y(0) = 0 . Galileo demonstrated that this system would stay at y = 0 for all time. If a perturbation set the system into motion somehow, the object would pick up speed exponentially in time, not quadratically.[39] Standing on the surface of the Moon in 1971, David Scott famously repeated Galileo’s experiment by dropping a feather and a hammer from each hand at the same time.


29.7. REFERENCES

321

In the absence of a substantial atmosphere, the two ob- [10] Aristotle, “Book 5, section 1013a”, Metaphysics, Hugh Tredennick (trans.) Aristotle in 23 Volumes, Vols. 17, jects fell and hit the Moon’s surface at the same time. 18, Cambridge, MA, Harvard University Press; Lon-

The first convincing mathematical theory of gravity – don, William Heinemann Ltd. 1933, 1989; (hosted at in which two masses are attracted toward each other by perseus.tufts.edu.) Aristotle also discusses the four causes a force whose effect decreases according to the inverse in his Physics, Book B, chapter 3. square of the distance between them – was Newton’s law of universal gravitation. This, in turn, was replaced by [11] Hankinson, R.J. “The Theory of the Physics”. Blackwell Companion to Aristotle. p. 216. the General theory of relativity due to Albert Einstein. Further information: Gravity

[12] Hankinson, R.J. “Causes”. Blackwell Companion to Aristotle. p. 217. [13] Aristotle. Parts of Animals I.1.

29.4 See also

[14] Hankinson, R.J. “Causes”. Blackwell Companion to Aristotle. p. 218.

Minima naturalia, a hylomorphic concept suggested by Aristotle broadly analogous in Peripatetic and Scholastic physical speculation to the atoms of Epicureanism.

[15] Henry, Devin M. (2009). “Generation of Animals”. Blackwell Companion to Aristotle. p. 368.

29.5 Works

[17] Caston, Victor (2009). “Phantasia and Thought”. Blackwell Companion to Aristotle. pp. 322–2233.

29.6 Notes

[18] De Caelo II. 13-14.

[16] Hankinson, R.J. “Causes”. Blackwell Companion to Aristotle. p. 222.

[19] For instance, by Simplicius in his Corollaries on Place. ^

a Here, the term “Earth” does not refer to planet Earth, [20] El-Bizri, Nader (2007). “In Defence of the Sovereignty of known by modern science to be composed of a large numPhilosophy: al-Baghdadi’s Critique of Ibn al-Haytham’s ber of chemical elements. Modern chemical elements are Geometrisation of Place”. Arabic Sciences and Philosonot conceptually similar to Aristotle’s elements; the term phy. 17: 57–80. doi:10.1017/s0957423907000367. “air”, for instance, does not refer to breathable air.

29.7 References [1] Lang, H.S. (2007). The Order of Nature in Aristotle’s Physics: Place and the Elements. Cambridge University Press. p. 290. ISBN 9780521042291. [2] White, Michael J. (2009). “Aristotle on the Infinite, Space, and Time”. Blackwell Companion to Aristotle. p. 260. [3] “Physics of Aristotle vs. The Physics of Galileo”. Archived from the original on 11 April 2009. Retrieved 6 April 2009. [4] "www.hep.fsu.edu" (PDF). Retrieved 26 March 2007. [5] “Aristotle’s physics”. Retrieved 6 April 2009. [6] Aristotle, meteorology. [7] Sorabji, R. (2005). The Philosophy of the Commentators, 200-600 AD: Physics. G - Reference, Information and Interdisciplinary Subjects Series. Cornell University Press. p. 352. ISBN 978-0-8014-8988-4. LCCN 2004063547. [8] Aristotle, Physics 194 b17–20; see also: Posterior Analytics 71 b9–11; 94 a20. [9] “Four Causes”. Falcon, Andrea. Aristotle on Causality. Stanford Encyclopedia of Philosophy 2008.

[21] Tim Maudlin (2012-07-22). Philosophy of Physics: Space and Time: Space and Time (Princeton Foundations of Contemporary Philosophy) (p. 2). Princeton University Press. Kindle Edition. “The element earth’s natural motion is to fall— that is, to move downward. Water also strives to move downward but with less initiative than earth: a stone will sink though water, demonstrating its overpowering natural tendency to descend. Fire naturally rises, as anyone who has watched a bonfire can attest, as does air, but with less vigor.” [22] Bodnar, Istvan, “Aristotle’s Natural Philosophy” in The Stanford Encyclopedia of Philosophy (Spring 2012 Edition, ed. Edward N. Zalta). [23] Gindikin, S.G. (1988). Tales of Physicists and Mathematicians. Birkh. p. 29. ISBN 9780817633172. LCCN 87024971.

[24] Lindberg, D. (2008), The beginnings of western science: The European scientific tradition in philosophical, religious, and institutional context, prehistory to AD 1450 (2nd ed.), University of Chicago Press. [25] Land, Helen, The Order of Nature in Aristotle’s Physics: Place and the Elements (1998). [26] Tully; Shaya; Karachentsev; Courtois; Kocevski; Rizzi; Peel (2008). “Our Peculiar Motion Away From the Local Void”. The Astrophysical Journal. 676 (1): 184. arXiv:0705.4139 . Bibcode:2008ApJ...676..184T. doi:10.1086/527428.


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[27] Aydin Sayili (1987), “Ibn Sīnā and Buridan on the Motion of the Projectile”, Annals of the New York Academy of Sciences 500 (1): 477–482 [477]: According to Aristotle, continuation of motion depends on continued action of a force. The motion of a hurled body, therefore, requires elucidation. Aristotle maintained that the air of the atmosphere was responsible for the continuation of such motion. John Philoponos of the 6th century rejected this Aristotelian view. He claimed that the hurled body acquires a motive power or an inclination for forced movement from the agent producing the initial motion and that this power or condition and not the ambient medium secures the continuation of such motion. According to Philoponos this impressed virtue was temporary. It was a self-expending inclination, and thus the violent motion thus produced comes to an end and changes into natural motion. Ibn Sina adopted this idea in its rough outline, but the violent inclination as he conceived it was a non-self-consuming one. It was a permanent force whose effect got dissipated only as a result of external agents such as air resistance. He is apparently the first to conceive such a permanent type of impressed virtue for nonnatural motion. [...] Indeed, self-motion of the type conceived by Ibn Sina is almost the opposite of the Aristotelian conception of violent motion of the projectile type, and it is rather reminiscent of the principle of inertia, i.e., Newton’s first law of motion. [28] Duhem, Pierre (1908, 1969). To Save the Phenomena: An Essay on the Idea of Physical theory from Plato to Galileo, University of Chicago Press, Chicago, p. 28. [29] O'Connor, John J.; Robertson, Edmund F., “Al-Biruni”, MacTutor History of Mathematics archive, University of St Andrews. [30] Rafik Berjak and Muzaffar Iqbal, “Ibn Sina--Al-Biruni correspondence”, Islam & Science, June 2003. [31] Mariam Rozhanskaya and I. S. Levinova (1996), “Statics”, in Roshdi Rashed, ed., Encyclopedia of the History of Arabic Science, vol. 2, pp. 614–642 [621-622]. (Routledge, London and New York.) [32] Shlomo Pines (1970). “Abu'l-Barakāt al-Baghdādī, Hibat Allah”. Dictionary of Scientific Biography. 1. New York: Charles Scribner’s Sons. pp. 26–28. ISBN 0-684-101149. (cf. Abel B. Franco (October 2003). “Avempace, Projectile Motion, and Impetus Theory”, Journal of the History of Ideas 64 (4), pp. 521–546 [528].) [33] A. C. Crombie, Augustine to Galileo 2, p. 67. [34] Aydin Sayili (1987), “Ibn Sīnā and Buridan on the Motion of the Projectile”, Annals of the New York Academy of Sciences 500 (1): 477–482

[35] Gutman, Oliver (2003). Pseudo-Avicenna, Liber Celi Et Mundi: A Critical Edition. Brill Publishers. p. 193. ISBN 90-04-13228-7. [36] (Ragep 2001b, pp. 63–4) [37] (Ragep 2001a, pp. 152–3) [38] Galileo Galilei, Dialogue Concerning the Two Chief World Systems. [39] Galileo Galilei, Two New Sciences.

29.8 Sources • Ragep, F. Jamil (2001a). “Tusi and Copernicus: The Earth’s Motion in Context”. Science in Context. Cambridge University Press. 14 (1–2): 145–163. doi:10.1017/s0269889701000060. • Ragep, F. Jamil; Al-Qushji, Ali (2001b). “Freeing Astronomy from Philosophy: An Aspect of Islamic Influence on Science”. Osiris, 2nd Series. 16 (Science in Theistic Contexts: Cognitive Dimensions): 49–64 and 66–71. Bibcode:2001Osir...16...49R. doi:10.1086/649338. • H. Carteron (1965) “Does Aristotle Have a Mechanics?" in Articles on Aristotle 1. Science eds. Jonathan Barnes, Malcolm Schofield, Richard Sorabji (London: General Duckworth and Company Limited), 161-174.

29.9 Further reading • Katalin Martinás, “Aristotelian Thermodynamics” in Thermodynamics: history and philosophy: facts, trends, debates (Veszprém, Hungary 23–28 July 1990), pp. 285–303.


Chapter 30

Gravity For other uses, see Gravity (disambiguation). “Gravitation” and “Law of Gravity” redirect here. For other uses, see Gravitation (disambiguation) and Law of Gravity (disambiguation). Gravity, or gravitation, is a natural phenomenon by

gravitational potential. However, for most applications, gravity is well approximated by Newton’s law of universal gravitation, which postulates that gravity causes a force where two bodies of mass are directly drawn (or 'attracted') to each other according to a mathematical relationship, where the attractive force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Gravity is the weakest of the four fundamental interactions of nature. The gravitational attraction is approximately 1038 times weaker than the strong force, 1036 times weaker than the electromagnetic force and 1029 times weaker than the weak force. As a consequence, gravity has a negligible influence on the behavior of subatomic particles, and plays no role in determining the internal properties of everyday matter (but see quantum gravity). On the other hand, gravity is the dominant interaction at the macroscopic scale, and is the cause of the formation, shape and trajectory (orbit) of astronomical bodies. It is responsible for various phenomena observed Hammer and feather drop: Apollo 15 astronaut David Scott on on Earth and throughout the Universe; for example, it the Moon enacting the legend of Galileo’s gravity experiment. causes the Earth and the other planets to orbit the Sun, (1.38 MB, ogg/Theora format). the Moon to orbit the Earth, the formation of tides, the formation and evolution of the Solar System, stars and which all things with mass are brought toward (or gravgalaxies. itate toward) one another, including planets, stars and galaxies. Since energy and mass are equivalent, all forms The earliest instance of gravity in the Universe, possiof energy, including light, also cause gravitation and are bly in the form of quantum gravity, supergravity or a under the influence of it. On Earth, gravity gives weight to gravitational singularity, along with ordinary space and physical objects and causes the ocean tides. The gravita- time, developed during the Planck epoch (up to 10−43 tional attraction of the original gaseous matter present in seconds after the birth of the Universe), possibly from a the Universe caused it to begin coalescing, forming stars primeval state, such as a false vacuum, quantum vacuum — and the stars to group together into galaxies — so grav- or virtual particle, in a currently unknown manner.[2] For ity is responsible for many of the large scale structures in this reason, in part, pursuit of a theory of everything, the the Universe. Gravity has an infinite range, although its merging of the general theory of relativity and quantum mechanics (or quantum field theory) into quantum graveffects become increasingly weaker on farther objects. ity, has become an area of research. Gravity is most accurately described by the general theory of relativity (proposed by Albert Einstein in 1915) which describes gravity not as a force, but as a consequence of the curvature of spacetime caused by the un- 30.1 History of gravitational theeven distribution of mass/energy. The most extreme exory ample of this curvature of spacetime is a black hole, from which nothing can escape once past its event horizon, not even light.[1] More gravity results in gravitational time di- Main article: History of gravitational theory lation, where time lapses more slowly at a lower (stronger) 323


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CHAPTER 30. GRAVITY

Earlier Concepts of Gravity

While the modern European thinkers are rightly credited with development of gravitational theory, there were pre-existing ideas which had identified the force of gravity. Some of the earliest descriptions came from early mathematician-astronomers, such as Aryabhata, who had identified the force of gravity to explain why objects do not fall out when the Earth rotates.[3]

lished Principia, which hypothesizes the inverse-square law of universal gravitation. In his own words, “I deduced that the forces which keep the planets in their orbs must [be] reciprocally as the squares of their distances from the centers about which they revolve: and thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the Earth; and found them answer pretty nearly.”[6] The equation is the following:

2 Later, the works of Brahmagupta referred to the presence F = G mr1 m 2 of this force. Where F is the force, m1 and m2 are the masses of the objects interacting, r is the distance between the centers of the masses and G is the gravitational constant.

30.1.2

Scientific revolution

Modern work on gravitational theory began with the work of Galileo Galilei in the late 16th and early 17th centuries. In his famous (though possibly apocryphal[4] ) experiment dropping balls from the Tower of Pisa, and later with careful measurements of balls rolling down inclines, Galileo showed that gravitational acceleration is the same for all objects. This was a major departure from Aristotle's belief that heavier objects have a higher gravitational acceleration.[5] Galileo postulated air resistance as the reason that objects with less mass may fall slower in an atmosphere. Galileo’s work set the stage for the formulation of Newton’s theory of gravity.

30.1.3

Newton’s theory of gravitation

Newton’s theory enjoyed its greatest success when it was used to predict the existence of Neptune based on motions of Uranus that could not be accounted for by the actions of the other planets. Calculations by both John Couch Adams and Urbain Le Verrier predicted the general position of the planet, and Le Verrier’s calculations are what led Johann Gottfried Galle to the discovery of Neptune. A discrepancy in Mercury's orbit pointed out flaws in Newton’s theory. By the end of the 19th century, it was known that its orbit showed slight perturbations that could not be accounted for entirely under Newton’s theory, but all searches for another perturbing body (such as a planet orbiting the Sun even closer than Mercury) had been fruitless. The issue was resolved in 1915 by Albert Einstein's new theory of general relativity, which accounted for the small discrepancy in Mercury’s orbit.

Main article: Newton’s law of universal gravitation In 1687, English mathematician Sir Isaac Newton pub- Although Newton’s theory has been superseded by the Einstein's general relativity, most modern non-relativistic gravitational calculations are still made using Newton’s theory because it is simpler to work with and it gives sufficiently accurate results for most applications involving sufficiently small masses, speeds and energies.

30.1.4 Equivalence principle

Sir Isaac Newton, an English physicist who lived from 1642 to 1727

The equivalence principle, explored by a succession of researchers including Galileo, Loránd Eötvös, and Einstein, expresses the idea that all objects fall in the same way, and that the effects of gravity are indistinguishable from certain aspects of acceleration and deceleration. The simplest way to test the weak equivalence principle is to drop two objects of different masses or compositions in a vacuum and see whether they hit the ground at the same time. Such experiments demonstrate that all objects fall at the same rate when other forces (such as air resistance and electromagnetic effects) are negligible. More sophisticated tests use a torsion balance of a type invented by Eötvös. Satellite experiments, for example STEP, are planned for more accurate experiments in space.[7] Formulations of the equivalence principle include:


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• The weak equivalence principle: The trajectory of a point mass in a gravitational field depends only on its initial position and velocity, and is independent of its composition.[8]

Einstein discovered the field equations of general relativity, which relate the presence of matter and the curvature of spacetime and are named after him. The Einstein field equations are a set of 10 simultaneous, non-linear, differential equations. The solutions of the field equations • The Einsteinian equivalence principle: The outcome are the components of the metric tensor of spacetime. A of any local non-gravitational experiment in a freely metric tensor describes a geometry of spacetime. The falling laboratory is independent of the velocity of geodesic paths for a spacetime are calculated from the the laboratory and its location in spacetime.[9] metric tensor. • The strong equivalence principle requiring both of Solutions the above. Notable solutions of the Einstein field equations include:

30.1.5

General relativity

See also: Introduction to general relativity In general relativity, the effects of gravitation are ascribed

• The Schwarzschild solution, which describes spacetime surrounding a spherically symmetric nonrotating uncharged massive object. For compact enough objects, this solution generated a black hole with a central singularity. For radial distances from the center which are much greater than the Schwarzschild radius, the accelerations predicted by the Schwarzschild solution are practically identical to those predicted by Newton’s theory of gravity. • The Reissner-Nordström solution, in which the central object has an electrical charge. For charges with a geometrized length which are less than the geometrized length of the mass of the object, this solution produces black holes with double event horizons.

Two-dimensional analogy of spacetime distortion generated by the mass of an object. Matter changes the geometry of spacetime, this (curved) geometry being interpreted as gravity. White lines do not represent the curvature of space but instead represent the coordinate system imposed on the curved spacetime, which would be rectilinear in a flat spacetime.

• The Kerr solution for rotating massive objects. This solution also produces black holes with multiple event horizons. • The Kerr-Newman solution for charged, rotating massive objects. This solution also produces black holes with multiple event horizons.

• The cosmological Friedmann-Lemaître-RobertsonWalker solution, which predicts the expansion of the to spacetime curvature instead of a force. The starting Universe. point for general relativity is the equivalence principle, which equates free fall with inertial motion and describes free-falling inertial objects as being accelerated relative to non-inertial observers on the ground.[10][11] In Newtonian Tests physics, however, no such acceleration can occur unless [12] at least one of the objects is being operated on by a force. The tests of general relativity included the following: Einstein proposed that spacetime is curved by matter, and that free-falling objects are moving along locally straight paths in curved spacetime. These straight paths are called geodesics. Like Newton’s first law of motion, Einstein’s theory states that if a force is applied on an object, it would deviate from a geodesic. For instance, we are no longer following geodesics while standing because the mechanical resistance of the Earth exerts an upward force on us, and we are non-inertial on the ground as a result. This explains why moving along the geodesics in spacetime is considered inertial.

• General relativity accounts for the anomalous perihelion precession of Mercury.[13] • The prediction that time runs slower at lower potentials (gravitational time dilation) has been confirmed by the Pound–Rebka experiment (1959), the Hafele–Keating experiment, and the GPS. • The prediction of the deflection of light was first confirmed by Arthur Stanley Eddington from his observations during the Solar eclipse of May 29,


326

CHAPTER 30. GRAVITY 1919.[14][15] Eddington measured starlight deflections twice those predicted by Newtonian corpuscular theory, in accordance with the predictions of general relativity. However, his interpretation of the results was later disputed.[16] More recent tests using radio interferometric measurements of quasars passing behind the Sun have more accurately and consistently confirmed the deflection of light to the degree predicted by general relativity.[17] See also gravitational lens.

30.2 Specifics 30.2.1 Earth’s gravity Main article: Earth’s gravity

Every planetary body (including the Earth) is surrounded by its own gravitational field, which can be conceptualized with Newtonian physics as exerting an attractive The time delay of light passing close to a massive force on all objects. Assuming a spherically symmetrical object was first identified by Irwin I. Shapiro in 1964 planet, the strength of this field at any given point above the surface is proportional to the planetary body’s mass in interplanetary spacecraft signals. and inversely proportional to the square of the distance Gravitational radiation has been indirectly con- from the center of the body. firmed through studies of binary pulsars. On 11 The strength of the gravitational field is numerically equal February 2016, the LIGO and Virgo collaborations to the acceleration of objects under its influence. The rate announced the first observation of a gravitational of acceleration of falling objects near the Earth’s surface wave. varies very slightly depending on latitude, surface features Alexander Friedmann in 1922 found that Einstein such as mountains and ridges, and perhaps unusually high [23] For purposes of weights equations have non-stationary solutions (even in the or low sub-surface densities. and measures, a standard gravity value is defined by the presence of the cosmological constant). In 1927 International Bureau of Weights and Measures, under the Georges Lemaître showed that static solutions of the International System of Units (SI). Einstein equations, which are possible in the presence of the cosmological constant, are unstable, and That value, denoted g, is g = 9.80665 m/s2 (32.1740 therefore the static Universe envisioned by Einstein ft/s2 ).[24][25] could not exist. Later, in 1931, Einstein himself 2 agreed with the results of Friedmann and Lemaître. The standard value of 9.80665 m/s is the one origiThus general relativity predicted that the Universe nally adopted by the International Committee on Weights had to be non-static—it had to either expand or con- and Measures in 1901 for 45° latitude, even though it to be too high by about five parts in ten tract. The expansion of the Universe discovered by has been shown [26] [18] thousand. This value has persisted in meteorology and Edwin Hubble in 1929 confirmed this prediction. in some standard atmospheres as the value for 45° latiThe theory’s prediction of frame dragging was con- tude even though it applies more precisely to latitude of sistent with the recent Gravity Probe B results.[19] 45°32'33”.[27]

Assuming the standardized value for g and ignoring air resistance, this means that an object falling freely near the Earth’s surface increases its velocity by 9.80665 m/s (32.1740 ft/s or 22 mph) for each second of its descent. Thus, an object starting from rest will attain a velocity of 9.80665 m/s (32.1740 ft/s) after one second, approximately 19.62 m/s (64.4 ft/s) after two seconds, and so 30.1.6 Gravity and quantum mechanics on, adding 9.80665 m/s (32.1740 ft/s) to each resulting Main articles: Graviton and Quantum gravity velocity. Also, again ignoring air resistance, any and all objects, when dropped from the same height, will hit the In the decades after the discovery of general relativity, it ground at the same time. was realized that general relativity is incompatible with According to Newton’s 3rd Law, the Earth itself experiquantum mechanics.[20] It is possible to describe gravity ences a force equal in magnitude and opposite in direction in the framework of quantum field theory like the other to that which it exerts on a falling object. This means that fundamental forces, such that the attractive force of grav- the Earth also accelerates towards the object until they ity arises due to exchange of virtual gravitons, in the same collide. Because the mass of the Earth is huge, however, way as the electromagnetic force arises from exchange of the acceleration imparted to the Earth by this opposite virtual photons.[21][22] This reproduces general relativity force is negligible in comparison to the object’s. If the in the classical limit. However, this approach fails at short object doesn't bounce after it has collided with the Earth, distances of the order of the Planck length,[20] where a each of them then exerts a repulsive contact force on the more complete theory of quantum gravity (or a new ap- other which effectively balances the attractive force of proach to quantum mechanics) is required. gravity and prevents further acceleration. • General relativity predicts that light should lose its energy when traveling away from massive bodies through gravitational redshift. This was verified on earth and in the solar system around 1960.


30.2. SPECIFICS

327

−7 — – −6 — – −5 — – −4 — – −3 — – −2 — – −1 — Equations for a falling body near – the surface of the Earth 0—

The force of gravity on Earth is the resultant (vector sum) of two forces:[28] (a) The gravitational attraction in accordance with Newton’s universal law of gravitation, and (b) the centrifugal force, which results from the choice of an earthbound, rotating frame of reference. The force of gravity is the weakest at the equator because of the centrifugal force caused by the Earth’s rotation and because points on the equator are furthest from the center of the Earth. The force of gravity varies with latitude and increases from about 9.780 m/s2 at the Equator to about 9.832 m/s2 at the poles.

30.2.2

Main article: Equations for a falling body Under an assumption of constant gravitational attraction, Newton’s law of universal gravitation simplifies to F = mg, where m is the mass of the body and g is a constant vector with an average magnitude of 9.81 m/s2 on Earth. This resulting force is the object’s weight. The acceleration due to gravity is equal to this g. An initially stationary object which is allowed to fall freely under gravity drops a distance which is proportional to the square of the elapsed time. The image on the right, spanning half a second, was captured with a stroboscopic flash at 20 flashes per second. During the first 1 ⁄20 of a second the ball drops one unit of distance (here, a unit is about 12 mm); by 2 ⁄20 it has dropped at total of 4 units; by 3 ⁄20 , 9 units and so on.

cosmic expansion Earliest light cosmic speed-up Solar System water

Single-celled life photosynthesis

Multicellular life Land life Earliest gravity Dark energy Dark matter

← Earliest universe (−13.8) ← Earliest galaxy ← Under the same constant gravity assumptions, the Earliest quasar potential energy, Ep, of a body at height h is given by Ep = ← mgh (or Ep = Wh, with W meaning weight). This expres- Omega Centauri forms sion is valid only over small distances h from the surface ← 2 of the Earth. Similarly, the expression h = v2g for the Andromeda Galaxy forms maximum height reached by a vertically projected body ← with initial velocity v is useful for small heights and small Milky Way Galaxy initial velocities only. spiral arms form ←

30.2.3

Gravity and astronomy

Nature timeline view • discuss •

−13 — – −12 — – −11 — – −10 — – −9 — – −8 — –

NGC 188 star cluster forms

← Alpha Centauri forms

← Earliest Earth (−4.54) ← Earliest life ← Earliest oxygen ← Atmospheric oxygen

← Earliest sexual reproduction ← Cambrian explosion


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CHAPTER 30. GRAVITY

← Earliest humans

L i f e P r i m o r d i a l Axis scale: billions of years.

time in binary pulsar systems such as PSR B1913+16. It is believed that neutron star mergers and black hole formation may create detectable amounts of gravitational radiation. Gravitational radiation observatories such as the Laser Interferometer Gravitational Wave Observatory (LIGO) have been created to study the problem. In February 2016, the Advanced LIGO team announced that they had detected gravitational waves from a black hole collision. On September 14, 2015 LIGO registered gravitational waves for the first time, as a result of the collision of two black holes 1.3 billion light-years from Earth.[30][31] This observation confirms the theoretical predictions of Einstein and others that such waves exist. The event confirms that binary black holes exist. It also opens the way for practical observation and understanding of the nature of gravity and events in the Universe including the Big Bang and what happened after it.[32][33]

30.2.5 Speed of gravity Main article: Speed of gravity

also see {{Human timeline}} and {{Life timeline}}

The application of Newton’s law of gravity has enabled the acquisition of much of the detailed information we have about the planets in the Solar System, the mass of the Sun, and details of quasars; even the existence of dark matter is inferred using Newton’s law of gravity. Although we have not traveled to all the planets nor to the Sun, we know their masses. These masses are obtained by applying the laws of gravity to the measured characteristics of the orbit. In space an object maintains its orbit because of the force of gravity acting upon it. Planets orbit stars, stars orbit galactic centers, galaxies orbit a center of mass in clusters, and clusters orbit in superclusters. The force of gravity exerted on one object by another is directly proportional to the product of those objects’ masses and inversely proportional to the square of the distance between them.

In December 2012, a research team in China announced that it had produced measurements of the phase lag of Earth tides during full and new moons which seem to prove that the speed of gravity is equal to the speed of light.[34] This means that if the Sun suddenly disappeared, the Earth would keep orbiting it normally for 8 minutes, which is the time light takes to travel that distance. The team’s findings were released in the Chinese Science Bulletin in February 2013.[35]

30.3 Anomalies and discrepancies

There are some observations that are not adequately accounted for, which may point to the need for better theoThe earliest gravity (possibly in the form of quantum ries of gravity or perhaps be explained in other ways. gravity, supergravity or a gravitational singularity), along • Extra-fast stars: Stars in galaxies follow a with ordinary space and time, developed during the distribution of velocities where stars on the outskirts Planck epoch (up to 10−43 seconds after the birth of the are moving faster than they should according to the Universe), possibly from a primeval state (such as a false observed distributions of normal matter. Galaxies vacuum, quantum vacuum or virtual particle), in a curwithin galaxy clusters show a similar pattern. Dark rently unknown manner.[2] matter, which would interact through gravitation but not electromagnetically, would account for the discrepancy. Various modifications to Newtonian dy30.2.4 Gravitational radiation namics have also been proposed. Main article: Gravitational wave • Flyby anomaly: Various spacecraft have experienced greater acceleration than expected during According to general relativity, gravitational radiation is gravity assist maneuvers. generated in situations where the curvature of spacetime is oscillating, such as is the case with co-orbiting objects. • Accelerating expansion: The metric expansion of The gravitational radiation emitted by the Solar System space seems to be speeding up. Dark energy has is far too small to measure. However, gravitational radibeen proposed to explain this. A recent alternaation has been indirectly observed as an energy loss over tive explanation is that the geometry of space is not


30.5. SEE ALSO

329

homogeneous (due to clusters of galaxies) and that 30.4.2 Modern alternative theories when the data are reinterpreted to take this into ac• Brans–Dicke theory of gravity (1961) [40] count, the expansion is not speeding up after all,[36] [37] however this conclusion is disputed. • Induced gravity (1967), a proposal by Andrei Sakharov according to which general relativity • Anomalous increase of the astronomical unit: might arise from quantum field theories of matter Recent measurements indicate that planetary orbits are widening faster than if this were solely through the Sun losing mass by radiating energy. • Extra energetic photons: Photons travelling through galaxy clusters should gain energy and then lose it again on the way out. The accelerating expansion of the Universe should stop the photons returning all the energy, but even taking this into account photons from the cosmic microwave background radiation gain twice as much energy as expected. This may indicate that gravity falls off faster than inversesquared at certain distance scales.[38] • Extra massive hydrogen clouds: The spectral lines of the Lyman-alpha forest suggest that hydrogen clouds are more clumped together at certain scales than expected and, like dark flow, may indicate that gravity falls off slower than inverse-squared at certain distance scales.[38] • Power: Proposed extra dimensions could explain why the gravity force is so weak.[39]

30.4 Alternative theories Main article: Alternatives to general relativity

30.4.1

Historical alternative theories

• Aristotelian theory of gravity • Le Sage’s theory of gravitation (1784) also called LeSage gravity, proposed by Georges-Louis Le Sage, based on a fluid-based explanation where a light gas fills the entire Universe. • Ritz’s theory of gravitation, Ann. Chem. Phys. 13, 145, (1908) pp. 267–271, Weber-Gauss electrodynamics applied to gravitation. Classical advancement of perihelia. • Nordström’s theory of gravitation (1912, 1913), an early competitor of general relativity. • Kaluza Klein theory (1921) • Whitehead’s theory of gravitation (1922), another early competitor of general relativity.

• ƒ(R) gravity (1970) • Horndeski theory (1974) [41] • Supergravity (1976) • String theory • In the modified Newtonian dynamics (MOND) (1981), Mordehai Milgrom proposes a modification of Newton’s Second Law of motion for small accelerations [42] • The self-creation cosmology theory of gravity (1982) by G.A. Barber in which the Brans-Dicke theory is modified to allow mass creation • Loop quantum gravity (1988) by Carlo Rovelli, Lee Smolin, and Abhay Ashtekar • Nonsymmetric gravitational theory (NGT) (1994) by John Moffat • Conformal gravity[43] • Tensor–vector–scalar gravity (TeVeS) (2004), a relativistic modification of MOND by Jacob Bekenstein • Gravity as an entropic force, gravity arising as an emergent phenomenon from the thermodynamic concept of entropy. • In the superfluid vacuum theory the gravity and curved space-time arise as a collective excitation mode of non-relativistic background superfluid. • Chameleon theory (2004) by Justin Khoury and Amanda Weltman. • Pressuron theory (2013) by Olivier Minazzoli and Aurélien Hees.

30.5 See also • Angular momentum • Anti-gravity, the idea of neutralizing or repelling gravity • Artificial gravity • Birkeland current • Cosmic gravitational wave background


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• Einstein–Infeld–Hoffmann equations

• Gauge gravitation theory

[5] Galileo (1638), Two New Sciences, First Day Salviati speaks: “If this were what Aristotle meant you would burden him with another error which would amount to a falsehood; because, since there is no such sheer height available on earth, it is clear that Aristotle could not have made the experiment; yet he wishes to give us the impression of his having performed it when he speaks of such an effect as one which we see.”

• Gauss’s law for gravity

[6]

• Escape velocity, the minimum velocity needed to escape from a gravity well • g-force, a measure of acceleration

• Gravitational binding energy • Gravitational wave • Gravitational wave background • Gravity assist • Gravity gradiometry • Gravity Recovery and Climate Experiment • Gravity Research Foundation

• Kepler’s third law of planetary motion

[8] Paul S Wesson (2006). Five-dimensional Physics. World Scientific. p. 82. ISBN 981-256-661-9.

• Lagrangian point • Micro-g environment, also called microgravity • Mixmaster dynamics • n-body problem

[9] Haugen, Mark P.; C. Lämmerzahl (2001). Principles of Equivalence: Their Role in Gravitation Physics and Experiments that Test Them. Springer. arXiv:gr-qc/0103067 . ISBN 978-3-540-41236-6. [10] “Gravity and Warped Spacetime”. black-holes.org. Retrieved 2010-10-16.

• Newton’s laws of motion • Pioneer anomaly

[11] Dmitri Pogosyan. “Lecture 20: Black Holes—The Einstein Equivalence Principle”. University of Alberta. Retrieved 2011-10-14.

• Scalar theories of gravitation • Speed of gravity

[12] Pauli, Wolfgang Ernst (1958). “Part IV. General Theory of Relativity”. Theory of Relativity. Courier Dover Publications. ISBN 978-0-486-64152-2.

• Standard gravitational parameter • Standard gravity

[13] Max Born (1924), Einstein’s Theory of Relativity (The 1962 Dover edition, page 348 lists a table documenting the observed and calculated values for the precession of the perihelion of Mercury, Venus, and Earth.)

• Weightlessness

30.6 Footnotes [1] “HubbleSite: Black Holes: Gravity’s Relentless Pull”. hubblesite.org. Retrieved 2016-10-07. [2] Staff. “Birth of the Universe”. University of Oregon. Retrieved September 24, 2016. - discusses "Planck time" and "Planck era" at the very beginning of the Universe • Sen, Amartya (2005). The Argumentative Indian. Allen Lane. p. 29. ISBN 978-0-7139-9687-6.

[4] Ball, Phil (June 2005). “Tall Tales”. doi:10.1038/news050613-10.

Linton, Christopher M. (2004). From Eudoxus to Einstein—A History of Mathematical Astronomy. Cambridge: Cambridge University Press. p. 225. ISBN 9780-521-82750-8. [7] M.C.W.Sandford (2008). “STEP: Satellite Test of the Equivalence Principle”. Rutherford Appleton Laboratory. Retrieved 2011-10-14.

• Jovian–Plutonian gravitational effect

[3]

• Chandrasekhar, Subrahmanyan (2003). Newton’s Principia for the common reader. Oxford: Oxford University Press. (pp.1–2). The quotation comes from a memorandum thought to have been written about 1714. As early as 1645 Ismaël Bullialdus had argued that any force exerted by the Sun on distant objects would have to follow an inverse-square law. However, he also dismissed the idea that any such force did exist. See, for example,

Nature News.

[14] Dyson, F.W.; Eddington, A.S.; Davidson, C.R. (1920). “A Determination of the Deflection of Light by the Sun’s Gravitational Field, from Observations Made at the Total Eclipse of May 29, 1919”. Phil. Trans. Roy. Soc. A. 220 (571–581): 291–333. Bibcode:1920RSPTA.220..291D. doi:10.1098/rsta.1920.0009.. Quote, p. 332: “Thus the results of the expeditions to Sobral and Principe can leave little doubt that a deflection of light takes place in the neighbourhood of the sun and that it is of the amount demanded by Einstein’s generalised theory of relativity, as attributable to the sun’s gravitational field.” [15] Weinberg, Steven (1972). Gravitation and cosmology. John Wiley & Sons.. Quote, p. 192: “About a dozen stars in all were studied, and yielded values 1.98 ± 0.11”


30.7. REFERENCES

and 1.61 ± 0.31”, in substantial agreement with Einstein’s prediction θ☉ = 1.75”." [16] Earman, John; Glymour, Clark (1980). “Relativity and Eclipses: The British eclipse expeditions of 1919 and their predecessors”. Historical Studies in the Physical Sciences. 11: 49–85. doi:10.2307/27757471.

331

[31] Castelvecchi, Davide; Witze, Witze (February 11, 2016). “Einstein’s gravitational waves found at last”. Nature News. doi:10.1038/nature.2016.19361. Retrieved 201602-11. [32] “Scientists announce finding Gravitational Waves confirming Einstein’s theory”. WorldBreakingNews.

[17] Weinberg, Steven (1972). Gravitation and cosmology. John Wiley & Sons. p. 194.

[33] “WHAT ARE GRAVITATIONAL WAVES AND WHY DO THEY MATTER?". popsci.com. Retrieved 12 February 2016.

[18] See W.Pauli, 1958, pp.219–220

[34] Chinese scientists find evidence for speed of gravity, astrowatch.com, 12/28/12.

[19] “NASA’s Gravity Probe B Confirms Two Einstein SpaceTime Theories”. Nasa.gov. Retrieved 2013-07-23. [20] Randall, Lisa (2005). Warped Passages: Unraveling the Universe’s Hidden Dimensions. Ecco. ISBN 0-06053108-8. [21] Feynman, R. P.; Morinigo, F. B.; Wagner, W. G.; Hatfield, B. (1995). Feynman lectures on gravitation. Addison-Wesley. ISBN 0-201-62734-5.

[35] TANG, Ke Yun; HUA ChangCai; WEN Wu; CHI ShunLiang; YOU QingYu; YU Dan (February 2013). “Observational evidences for the speed of the gravity based on the Earth tide” (PDF). Chinese Science Bulletin. 58 (4-5): 474–477. doi:10.1007/s11434-012-56033. Retrieved 12 June 2013. [36] Dark energy may just be a cosmic illusion, New Scientist, issue 2646, 7 March 2008.

[22] Zee, A. (2003). Quantum Field Theory in a Nutshell. Princeton University Press. ISBN 0-691-01019-6.

[37] Swiss-cheese model of the cosmos is full of holes, New Scientist, issue 2678, 18 October 2008.

[23] Nemiroff, R.; Bonnell, J., eds. (15 December 2014). “The Potsdam Gravity Potato”. Astronomy Picture of the Day. NASA.

[38] Chown, Marcus (16 March 2009). “Gravity may venture where matter fears to tread”. New Scientist. Retrieved 4 August 2013.

[24] Bureau International des Poids et Mesures (2006). “The International System of Units (SI)" (PDF) (8th ed.): 131. Retrieved 2009-11-25. Unit names are normally printed in Roman (upright) type ... Symbols for quantities are generally single letters set in an italic font, although they may be qualified by further information in subscripts or superscripts or in brackets. [25] “SI Unit rules and style conventions”. National Institute For Standards and Technology (USA). September 2004. Retrieved 2009-11-25. Variables and quantity symbols are in italic type. Unit symbols are in Roman type. [26] List, R. J. editor, 1968, Acceleration of Gravity, Smithsonian Meteorological Tables, Sixth Ed. Smithsonian Institution, Washington, D.C., p. 68. [27] U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, D.C., 1976. (Linked file is very large.) [28] Hofmann-Wellenhof, B.; Moritz, H. (2006). Physical Geodesy (2nd ed.). Springer. ISBN 978-3-211-335444. § 2.1: “The total force acting on a body at rest on the earth’s surface is the resultant of gravitational force and the centrifugal force of the earth’s rotation and is called gravity.” [29] “Milky Way Emerges as Sun Sets over Paranal”. www. eso.org. European Southern Obseevatory. Retrieved 29 April 2015. [30] Clark, Stuart (2016-02-11). “Gravitational waves: scientists announce 'we did it!' – live”. the Guardian. Retrieved 2016-02-11.

[39] CERN (20 January 2012). “Extra dimensions, gravitons, and tiny black holes”. [40] Brans, C.H. (Mar 2014). “Jordan-Brans-Dicke Theory”. Scholarpedia. 9: 31358. Bibcode:2014Schpj...931358B. doi:10.4249/scholarpedia.31358. [41] Horndeski, G.W. (Sep 1974). “Second-Order ScalarTensor Field Equations in a Four-Dimensional Space”. International Journal of Theoretical Physics. 88 (10): 363–384. Bibcode:1974IJTP...10..363H. doi:10.1007/BF01807638. [42] Milgrom, M. (Jun 2014). “The MOND paradigm of modified dynamics”. Scholarpedia. 9: 31410. Bibcode:2014SchpJ...931410M. doi:10.4249/scholarpedia.31410. [43] Einstein gravity from conformal gravity

30.7 References • Halliday, David; Robert Resnick; Kenneth S. Krane (2001). Physics v. 1. New York: John Wiley & Sons. ISBN 0-471-32057-9. • Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks/Cole. ISBN 0-534-40842-7. • Tipler, Paul (2004). Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics (5th ed.). W. H. Freeman. ISBN 0-71670809-4.


332

30.8 Further reading • Thorne, Kip S.; Misner, Charles W.; Wheeler, John Archibald (1973). Gravitation. W.H. Freeman. ISBN 0-7167-0344-0.

30.9 External links • Hazewinkel, Michiel, ed. (2001), “Gravitation”, Encyclopedia of Mathematics, Springer, ISBN 9781-55608-010-4 • Hazewinkel, Michiel, ed. (2001), “Gravitation, theory of”, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4

CHAPTER 30. GRAVITY


30.9. EXTERNAL LINKS

333

If an object with comparable mass to that of the Earth were to fall towards it, then the corresponding acceleration of the Earth would be observable.

Velocity

Gravity acts on stars that form our Milky Way.[29]

B

A Distance Rotation curve of a typical spiral galaxy: predicted (A) and observed (B). The discrepancy between the curves is attributed to dark matter.

An initially-stationary object which is allowed to fall freely under gravity drops a distance which is proportional to the square of the elapsed time. This image spans half a second and was captured at 20 ashes per second.


Chapter 31

Planet This article is about the astronomical object. For other probes has found that Earth and the other planets share uses, see Planet (disambiguation). characteristics such as volcanism, hurricanes, tectonics, and even hydrology. A planet is an astronomical object orbiting a star or stellar Planets are generally divided into two main types: large remnant that low-density giant planets, and smaller rocky terrestrials. Under IAU definitions, there are eight planets in the Solar • is massive enough to be rounded by its own gravity, System. In order of increasing distance from the Sun, they are the four terrestrials, Mercury, Venus, Earth, and • is not massive enough to cause thermonuclear fu- Mars, then the four giant planets, Jupiter, Saturn, Uranus, sion, and and Neptune. Six of the planets are orbited by one or more natural satellites. • has cleared its neighbouring region of [lower-alpha 1][1][2] More than two thousand planets around other stars planetesimals. ("extrasolar planets" or “exoplanets”) have been discovThe term planet is ancient, with ties to history, astrology, ered in the Milky Way. As of 1 October 2016, 3,532 science, mythology, and religion. Several planets in the known extrasolar planets in 2,649 planetary systems (inSolar System can be seen with the naked eye. These were cluding 595 multiple planetary systems), ranging in size regarded by many early cultures as divine, or as emis- from just above the size of the Moon to gas giants about saries of deities. As scientific knowledge advanced, hu- twice as large as Jupiter have been discovered, out of man perception of the planets changed, incorporating a which more than 100 planets are the same size as Earth, number of disparate objects. In 2006, the International nine of which are at the same relative distance from their [3][4] Astronomical Union (IAU) officially adopted a resolution star as Earth from the Sun, i.e. in the habitable zone. defining planets within the Solar System. This defini- On December 20, 2011, the Kepler Space Telescope extion is controversial because it excludes many objects of team reported the discovery[5]of the first Earth-sized [6] trasolar planets, Kepler-20e and Kepler-20f, orbiting planetary mass based on where or what they orbit. Al[7][8][9] A 2012 study, analyzthough eight of the planetary bodies discovered before a Sun-like star, Kepler-20. ing gravitational microlensing data, estimates an average 1950 remain “planets” under the modern definition, some of at least 1.6 bound planets for every star in the Milky celestial bodies, such as Ceres, Pallas, Juno and Vesta [10] [lower-alpha 2] Way. Around one in five Sun-like stars is (each an object in the solar asteroid belt), and Pluto (the [lower-alpha 3] thought to have an Earth-sized planet in its first trans-Neptunian object discovered), that were once [lower-alpha 4] habitable zone. considered planets by the scientific community, are no longer viewed as such. The planets were thought by Ptolemy to orbit Earth in deferent and epicycle motions. Although the idea that the planets orbited the Sun had been suggested many times, it was not until the 17th century that this view was supported by evidence from the first telescopic astronomical observations, performed by Galileo Galilei. At about the same time, by careful analysis of pre-telescopic observation data collected by Tycho Brahe, Johannes Kepler found the planets’ orbits were not circular but elliptical. As observational tools improved, astronomers saw that, like Earth, the planets rotated around tilted axes, and some shared such features as ice caps and seasons. Since the dawn of the Space Age, close observation by space

31.1 History Further information: History of astronomy, Definition of planet, and Timeline of Solar System astronomy The word “planet” derives from the Ancient Greek ἀστήρ πλανήτης astēr planētēs, or πλάνης ἀστήρ plánēs astēr, which means "wandering star,”[11] and originally referred to those objects in the night sky that moved relative to one another, as opposed to the "fixed stars", which maintained a constant relative position in the sky.[12]

334


31.1. HISTORY

335 Venus, that probably dates as early as the second millennium BC.[19] The MUL.APIN is a pair of cuneiform tablets dating from the 7th century BC that lays out the motions of the Sun, Moon and planets over the course of the year.[20] The Babylonian astrologers also laid the foundations of what would eventually become Western astrology.[21] The Enuma anu enlil, written during the NeoAssyrian period in the 7th century BC,[22] comprises a list of omens and their relationships with various celestial phenomena including the motions of the planets.[23][24] Venus, Mercury and the outer planets Mars, Jupiter and Saturn were all identified by Babylonian astronomers. These would remain the only known planets until the invention of the telescope in early modern times.[25]

Printed rendition of a geocentric cosmological model from Cosmographia, Antwerp, 1539

The idea of planets has evolved over its history, from the divine lights of antiquity to the earthly objects of the scientific age. The concept has expanded to include worlds not only in the Solar System, but in hundreds of other extrasolar systems. The ambiguities inherent in defining planets have led to much scientific controversy. The five classical planets, being visible to the naked eye, have been known since ancient times and have had a significant impact on mythology, religious cosmology, and ancient astronomy. In ancient times, astronomers noted how certain lights moved across the sky in relation to the other stars. Ancient Greeks called these lights πλάνητες ἀστέρες (planētes asteres, “wandering stars”) or simply πλανῆται (planētai, “wanderers”),[13] from which today’s word “planet” was derived.[14][15] In ancient Greece, China, Babylon, and indeed all premodern civilizations,[16][17] it was almost universally believed that Earth was the center of the Universe and that all the “planets” circled Earth. The reasons for this perception were that stars and planets appeared to revolve around Earth each day[18] and the apparently commonsense perceptions that Earth was solid and stable and that it was not moving but at rest.

31.1.1

Babylon

Main article: Babylonian astronomy The first civilization known to have a functional theory of the planets were the Babylonians, who lived in Mesopotamia in the first and second millennia BC. The oldest surviving planetary astronomical text is the Babylonian Venus tablet of Ammisaduqa, a 7th-century BC copy of a list of observations of the motions of the planet

31.1.2 Greco-Roman astronomy See also: Greek astronomy The ancient Greeks initially did not attach as much significance to the planets as the Babylonians. The Pythagoreans, in the 6th and 5th centuries BC appear to have developed their own independent planetary theory, which consisted of the Earth, Sun, Moon, and planets revolving around a “Central Fire” at the center of the Universe. Pythagoras or Parmenides is said to have been the first to identify the evening star (Hesperos) and morning star (Phosphoros) as one and the same (Aphrodite, Greek corresponding to Latin Venus).[26] In the 3rd century BC, Aristarchus of Samos proposed a heliocentric system, according to which Earth and the planets revolved around the Sun. The geocentric system remained dominant until the Scientific Revolution. By the 1st century BC, during the Hellenistic period, the Greeks had begun to develop their own mathematical schemes for predicting the positions of the planets. These schemes, which were based on geometry rather than the arithmetic of the Babylonians, would eventually eclipse the Babylonians’ theories in complexity and comprehensiveness, and account for most of the astronomical movements observed from Earth with the naked eye. These theories would reach their fullest expression in the Almagest written by Ptolemy in the 2nd century CE. So complete was the domination of Ptolemy’s model that it superseded all previous works on astronomy and remained the definitive astronomical text in the Western world for 13 centuries.[19][27] To the Greeks and Romans there were seven known planets, each presumed to be circling Earth according to the complex laws laid out by Ptolemy. They were, in increasing order from Earth (in Ptolemy’s order): the Moon, Mercury, Venus, the Sun, Mars, Jupiter, and Saturn.[15][27][28]


336

31.1.3

CHAPTER 31. PLANET

India

used interchangeably – although the latter would gradually become more prevalent in the following century.[37] Until the mid-19th century, the number of “planets” rose Main articles: Indian astronomy and Hindu cosmology rapidly because any newly discovered object directly orbiting the Sun was listed as a planet by the scientific comIn 499 CE, the Indian astronomer Aryabhata propounded munity. a planetary model that explicitly incorporated Earth’s rotation about its axis, which he explains as the cause of what appears to be an apparent westward motion of 31.1.6 19th century the stars. He also believed that the orbits of planets are elliptical.[29] Aryabhata’s followers were particularly In the 19th century astronomers began to realize that strong in South India, where his principles of the diur- recently discovered bodies that had been classified as nal rotation of Earth, among others, were followed and a planets for almost half a century (such as Ceres, Pallas, number of secondary works were based on them.[30] and Vesta) were very different from the traditional In 1500, Nilakantha Somayaji of the Kerala school of astronomy and mathematics, in his Tantrasangraha, revised Aryabhata’s model.[31] In his Aryabhatiyabhasya, a commentary on Aryabhata’s Aryabhatiya, he developed a planetary model where Mercury, Venus, Mars, Jupiter and Saturn orbit the Sun, which in turn orbits Earth, similar to the Tychonic system later proposed by Tycho Brahe in the late 16th century. Most astronomers of the Kerala school who followed him accepted his planetary model.[31][32]

ones. These bodies shared the same region of space between Mars and Jupiter (the asteroid belt), and had a much smaller mass; as a result they were reclassified as "asteroids". In the absence of any formal definition, a “planet” came to be understood as any “large” body that orbited the Sun. Because there was a dramatic size gap between the asteroids and the planets, and the spate of new discoveries seemed to have ended after the discovery of Neptune in 1846, there was no apparent need to have a formal definition.[38]

31.1.4

31.1.7 20th century

Medieval Muslim astronomy

Main articles: Astronomy in the medieval Islamic world In the 20th century, Pluto was discovered. After initial observations led to the belief it was larger than Earth,[39] and Cosmology in medieval Islam the object was immediately accepted as the ninth planet. Further monitoring found the body was actually much In the 11th century, the transit of Venus was observed by smaller: in 1936, Raymond Lyttleton suggested that Pluto Avicenna, who established that Venus was, at least some- may be an escaped satellite of Neptune,[40] and Fred times, below the Sun.[33] In the 12th century, Ibn Bajjah Whipple suggested in 1964 that Pluto may be a comet.[41] observed “two planets as black spots on the face of the As it was still larger than all known asteroids and seemSun”, which was later identified as a transit of Mercury ingly did not exist within a larger population,[42] it kept and Venus by the Maragha astronomer Qotb al-Din Shi- its status until 2006. razi in the 13th century.[34] Ibn Bajjah could not have observed a transit of Venus, because none occurred in his In 1992, astronomers Aleksander Wolszczan and Dale Frail announced the discovery of planets around a pulsar, lifetime.[35] PSR B1257+12.[43] This discovery is generally considered to be the first definitive detection of a planetary system around another star. Then, on October 6, 1995, 31.1.5 European Renaissance Michel Mayor and Didier Queloz of the Geneva Observatory announced the first definitive detection of an exSee also: Heliocentrism oplanet orbiting an ordinary main-sequence star (51 Pegasi).[44] With the advent of the Scientific Revolution, use of the The discovery of extrasolar planets led to another ambiterm “planet” changed from something that moved across guity in defining a planet: the point at which a planet bethe sky (in relation to the star field); to a body that orbited comes a star. Many known extrasolar planets are many Earth (or that were believed to do so at the time); and by times the mass of Jupiter, approaching that of stellar obthe 18th century to something that directly orbited the jects known as brown dwarfs. Brown dwarfs are generSun when the heliocentric model of Copernicus, Galileo ally considered stars due to their ability to fuse deuterium, and Kepler gained sway. a heavier isotope of hydrogen. Although objects more Thus, Earth became included in the list of planets,[36] whereas the Sun and Moon were excluded. At first, when the first satellites of Jupiter and Saturn were discovered in the 17th century, the terms “planet” and “satellite” were

massive than 75 times that of Jupiter fuse hydrogen, objects of only 13 Jupiter masses can fuse deuterium. Deuterium is quite rare, and most brown dwarfs would have ceased fusing deuterium long before their discov-


31.1. HISTORY ery, making them effectively indistinguishable from supermassive planets.[45]

31.1.8

21st century

337 are "brown dwarfs", no matter how they formed or where they are located. 3. Free-floating objects in young star clusters with masses below the limiting mass for thermonuclear fusion of deuterium are not “planets”, but are “subbrown dwarfs” (or whatever name is most appropriate).

With the discovery during the latter half of the 20th century of more objects within the Solar System and large objects around other stars, disputes arose over what should constitute a planet. There were particular disagreements over whether an object should be considered This working definition has since been widely used by a planet if it was part of a distinct population such as a astronomers when publishing discoveries of exoplanets in belt, or if it was large enough to generate energy by the academic journals.[48] Although temporary, it remains an thermonuclear fusion of deuterium. effective working definition until a more permanent one A growing number of astronomers argued for Pluto to is formally adopted. It does not address the dispute over be declassified as a planet, because many similar objects the lower mass limit,[49] and so it steered clear of the conapproaching its size had been found in the same region of troversy regarding objects within the Solar System. This the Solar System (the Kuiper belt) during the 1990s and definition also makes no comment on the planetary status early 2000s. Pluto was found to be just one small body in of objects orbiting brown dwarfs, such as 2M1207b. a population of thousands. One definition of a sub-brown dwarf is a planet-mass Some of them, such as Quaoar, Sedna, and Eris, were object that formed through cloud collapse rather than heralded in the popular press as the tenth planet, failing to accretion. This formation distinction between a subreceive widespread scientific recognition. The announce- brown dwarf and a planet is not universally agreed upon; ment of Eris in 2005, an object then thought of as 27% astronomers are divided into two camps as whether to more massive than Pluto, created the necessity and public consider the formation process of a planet as part of its desire for an official definition of a planet. division in classification.[50] One reason for the dissent is Acknowledging the problem, the IAU set about creat- that often it may not be possible to determine the formaing the definition of planet, and produced one in August tion process. For example, a planet formed by accretion 2006. The number of planets dropped to the eight signifi- around a star may get ejected from the system to become cantly larger bodies that had cleared their orbit (Mercury, free-floating, and likewise a sub-brown dwarf that formed Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Nep- on its own in a star cluster through cloud collapse may get tune), and a new class of dwarf planets was created, ini- captured into orbit around a star. tially containing three objects (Ceres, Pluto and Eris).[46] Extrasolar planets There is no official definition of extrasolar planets. In 2003, the International Astronomical Union (IAU) Working Group on Extrasolar Planets issued a position statement, but this position statement was never proposed as an official IAU resolution and was never voted on by IAU members. The positions statement incorporates the following guidelines, mostly focused upon the boundary between planets and brown dwarfs:[2]

The 13 Jupiter-mass cutoff represents an average mass rather than a precise threshold value. Large objects will fuse most of their deuterium and smaller ones will fuse only a little, and the 13 MJ value is somewhere in between. In fact, calculations show that an object fuses 50% of its initial deuterium content when the total mass ranges between 12 and 14 MJ.[51] The amount of deuterium fused depends not only on mass but also on the composition of the object, on the amount of helium and deuterium present.[52] The Extrasolar Planets Encyclopaedia includes objects up to 25 Jupiter masses, saying, “The fact that there is no special feature around 13 MJ in the observed mass spectrum reinforces the choice to forget this mass limit.”[53] The Exoplanet Data Explorer includes objects up to 24 Jupiter masses with the advisory: “The 13 Jupiter-mass distinction by the IAU Working Group is physically unmotivated for planets with rocky cores, and observationally problematic due to the sin i ambiguity.”[54] The NASA Exoplanet Archive includes objects with a mass (or minimum mass) equal to or less than 30 Jupiter masses.[55]

1. Objects with true masses below the limiting mass for thermonuclear fusion of deuterium (currently calculated to be 13 times the mass of Jupiter for objects with the same isotopic abundance as the Sun[47] ) that orbit stars or stellar remnants are “planets” (no matter how they formed). The minimum mass and size required for an extrasolar object to be considered a planet should be the same as that used in the Solar Another criterion for separating planets and brown System. dwarfs, rather than deuterium fusion, formation process 2. Substellar objects with true masses above the lim- or location, is whether the core pressure is dominated by iting mass for thermonuclear fusion of deuterium coulomb pressure or electron degeneracy pressure.[56][57]


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2006 IAU definition of planet Main article: IAU definition of planet The matter of the lower limit was addressed during the Planets

Satellites (natural)

Dwarf planets Minor planets Centaurs

orbits, which prevent collisions between them. Minor planets and comets, including KBOs [Kuiper belt objects], differ from planets in that they can collide with each other and with planets.”

Trans-Neptunian objects Plutoids

Small Solar System bodies

Comets

Centaurs

Euler diagram showing the types of bodies in the Solar System.

The 2006 IAU definition presents some challenges for exoplanets because the language is specific to the Solar System and because the criteria of roundness and orbital zone clearance are not presently observable. Astronomer Jean-Luc Margot proposed a mathematical criterion that determines whether an object can clear its orbit during the lifetime of its host star, based on the mass of the planet, its semimajor axis, and the mass of its host star.[61][62] This formula produces a value π that is greater than 1 for planets. The eight known planets and all known exoplanets have π values above 100, while Ceres, Pluto, and Eris have π values of 0.1 or less. Objects with π values of 1 or more are also expected to be approximately spherical, so that objects that fulfill the orbital zone clearance requirement automatically fulfill the roundness requirement.[63]

2006 meeting of the IAU’s General Assembly. After much debate and one failed proposal, 232 members of the 10,000 member assembly, who nevertheless consti- 31.1.9 Objects formerly considered planets tuted a large majority of those remaining at the meeting, voted to pass a resolution. The 2006 resolution defines The table below lists Solar System bodies once considered to be planets. planets within the Solar System as follows:[1] A “planet” [1] is a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighbourhood around its orbit. [1] The eight planets are: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. Under this definition, the Solar System is considered to have eight planets. Bodies that fulfill the first two conditions but not the third (such as Ceres, Pluto, and Eris) are classified as dwarf planets, provided they are not also natural satellites of other planets. Originally an IAU committee had proposed a definition that would have included a much larger number of planets as it did not include (c) as a criterion.[58] After much discussion, it was decided via a vote that those bodies should instead be classified as dwarf planets.[59] This definition is based in theories of planetary formation, in which planetary embryos initially clear their orbital neighborhood of other smaller objects. As described by astronomer Steven Soter:[60] “The end product of secondary disk accretion is a small number of relatively large bodies (planets) in either non-intersecting or resonant

Beyond the scientific community, Pluto still holds cultural significance for many in the general public due to its historical classification as a planet from 1930 to 2006.[69] A few astronomers, such as Alan Stern, consider dwarf planets and the larger moons to be planets, based on a purely geophysical definition of planet.[70]

31.2 Mythology and naming See also: Weekday names and Naked-eye planet The names for the planets in the Western world are derived from the naming practices of the Romans, which ultimately derive from those of the Greeks and the Babylonians. In ancient Greece, the two great luminaries the Sun and the Moon were called Helios and Selene; the farthest planet (Saturn) was called Phainon, the shiner; followed by Phaethon (Jupiter), “bright"; the red planet (Mars) was known as Pyroeis, the “fiery"; the brightest (Venus) was known as Phosphoros, the light bringer; and the fleeting final planet (Mercury) was called Stilbon, the gleamer. The Greeks also made each planet sacred to one among their pantheon of gods, the Olympians: Helios and Selene were the names of both planets and gods; Phainon was sacred to Cronus, the Titan who fathered the Olympians; Phaethon was sacred to Zeus, Cronus’s son who deposed him as king; Pyroeis was given to Ares, son of Zeus and god of war; Phosphoros was ruled by Aphrodite, the goddess of love; and Hermes, messenger of the gods and god of learning and wit, ruled over Stilbon.[19]


31.2. MYTHOLOGY AND NAMING

339 their own gods’ names: Mercurius (for Hermes), Venus (Aphrodite), Mars (Ares), Iuppiter (Zeus) and Saturnus (Cronus). When subsequent planets were discovered in the 18th and 19th centuries, the naming practice was retained with Neptūnus (Poseidon). Uranus is unique in that it is named for a Greek deity rather than his Roman counterpart. Some Romans, following a belief possibly originating in Mesopotamia but developed in Hellenistic Egypt, believed that the seven gods after whom the planets were named took hourly shifts in looking after affairs on Earth. The order of shifts went Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon (from the farthest to the closest planet).[74] Therefore, the first day was started by Saturn (1st hour), second day by Sun (25th hour), followed by Moon (49th hour), Mars, Mercury, Jupiter and Venus. Because each day was named by the god that started it, this is also the order of the days of the week in the Roman calendar after the Nundinal cycle was rejected – and still preserved in many modern languages.[75] In English, Saturday, Sunday, and Monday are straightforward translations of these Roman names. The other days were renamed after Tiw (Tuesday), Wóden (Wednesday), Thunor (Thursday), and Fríge (Friday), the Anglo-Saxon gods considered similar or equivalent to Mars, Mercury, Jupiter, and Venus, respectively.

The Greek gods of Olympus, after whom the Solar System's Roman names of the planets are derived

The Greek practice of grafting of their gods’ names onto the planets was almost certainly borrowed from the Babylonians. The Babylonians named Phosphoros after their goddess of love, Ishtar; Pyroeis after their god of war, Nergal, Stilbon after their god of wisdom Nabu, and Phaethon after their chief god, Marduk.[71] There are too many concordances between Greek and Babylonian naming conventions for them to have arisen separately.[19] The translation was not perfect. For instance, the Babylonian Nergal was a god of war, and thus the Greeks identified him with Ares. Unlike Ares, Nergal was also god of pestilence and the underworld.[72] Today, most people in the western world know the planets by names derived from the Olympian pantheon of gods. Although modern Greeks still use their ancient names for the planets, other European languages, because of the influence of the Roman Empire and, later, the Catholic Church, use the Roman (Latin) names rather than the Greek ones. The Romans, who, like the Greeks, were Indo-Europeans, shared with them a common pantheon under different names but lacked the rich narrative traditions that Greek poetic culture had given their gods. During the later period of the Roman Republic, Roman writers borrowed much of the Greek narratives and applied them to their own pantheon, to the point where they became virtually indistinguishable.[73] When the Romans studied Greek astronomy, they gave the planets

Earth is the only planet whose name in English is not derived from Greco-Roman mythology. Because it was only generally accepted as a planet in the 17th century,[36] there is no tradition of naming it after a god. (The same is true, in English at least, of the Sun and the Moon, though they are no longer generally considered planets.) The name originates from the 8th century Anglo-Saxon word erda, which means ground or soil and was first used in writing as the name of the sphere of Earth perhaps around 1300.[76][77] As with its equivalents in the other Germanic languages, it derives ultimately from the ProtoGermanic word ertho, “ground”,[77] as can be seen in the English earth, the German Erde, the Dutch aarde, and the Scandinavian jord. Many of the Romance languages retain the old Roman word terra (or some variation of it) that was used with the meaning of “dry land” as opposed to “sea”.[78] The non-Romance languages use their own native words. The Greeks retain their original name, Γή (Ge). Non-European cultures use other planetary-naming systems. India uses a system based on the Navagraha, which incorporates the seven traditional planets (Surya for the Sun, Chandra for the Moon, and Budha, Shukra, Mangala, Bṛhaspati and Shani for Mercury, Venus, Mars, Jupiter and Saturn) and the ascending and descending lunar nodes Rahu and Ketu. China and the countries of eastern Asia historically subject to Chinese cultural influence (such as Japan, Korea and Vietnam) use a naming system based on the five Chinese elements: water (Mercury), metal (Venus), fire (Mars), wood (Jupiter) and earth (Saturn).[75] In traditional Hebrew astronomy, the


340

CHAPTER 31. PLANET

seven traditional planets have (for the most part) descriptive names - the Sun is ‫ חמה‬Ḥammah or “the hot one,” the Moon is ‫ לבנה‬Levanah or “the white one,” Venus is ‫ כוכב נוגה‬Kokhav Nogah or “the bright planet,” Mercury is ‫ כוכב‬Kokhav or “the planet” (given its lack of distinguishing features), Mars is ‫ מאדים‬Ma'adim or “the red one,” and Saturn is ‫ שבתאי‬Shabbatai or “the resting one” (in reference to its slow movement compared to the other visible planets).[79] The odd one out is Jupiter, called ‫צדק‬ Tzedeq or “justice.” Steiglitz suggests that this may be a euphemism for the original name of ‫ כוכב בעל‬Kokhav Ba'al or "Baal's planet,” seen as idolatrous and euphem- Asteroid collision - building planets (artist concept). ized in a similar manner to Ishbosheth from II Samuel [79]

31.3 Formation Main article: Nebular hypothesis It is not known with certainty how planets are formed.

protoplanets or planets to absorb.[89] Those objects that have become massive enough will capture most matter in An artist’s impression of protoplanetary disk their orbital neighbourhoods to become planets. ProtoThe prevailing theory is that they are formed during the planets that have avoided collisions may become natural collapse of a nebula into a thin disk of gas and dust. satellites of planets through a process of gravitational capA protostar forms at the core, surrounded by a rotat- ture, or remain in belts of other objects to become either dwarf planets or small bodies. ing protoplanetary disk. Through accretion (a process of sticky collision) dust particles in the disk steadily ac- The energetic impacts of the smaller planetesimals (as cumulate mass to form ever-larger bodies. Local con- well as radioactive decay) will heat up the growing planet, centrations of mass known as planetesimals form, and causing it to at least partially melt. The interior of these accelerate the accretion process by drawing in ad- the planet begins to differentiate by mass, developing a ditional material by their gravitational attraction. These denser core.[90] Smaller terrestrial planets lose most of concentrations become ever denser until they collapse their atmospheres because of this accretion, but the lost inward under gravity to form protoplanets.[80] After a gases can be replaced by outgassing from the mantle and planet reaches a mass somewhat larger than Mars' mass, it from the subsequent impact of comets.[91] (Smaller planbegins to accumulate an extended atmosphere,[81] greatly ets will lose any atmosphere they gain through various increasing the capture rate of the planetesimals by means escape mechanisms.) of atmospheric drag.[82][83] Depending on the accretion With the discovery and observation of planetary systems history of solids and gas, a giant planet, an ice giant, or a around stars other than the Sun, it is becoming possible terrestrial planet may result.[84][85][86] to elaborate, revise or even replace this account. The When the protostar has grown such that it ignites to form a star, the surviving disk is removed from the inside outward by photoevaporation, the solar wind, Poynting– Robertson drag and other effects.[87][88] Thereafter there still may be many protoplanets orbiting the star or each other, but over time many will collide, either to form a single larger planet or release material for other larger

level of metallicity—an astronomical term describing the abundance of chemical elements with an atomic number greater than 2 (helium)—is now thought to determine the likelihood that a star will have planets.[92] Hence, it is thought that a metal-rich population I star will likely have a more substantial planetary system than a metal-poor, population II star.


31.4. SOLAR SYSTEM

341

The four giant planets Jupiter, Saturn, Uranus, and Neptune against the Sun and some sunspots Main article: Solar System See also: List of gravitationally rounded objects of the Solar System There are eight planets in the Solar System, which are in increasing distance from the Sun:

Supernova remnant ejecta producing planet-forming material.

31.4 Solar System Solar System – sizes but not distances are to scale

1.

Mercury

2.

Venus

3.

Earth

4.

Mars

5.

Jupiter

6.

Saturn

7.

Uranus

8.

Neptune

Jupiter is the largest, at 318 Earth masses, whereas Mercury is the smallest, at 0.055 Earth masses. The planets of the Solar System can be divided into categories based on their composition: • Terrestrials: Planets that are similar to Earth, with bodies largely composed of rock: Mercury, Venus, Earth and Mars. At 0.055 Earth masses, Mercury is the smallest terrestrial planet (and smallest planet) in the Solar System. Earth is the largest terrestrial The planet.

Sun and the eight planets of the Solar System

• Giant planets (Jovians): Massive planets significantly more massive than the terrestrials: Jupiter, Saturn, Uranus, Neptune.

The inner planets, Mercury, Venus, Earth, and Mars

• Gas giants, Jupiter and Saturn, are giant planets primarily composed of hydrogen and helium and are the most massive planets in the Solar System. Jupiter, at 318 Earth masses, is the largest planet in the Solar System, and Saturn is one third as massive, at 95 Earth masses.


342

CHAPTER 31. PLANET • Ice giants, Uranus and Neptune, are primarily composed of low-boiling-point materials such as water, methane, and ammonia, with thick atmospheres of hydrogen and helium. They have a significantly lower mass than the gas giants (only 14 and 17 Earth masses).

31.4.1

Planetary attributes

31.5 Exoplanets Main article: Exoplanet An exoplanet (extrasolar planet) is a planet outside the

Sizes of Kepler Planet Candidates – based on 2,740 candidates orbiting 2,036 stars as of 4 November 2013 (NASA).

sible dividing line between the two types of planet.[97] There are hot Jupiters that orbit very close to their star and may evaporate to become chthonian planets, which are the leftover cores. Another possible type of planet is carbon planets, which form in systems with a higher proportion of carbon than in the Solar System. Exoplanets, by year of discovery, through September 2014.

A 2012 study, analyzing gravitational microlensing data, estimates an average of at least 1.6 bound planets for every star in the Milky Way.[10]

Solar System. More than 2000 such planets have been discovered[94][95][96] (3,532 planets in 2,649 planetary systems including 595 multiple planetary systems as of 1 October 2016).[4]

On December 20, 2011, the Kepler Space Telescope team reported the discovery of the first Earth-size exoplanets, Kepler-20e[5] and Kepler-20f,[6] orbiting a Sun-like star, Kepler-20.[7][8][9]

In early 1992, radio astronomers Aleksander Wolszczan and Dale Frail announced the discovery of two planets orbiting the pulsar PSR 1257+12.[43] This discovery was confirmed, and is generally considered to be the first definitive detection of exoplanets. These pulsar planets are believed to have formed from the unusual remnants of the supernova that produced the pulsar, in a second round of planet formation, or else to be the remaining rocky cores of giant planets that survived the supernova and then decayed into their current orbits.

Around 1 in 5 Sun-like[lower-alpha 2] stars have an “Earthsized”[lower-alpha 3] planet in the habitable[lower-alpha 4] zone, so the nearest would be expected to be within 12 lightyears distance from Earth.[98][99] The frequency of occurrence of such terrestrial planets is one of the variables in the Drake equation, which estimates the number of intelligent, communicating civilizations that exist in the Milky Way.[100]

The first confirmed discovery of an extrasolar planet orbiting an ordinary main-sequence star occurred on 6 October 1995, when Michel Mayor and Didier Queloz of the University of Geneva announced the detection of an exoplanet around 51 Pegasi. From then until the Kepler mission most known extrasolar planets were gas giants comparable in mass to Jupiter or larger as they were more easily detected. The catalog of Kepler candidate planets consists mostly of planets the size of Neptune and smaller, down to smaller than Mercury.

There are exoplanets that are much closer to their parent star than any planet in the Solar System is to the Sun, and there are also exoplanets that are much farther from their star. Mercury, the closest planet to the Sun at 0.4 AU, takes 88-days for an orbit, but the shortest known orbits for exoplanets take only a few hours, e.g. Kepler-70b. The Kepler-11 system has five of its planets in shorter orbits than Mercury’s, all of them much more massive than Mercury. Neptune is 30 AU from the Sun and takes 165 years to orbit, but there are exoplanets that are hundreds of AU from their star and take more than a thousand years to orbit, e.g. 1RXS1609 b.

There are types of planets that do not exist in the Solar System: super-Earths and mini-Neptunes, which could be rocky like Earth or a mixture of volatiles and gas like Neptune—a radius of 1.75 times that of Earth is a pos-

The next few space telescopes to study exoplanets are expected to be Gaia launched in December 2013, CHEOPS in 2017, TESS in 2017, and the James Webb Space Telescope in 2018.


31.6. PLANETARY-MASS OBJECTS

31.6 Planetary-mass objects

343 though others have suggested that they should be called low-mass brown dwarfs.[106][107]

31.6.2 Sub-brown dwarfs Main article: Sub-brown dwarf Stars form via the gravitational collapse of gas clouds, but smaller objects can also form via cloud-collapse. Planetary-mass objects formed this way are sometimes called sub-brown dwarfs. Sub-brown dwarfs may be free-floating such as Cha 110913-773444[106] and OTS 44,[108] or orbiting a larger object such as 2MASS J04414489+2301513. Binary systems of sub-brown dwarfs are theoretically possible; Oph 162225-240515 was initially thought to be a binary system of a brown dwarf of 14 Jupiter masses and a sub-brown dwarf of 7 Jupiter masses, but further observations revised the estimated masses upwards to greater than 13 Jupiter masses, making them brown dwarfs according to the IAU working definitions.[109][110][111]

Artist’s impression of a super-Jupiter around the brown dwarf 2M1207.[101]

31.6.3 Former stars

In close binary star systems one of the stars can lose mass See also: List of gravitationally rounded objects of the to a heavier companion. Accretion-powered pulsars may Solar System drive mass loss. The shrinking star can then become a planetary-mass object. An example is a Jupiter-mass object orbiting the pulsar PSR J1719-1438.[112] These [102] A planetary-mass object (PMO), planemo /ˈplænᵻmoʊ/, or planetary body is a celestial object shrunken white dwarfs may become a helium planet or with a mass that falls within the range of the definition carbon planet. of a planet: massive enough to achieve hydrostatic equilibrium (to be rounded under its own gravity), but not enough to sustain core fusion like a star.[103][104] By definition, all planets are planetary-mass objects, but the purpose of this term is to refer to objects that do not conform to typical expectations for a planet. These include dwarf planets, which are rounded by their own gravity but not massive enough to clear their own orbit, the larger moons, and free-floating planemos, which may have been ejected from a system (rogue planets) or formed through cloud-collapse rather than accretion (sometimes called sub-brown dwarfs).

31.6.1

Rogue planets

Main article: Rogue planet Several computer simulations of stellar and planetary system formation have suggested that some objects of planetary mass would be ejected into interstellar space.[105] Some scientists have argued that such objects found roaming in deep space should be classed as “planets”, al-

31.6.4 Satellite planets and belt planets Some large satellites are of similar size or larger than the planet Mercury, e.g. Jupiter’s Galilean moons and Titan. Alan Stern has argued that location should not matter and that only geophysical attributes should be taken into account in the definition of a planet, and proposes the term satellite planet for a planet-sized satellite. Likewise, dwarf planets in the asteroid belt and Kuiper belt should be considered planets according to Stern.[70]

31.6.5 Captured planets Free-floating planets in stellar clusters have similar velocities to the stars and so can be recaptured. They are typically captured into wide orbits between 100 and 105 AU. The capture efficiency decreases with increasing cluster volume, and for a given cluster size it increases with the host/primary mass. It is almost independent of the planetary mass. Single and multiple planets could be captured into arbitrary unaligned orbits, non-coplanar with each


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other or with the stellar host spin, or pre-existing plane- Each planet’s orbit is delineated by a set of elements: tary system.[113] • The eccentricity of an orbit describes how elongated a planet’s orbit is. Planets with low eccentricities have more circular orbits, whereas planets with high eccentricities have more elliptical orbits. The planets in the Solar System have very low eccentricities, and thus nearly circular orbits.[115] Comets and Kuiper belt objects (as well as several extrasolar planets) have very high eccentricities, and thus exceedingly elliptical orbits.[117][118]

31.7 Attributes Although each planet has unique physical characteristics, a number of broad commonalities do exist among them. Some of these characteristics, such as rings or natural satellites, have only as yet been observed in planets in the Solar System, whereas others are also commonly observed in extrasolar planets.

31.7.1

Dynamic characteristics

Orbit Main articles: Orbit and Orbital elements See also: Kepler’s laws of planetary motion According to current definitions, all planets must revolve • Illustration of the semi-major axis

q Q

Pluto Neptune q Q

The orbit of the planet Neptune compared to that of Pluto. Note the elongation of Pluto’s orbit in relation to Neptune’s (eccentricity), as well as its large angle to the ecliptic (inclination).

around stars; thus, any potential "rogue planets" are excluded. In the Solar System, all the planets orbit the Sun in the same direction as the Sun rotates (counterclockwise as seen from above the Sun’s north pole). At least one extrasolar planet, WASP-17b, has been found to orbit in the opposite direction to its star’s rotation.[114] The period of one revolution of a planet’s orbit is known as its sidereal period or year.[115] A planet’s year depends on its distance from its star; the farther a planet is from its star, not only the longer the distance it must travel, but also the slower its speed, because it is less affected by its star’s gravity. No planet’s orbit is perfectly circular, and hence the distance of each varies over the course of its year. The closest approach to its star is called its periastron (perihelion in the Solar System), whereas its farthest separation from the star is called its apastron (aphelion). As a planet approaches periastron, its speed increases as it trades gravitational potential energy for kinetic energy, just as a falling object on Earth accelerates as it falls; as the planet reaches apastron, its speed decreases, just as an object thrown upwards on Earth slows down as it reaches the apex of its trajectory.[116]

The semi-major axis is the distance from a planet to the half-way point along the longest diameter of its elliptical orbit (see image). This distance is not the same as its apastron, because no planet’s orbit has its star at its exact centre.[115] • The inclination of a planet tells how far above or below an established reference plane its orbit lies. In the Solar System, the reference plane is the plane of Earth’s orbit, called the ecliptic. For extrasolar planets, the plane, known as the sky plane or plane of the sky, is the plane perpendicular to the observer’s line of sight from Earth.[119] The eight planets of the Solar System all lie very close to the ecliptic; comets and Kuiper belt objects like Pluto are at far more extreme angles to it.[120] The points at which a planet crosses above and below its reference plane are called its ascending and descending nodes.[115] The longitude of the ascending node is the angle between the reference plane’s 0 longitude and the planet’s ascending node. The argument of periapsis (or perihelion in the Solar System) is the angle between a planet’s ascending node and its closest approach to its star.[115] Axial tilt Main article: Axial tilt Planets also have varying degrees of axial tilt; they lie at an angle to the plane of their stars’ equators. This causes the amount of light received by each hemisphere to vary over the course of its year; when the northern hemisphere points away from its star, the southern hemisphere


31.7. ATTRIBUTES

345 domly alter the spin axis of the planet.[126] There is great variation in the length of day between the planets, with Venus taking 243 days to rotate, and the giant planets only a few hours.[127] The rotational periods of extrasolar planets are not known. However, for “hot” Jupiters, their proximity to their stars means that they are tidally locked (i.e., their orbits are in sync with their rotations). This means, they always show one face to their stars, with one side in perpetual day, the other in perpetual night.[128] Orbital clearing Main article: Clearing the neighbourhood

Earth’s axial tilt is about 23.4°. It oscillates between 22.1° and 24.5° on a 41,000-year cycle and is currently decreasing.

The defining dynamic characteristic of a planet is that it has cleared its neighborhood. A planet that has cleared its neighborhood has accumulated enough mass to gather up or sweep away all the planetesimals in its orbit. In effect, it orbits its star in isolation, as opposed to sharing its orbit with a multitude of similar-sized objects. This characteristic was mandated as part of the IAU's official definition of a planet in August, 2006. This criterion excludes such planetary bodies as Pluto, Eris and Ceres from full-fledged planethood, making them instead dwarf planets.[1] Although to date this criterion only applies to the Solar System, a number of young extrasolar systems have been found in which evidence suggests orbital clearing is taking place within their circumstellar discs.[129]

points towards it, and vice versa. Each planet therefore has seasons, changes to the climate over the course of its year. The time at which each hemisphere points farthest or nearest from its star is known as its solstice. Each planet has two in the course of its orbit; when one hemisphere has its summer solstice, when its day is longest, the other has its winter solstice, when its day is shortest. The varying amount of light and heat received by each hemisphere creates annual changes in weather patterns for each half of the planet. Jupiter’s axial tilt is very small, so its seasonal variation is minimal; Uranus, on the other hand, has an axial tilt so extreme it is virtually on its side, which means that its hemispheres are either per31.7.2 Physical characteristics petually in sunlight or perpetually in darkness around the [121] time of its solstices. Among extrasolar planets, axial Mass tilts are not known for certain, though most hot Jupiters are believed to have negligible to no axial tilt as a result Main article: Planetary mass of their proximity to their stars.[122] Rotation The planets rotate around invisible axes through their centres. A planet’s rotation period is known as a stellar day. Most of the planets in the Solar System rotate in the same direction as they orbit the Sun, which is counterclockwise as seen from above the Sun’s north pole, the exceptions being Venus[123] and Uranus,[124] which rotate clockwise, though Uranus’s extreme axial tilt means there are differing conventions on which of its poles is “north”, and therefore whether it is rotating clockwise or anti-clockwise.[125] Regardless of which convention is used, Uranus has a retrograde rotation relative to its orbit. The rotation of a planet can be induced by several factors during formation. A net angular momentum can be induced by the individual angular momentum contributions of accreted objects. The accretion of gas by the giant planets can also contribute to the angular momentum. Finally, during the last stages of planet building, a stochastic process of protoplanetary accretion can ran-

A planet’s defining physical characteristic is that it is massive enough for the force of its own gravity to dominate over the electromagnetic forces binding its physical structure, leading to a state of hydrostatic equilibrium. This effectively means that all planets are spherical or spheroidal. Up to a certain mass, an object can be irregular in shape, but beyond that point, which varies depending on the chemical makeup of the object, gravity begins to pull an object towards its own centre of mass until the object collapses into a sphere.[130] Mass is also the prime attribute by which planets are distinguished from stars. The upper mass limit for planethood is roughly 13 times Jupiter’s mass for objects with solar-type isotopic abundance, beyond which it achieves conditions suitable for nuclear fusion. Other than the Sun, no objects of such mass exist in the Solar System; but there are exoplanets of this size. The 13-Jupiter-mass limit is not universally agreed upon and the Extrasolar Planets Encyclopaedia includes objects up to 20 Jupiter masses,[131] and the Exoplanet Data Explorer up to 24 Jupiter masses.[132]


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The smallest known planet is PSR B1257+12A, one of the first extrasolar planets discovered, which was found in 1992 in orbit around a pulsar. Its mass is roughly half that of the planet Mercury.[4] The smallest known planet orbiting a main-sequence star other than the Sun is Kepler37b, with a mass (and radius) slightly higher than that of the Moon. Internal differentiation Main article: Planetary differentiation Every planet began its existence in an entirely fluid state; Earth’s atmosphere

ant planets are massive enough to keep large amounts of the light gases hydrogen and helium, whereas the smaller planets lose these gases into space.[137] The composition of Earth’s atmosphere is different from the other planets because the various life processes that have transpired on the planet have introduced free molecular oxygen.[138] Planetary atmospheres are affected by the varying insolation or internal energy, leading to the formation of dynamic weather systems such as hurricanes, (on Earth), planet-wide dust storms (on Mars), a greater-than-Earthsized anticyclone on Jupiter (called the Great Red Spot), and holes in the atmosphere (on Neptune).[121] At least one extrasolar planet, HD 189733 b, has been claimed to have such a weather system, similar to the Great Red Spot but twice as large.[139] Illustration of the interior of Jupiter, with a rocky core overlaid by a deep layer of metallic hydrogen

in early formation, the denser, heavier materials sank to the centre, leaving the lighter materials near the surface. Each therefore has a differentiated interior consisting of a dense planetary core surrounded by a mantle that either is or was a fluid. The terrestrial planets are sealed within hard crusts,[133] but in the giant planets the mantle simply blends into the upper cloud layers. The terrestrial planets have cores of elements such as iron and nickel, and mantles of silicates. Jupiter and Saturn are believed to have cores of rock and metal surrounded by mantles of metallic hydrogen.[134] Uranus and Neptune, which are smaller, have rocky cores surrounded by mantles of water, ammonia, methane and other ices.[135] The fluid action within these planets’ cores creates a geodynamo that generates a magnetic field.[133] Atmosphere Main articles: Atmosphere and Extraterrestrial atmospheres See also: Extraterrestrial skies All of the Solar System planets except Mercury[136] have substantial atmospheres because their gravity is strong enough to keep gases close to the surface. The larger gi-

Hot Jupiters, due to their extreme proximities to their host stars, have been shown to be losing their atmospheres into space due to stellar radiation, much like the tails of comets.[140][141] These planets may have vast differences in temperature between their day and night sides that produce supersonic winds,[142] although the day and night sides of HD 189733 b appear to have very similar temperatures, indicating that that planet’s atmosphere effectively redistributes the star’s energy around the planet.[139]

Magnetosphere Main article: Magnetosphere One important characteristic of the planets is their intrinsic magnetic moments, which in turn give rise to magnetospheres. The presence of a magnetic field indicates that the planet is still geologically alive. In other words, magnetized planets have flows of electrically conducting material in their interiors, which generate their magnetic fields. These fields significantly change the interaction of the planet and solar wind. A magnetized planet creates a cavity in the solar wind around itself called the magnetosphere, which the wind cannot penetrate. The magnetosphere can be much larger than the planet itself. In contrast, non-magnetized planets have only small magnetospheres induced by interaction of the ionosphere


31.8. SEE ALSO

347

Magnetotail Deflected solar wind particles Incoming solar wind particles Plasma sheet Van Allen radiation belt

Solar wind

Neutral sheet Earth's atmosphere 0 - 100 km Polar cusp Bow shock

Magnetosheath

Earth’s magnetosphere (diagram)

with the solar wind, which cannot effectively protect the planet.[143] Of the eight planets in the Solar System, only Venus and Mars lack such a magnetic field.[143] In addition, the moon of Jupiter Ganymede also has one. Of the magnetized planets the magnetic field of Mercury is the weakest, and is barely able to deflect the solar wind. Ganymede’s magnetic field is several times larger, and Jupiter’s is the strongest in the Solar System (so strong in fact that it poses a serious health risk to future manned missions to its moons). The magnetic fields of the other giant planets are roughly similar in strength to that of Earth, but their magnetic moments are significantly larger. The magnetic fields of Uranus and Neptune are strongly tilted relative the rotational axis and displaced from the centre of the planet.[143]

The rings of Saturn

of varying size and complexity. The rings are composed primarily of dust or particulate matter, but can host tiny 'moonlets' whose gravity shapes and maintains their structure. Although the origins of planetary rings is not precisely known, they are believed to be the result of natural satellites that fell below their parent planet’s Roche limit and were torn apart by tidal forces.[148][149]

No secondary characteristics have been observed around extrasolar planets. The sub-brown dwarf Cha 110913773444, which has been described as a rogue planet, is believed to be orbited by a tiny protoplanetary disc[106] and the sub-brown dwarf OTS 44 was shown to be surIn 2004, a team of astronomers in Hawaii observed an rounded by a substantial protoplanetary disk of at least 10 extrasolar planet around the star HD 179949, which ap- Earth masses.[108] peared to be creating a sunspot on the surface of its parent star. The team hypothesized that the planet’s magnetosphere was transferring energy onto the star’s surface, increasing its already high 7,760 °C temperature by an 31.8 See also additional 400 °C.[144] • Double planet – Two planetary mass objects orbiting each other

31.7.3

Secondary characteristics

Main articles: Natural satellite and Planetary ring Several planets or dwarf planets in the Solar System (such as Neptune and Pluto) have orbital periods that are in resonance with each other or with smaller bodies (this is also common in satellite systems). All except Mercury and Venus have natural satellites, often called “moons”. Earth has one, Mars has two, and the giant planets have numerous moons in complex planetary-type systems. Many moons of the giant planets have features similar to those on the terrestrial planets and dwarf planets, and some have been studied as possible abodes of life (especially Europa).[145][146][147] The four giant planets are also orbited by planetary rings

• List of exoplanets • List of hypothetical Solar System objects • List of landings on extraterrestrial bodies • Lists of planets – A list of lists of planets sorted by diverse attributes • Mesoplanet – A planet smaller than Mercury but larger than Ceres • Minor planet – A celestial body smaller than a planet • Planetary habitability – The measure of a planet’s ability to sustain life


348 • Planetary mnemonic – A phrase used to remember the names of the planets • Planetary science – The scientific study of planets • Planets in astrology • Planets in science fiction • Theoretical planetology

31.9 Notes [1] This definition is drawn from two separate IAU declarations; a formal definition agreed by the IAU in 2006, and an informal working definition established by the IAU in 2001/2003 for objects outside of the Solar System. The official 2006 definition applies only to the Solar System, whereas the 2003 definition applies to planets around other stars. The extrasolar planet issue was deemed too complex to resolve at the 2006 IAU conference. [2] For the purpose of this 1 in 5 statistic, “Sun-like” means G-type star. Data for Sun-like stars wasn't available so this statistic is an extrapolation from data about K-type stars [3] For the purpose of this 1 in 5 statistic, Earth-sized means 1–2 Earth radii [4] For the purpose of this 1 in 5 statistic, “habitable zone” means the region with 0.25 to 4 times Earth’s stellar flux (corresponding to 0.5–2 AU for the Sun). [5] Referred to by Huygens as a Planetes novus (“new planet”) in his Systema Saturnium [6] Both labelled nouvelles planètes (new planets) by Cassini in his Découverte de deux nouvelles planetes autour de Saturne[66] [7] Both once referred to as “planets” by Cassini in his An Extract of the Journal Des Scavans.... The term “satellite” had already begun to be used to distinguish such bodies from those around which they orbited (“primary planets”). [8] Measured relative to Earth. [9] Jupiter has the most verified satellites (67) in the Solar System.[93]

31.10 References

CHAPTER 31. PLANET

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Bibcode:1963Sci...139..910G. nal. 660 (2): 1492–1506. arXiv:astro-ph/0608574 . doi:10.1126/science.139.3558.910. PMID 17743054. Bibcode:2007ApJ...660.1492C. doi:10.1086/513417. [110] Luhman, K. L.; Allers, K. N.; Jaffe, D. T.; Cush- [124] Belton, M. J. S.; Terrile, R. J. (1984). Bergstralh, ing, M. C.; et al. (2007). “Ophiuchus 1622–2405: J. T., ed. “Rotational properties of Uranus and NepNot a Planetary-Mass Binary”. The Astrophysical Jourtune”. Uranus and Neptune. NASA. CP-2330: 327–347. Bibcode:1984urnp.nasa..327B. nal. 659 (2): 1629–36. arXiv:astro-ph/0701242 . Bibcode:2007ApJ...659.1629L. doi:10.1086/512539. [125] Borgia, Michael P. (2006). The Outer Worlds; Uranus, [111] Britt, Robert Roy (2004-09-10). “Likely First Photo of Neptune, Pluto, and Beyond. Springer New York. pp. Planet Beyond the Solar System”. Space.com. Retrieved 195–206. 2008-08-23. [126] Lissauer, Jack J. (1993). “Planet formation”. Annual Re[112] Bailes, M.; Bates, S. D.; Bhalerao, V.; Bhat, N. D. R.; et view of Astronomy and Astrophysics. 31. (A94-12726 al. (2011). “Transformation of a Star into a Planet in a 02–90) (1): 129–174. Bibcode:1993ARA&A..31..129L. Millisecond Pulsar Binary”. Science. 333 (6050): 1717– doi:10.1146/annurev.aa.31.090193.001021. 20. arXiv:1108.5201 . Bibcode:2011Sci...333.1717B. doi:10.1126/science.1208890. PMID 21868629. [127] Strobel, Nick. “Planet tables”. astronomynotes.com. Retrieved 2008-02-01. [113] On the origin of planets at very wide orbits from the recapture of free floating planets, Hagai B. Perets, M. B. N. [128] Zarka, Philippe; Treumann, Rudolf A.; Ryabov, Boris Kouwenhoven, 2012 P.; Ryabov, Vladimir B. (2001). “MagneticallyDriven Planetary Radio Emissions and Application to [114] D. R. Anderson; Hellier, C.; Gillon, M.; Triaud, A. H. M. Extrasolar Planets”. Astrophysics & Space Science. J.; Smalley, B.; Hebb, L.; Collier Cameron, A.; Maxted, 277 (1/2): 293–300. Bibcode:2001Ap&SS.277..293Z. P. F. L.; Queloz, D.; West, R. G.; Bentley, S. J.; Enoch, doi:10.1023/A:1012221527425. B.; Horne, K.; Lister, T. A.; Mayor, M.; Parley, N. R.; Pepe, F.; Pollacco, D.; Ségransan, D.; Udry, S.; Wilson, D. M. (2009). “WASP-17b: an ultra-low density planet in [129] Faber, Peter; Quillen, Alice C. (2007-07-12). “The Total Number of Giant Planets in Debris Disks with Central a probable retrograde orbit”. arXiv:0908.1553 [astroClearings”. arXiv:0706.1684 [astro-ph]. ph.EP]. [115] Young, Charles Augustus (1902). Manual of Astronomy: [130] Brown, Michael E. (2006). “The Dwarf Planets”. California Institute of Technology. Retrieved 2008-02-01. A Text Book. Ginn & company. pp. 324–7. [116] Dvorak, R.; Kurths, J.; Freistetter, F. (2005). Chaos And [131] How One Astronomer Became the Unofficial Exoplanet Stability in Planetary Systems. New York: Springer. ISBN Record-Keeper, www.scientificamerican.com 3-540-28208-4. [132] Jason T Wright; Onsi Fakhouri; Marcy; Eunkyu Han; [117] Moorhead, Althea V.; Adams, Fred C. (2008). “EcYing Feng; John Asher Johnson; Howard; Fischer; centricity evolution of giant planet orbits due to cirValenti; Anderson, Jay; Piskunov, Nikolai (2010). “The cumstellar disk torques”. Icarus. 193 (2): 475– Exoplanet Orbit Database”. arXiv:1012.5676 [astro484. arXiv:0708.0335 . Bibcode:2008Icar..193..475M. ph.SR]. doi:10.1016/j.icarus.2007.07.009. [118] “Planets – Kuiper Belt Objects”. The Astrophysics Spec- [133] “Planetary Interiors”. Department of Physics, University of Oregon. Retrieved 2008-08-23. tator. 2004-12-15. Retrieved 2008-08-23. [119] Tatum, J. B. (2007). “17. Visual binary stars”. Celestial [134] Elkins-Tanton, Linda T. (2006). Jupiter and Saturn. New York: Chelsea House. ISBN 0-8160-5196-8. Mechanics. Personal web page. Retrieved 2008-02-02. [120] Trujillo, Chadwick A.; Brown, Michael E. (2002). [135] Podolak, M.; Weizman, A.; Marley, M. 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[136] Hunten D. M., Shemansky D. E., Morgan T. H. (1988), [148] Molnar, L. A.; Dunn, D. E. (1996). “On the Formation of The Mercury atmosphere, In: Mercury (A89-43751 19– Planetary Rings”. Bulletin of the American Astronomical 91). University of Arizona Press, pp. 562–612 Society. 28: 77–115. Bibcode:1996DPS....28.1815M. [137] Sheppard, S. S.; Jewitt, D.; Kleyna, J. (2005). “An [149] Thérèse, Encrenaz (2004). The Solar System (Third ed.). Springer. pp. 388–390. ISBN 3-540-00241-3. Ultradeep Survey for Irregular Satellites of Uranus: Limits to Completeness”. The Astronomical Journal. 129: 518–525. arXiv:astro-ph/0410059 . Bibcode:2005AJ....129..518S. doi:10.1086/426329.

31.11 External links

[138] Zeilik, Michael A.; Gregory, Stephan A. (1998). Introductory Astronomy & Astrophysics (4th ed.). Saunders College Publishing. p. 67. ISBN 0-03-006228-4.

• International Astronomical Union website

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[140] Weaver, Donna; Villard, Ray (2007-01-31). “Hubble Probes Layer-cake Structure of Alien World’s Atmosphere” (Press release). Space Telescope Science Institute. Retrieved 2011-10-23. [141] Ballester, Gilda E.; Sing, David K.; Herbert, Floyd (2007). “The signature of hot hydrogen in the atmosphere of the extrasolar planet HD 209458b”. Nature. 445 (7127): 511–4. Bibcode:2007Natur.445..511B. doi:10.1038/nature05525. PMID 17268463. [142] Harrington, Jason; Hansen, Brad M.; Luszcz, Statia H.; Seager, Sara (2006). “The phase-dependent infrared brightness of the extrasolar planet Andromeda b”. Science. 314 (5799): 623–6. arXiv:astroph/0610491 . Bibcode:2006Sci...314..623H. doi:10.1126/science.1133904. PMID 17038587. Lay summary – NASA press release (2006-10-12). [143] Kivelson, Margaret Galland; Bagenal, Fran (2007). “Planetary Magnetospheres”. In Lucyann Mcfadden; Paul Weissman; Torrence Johnson. Encyclopedia of the Solar System. Academic Press. p. 519. ISBN 978-0-12088589-3. [144] Gefter, Amanda (2004-01-17). “Magnetic planet”. Astronomy. Retrieved 2008-01-29. [145] Grasset, O.; Sotin C.; Deschamps F. (2000). “On the internal structure and dynamic of Titan”. Planetary and Space Science. 48 (7–8): 617–636. Bibcode:2000P&SS...48..617G. doi:10.1016/S00320633(00)00039-8. [146] Fortes, A. D. (2000). “Exobiological implications of a possible ammonia-water ocean inside Titan”. Icarus. Bibcode:2000Icar..146..444F. 146 (2): 444–452. doi:10.1006/icar.2000.6400. [147] Jones, Nicola (2001-12-11). “Bacterial explanation for Europa’s rosy glow”. New Scientist Print Edition. Retrieved 2008-08-23.

• Photojournal NASA

• Illustration comparing the sizes of the planets with each other, the Sun, and other stars • “IAU Press Releases since 1999 “The status of Pluto: A Clarification"". Archived from the original on 2007-12-14. • “Regarding the criteria for planethood and proposed planetary classification schemes.” article by Stern and Levinson • Planetary Science Research Discoveries (educational site with illustrated articles)


Chapter 32

Ecliptic

The Sun seems to move against the background stars as seen from the orbiting Earth. The ecliptic is the path the Sun appears to trace through the stars. This process repeats itself on a cycle lasting a little over 365 days.

The ecliptic is the apparent path of the Sun on the celestial sphere, and is the basis for the ecliptic coordinate system. It also refers to the plane of this path, which is coplanar with the orbit of Earth around the Sun (and hence the apparent orbit of the Sun around Earth).[1] The path of the Sun is not normally noticeable from Earth’s surface because Earth rotates, carrying the observer through the cycles of sunrise and sunset, obscuring the apparent motion of the Sun with respect to the stars.

32.1 Sun’s apparent motion

rectly north or south of) the Sun about four minutes later each day than it would if Earth would not orbit; a day on Earth is therefore 24 hours long rather than the approximately 23-hour 56-minute sidereal day. Again, this is a simplification, based on a hypothetical Earth that orbits at uniform speed around the Sun. The actual speed with which Earth orbits the Sun varies slightly during the year, so the speed with which the Sun seems to move along the ecliptic also varies. For example, the Sun is north of the celestial equator for about 185 days of each year, and south of it for about 180 days.[4] The variation of orbital speed accounts for part of the equation of time.[5]

32.2 Relationship to the celestial equator Main article: Axial tilt Because Earth’s rotational axis is not perpendicular to its orbital plane, Earth’s equatorial plane is not coplanar with the ecliptic plane, but is inclined to it by an angle of about 23.4°, which is known as the obliquity of the ecliptic.[6] If the equator is projected outward to the celestial sphere, forming the celestial equator, it crosses the ecliptic at two points known as the equinoxes. The Sun, in its apparent motion along the ecliptic, crosses the celestial equator at these points, one from south to north, the other from north to south.[3] The crossing from south to north is known as the vernal equinox, also known as the first point of Aries and the ascending node of the ecliptic on the celestial equator.[7] The crossing from north to south is the autumnal equinox or descending node.

The motions as described above are simplifications. Due to the movement of Earth around the Earth–Moon center of mass, the apparent path of the Sun wobbles slightly, with a period of about one month. Due to further perturbations by the other planets of the Solar System, the Earth–Moon barycenter wobbles slightly around a mean Main article: Axial precession (astronomy) position in a complex fashion. The ecliptic is actually the apparent path of the Sun throughout the course of a The orientation of Earth’s axis and equator are not fixed year.[2] in space, but rotate about the poles of the ecliptic with Because Earth takes one year to orbit the Sun, the appar- a period of about 26,000 years, a process known as luent position of the Sun also takes the same length of time nisolar precession, as it is due mostly to the gravitational to make a complete circuit of the ecliptic. With slightly effect of the Moon and Sun on Earth’s equatorial bulge. more than 365 days in one year, the Sun moves a little Likewise, the ecliptic itself is not fixed. The gravitational less than 1° eastward[3] every day. This small difference perturbations of the other bodies of the Solar System in the Sun’s position against the stars causes any particu- cause a much smaller motion of the plane of Earth’s orbit, lar spot on Earth’s surface to catch up with (and stand di- and hence of the ecliptic, known as planetary precession. 354


32.3. OBLIQUITY OF THE ECLIPTIC

355 The angular value of the obliquity is found by observation of the motions of Earth and other planets over many years. Astronomers produce new fundamental ephemerides as the accuracy of observation improves and as the understanding of the dynamics increases, and from these ephemerides various astronomical values, including the obliquity, are derived.

The plane of Earth's orbit projected in all directions forms the reference plane known as the ecliptic. Here, it is shown projected outward (gray) to the celestial sphere, along with Earth’s equator and polar axis (green). The plane of the ecliptic intersects the celestial sphere along a great circle (black), the same circle on which the Sun seems to move as Earth orbits it. The intersections of the ecliptic and the equator on the celestial sphere are the vernal and autumnal equinoxes (red), where the Sun seems to cross the celestial equator.

Obliquity of the ecliptic for 20,000 years, from Laskar (1986).[12] Note that the obliquity varies only from 24.2° to 22.5° during this time. The red point represents the year 2000.

Until 1983 the obliquity for any date was calculated from The combined action of these two motions is called gen- work of Newcomb, who analyzed positions of the planets eral precession, and changes the position of the equinoxes until about 1895: by about 50 arc seconds (about 0°.014) per year.[8] ε = 23° 27′ 08″.26 − 46″.845 T − 0″.0059 T 2 + 0″.00181 T3 Main article: Nutation where ε is the obliquity and T is tropical centuries from [13] Once again, this is a simplification. Periodic motions B1900.0 to the date in question. of the Moon and apparent periodic motions of the Sun From 1984, the Jet Propulsion Laboratory’s DE series (actually of Earth in its orbit) cause short-term small- of computer-generated ephemerides took over as the amplitude periodic oscillations of Earth’s axis, and hence fundamental ephemeris of the Astronomical Almanac. the celestial equator, known as nutation.[9] This adds a pe- Obliquity based on DE200, which analyzed observations riodic component to the position of the equinoxes; the po- from 1911 to 1979, was calculated: sitions of the celestial equator and (vernal) equinox with ε = 23° 26′ 21″.45 − 46″.815 T − 0″.0006 T 2 + 0″.00181 fully updated precession and nutation are called the true T3 equator and equinox; the positions without nutation are where hereafter T is Julian centuries from J2000.0.[14] the mean equator and equinox.[10]

32.3 Obliquity of the ecliptic Main article: Axial tilt § Earth

JPL’s fundamental ephemerides have been continually updated. The Astronomical Almanac for 2010 specifies:[15] ε = 23° 26′ 21″.406 − 46″.836769 T − 0″.0001831 T 2 + 0″.00200340 T 3 − 0″.576×10−6 T 4 − 4″.34×10−8 T 5

These expressions for the obliquity are intended for high a relatively short time span, perhaps ± sevObliquity of the ecliptic is the term used by astronomers precision over[16] J. Laskar computed an expression to oreral centuries. for the inclination of Earth's equator with respect to the 10 der T good to 0″.04/1000 years over 10,000 years.[12] ecliptic, or of Earth’s rotation axis to a perpendicular to the ecliptic. It is about 23.4° and is currently decreasing All of these expressions are for the mean obliquity, that 0.013 degrees (47 arcseconds) per hundred years due to is, without the nutation of the equator included. The true or instantaneous obliquity includes the nutation.[17] planetary perturbations.[11]


356

CHAPTER 32. ECLIPTIC

32.4 Plane of the Solar System

used as reference for positions on the celestial sphere, the other being the celestial equator. Perpendicular to the ecliptic are the ecliptic poles, the north ecliptic pole beMain article: Solar System ing the pole north of the equator. Of the two fundamental planes, the ecliptic is closer to unmoving against the backMost of the major bodies of the Solar System orbit the ground stars, its motion due to planetary precession being Sun in nearly the same plane. This is likely due to the way roughly 1/100 that of the celestial equator.[20] in which the Solar System formed from a protoplanetary disk. Probably the closest current representation of the Spherical coordinates, known as ecliptic longitude and disk is known as the invariable plane of the Solar Sys- latitude or celestial longitude and latitude, are used to tem. Earth’s orbit, and hence, the ecliptic, is inclined a specify positions of bodies on the celestial sphere with little more than 1° to the invariable plane, and the other respect to[3]the ecliptic. Longitude is measured positively major planets are also within about 6° of it. Because of eastward 0° to 360° along the ecliptic from the vernal this, most Solar System bodies appear very close to the equinox, the same direction in which the Sun appears to ecliptic in the sky. The ecliptic is well defined by the move. Latitude is measured perpendicular to the eclipmotion of the Sun. The invariable plane is defined by tic, to +90° northward or −90° southward to the poles the angular momentum of the entire Solar System, es- of the ecliptic, the ecliptic itself being 0° latitude. For a sentially the summation of all of the orbital motions and complete spherical position, a distance parameter is also rotations of all the bodies of the system, a somewhat un- necessary. Different distance units are used for different certain value that requires precise knowledge of every objects. Within the Solar System, astronomical units are object in the system. For these reasons, the ecliptic is used, and for objects near Earth, Earth radii or kilometers used as the reference plane of the Solar System out of are used. A corresponding right-handed rectangular coordinate system is also used occasionally; the x-axis is convenience.[18][19] directed toward the vernal equinox, the y-axis 90° to the east, and the z-axis toward the north ecliptic pole; the astronomical unit is the unit of measure. Symbols for 32.5 Celestial reference plane ecliptic coordinates are somewhat standardized; see the table.[21] Main articles: Celestial equator and Ecliptic coordinate Ecliptic coordinates are convenient for specifying posisystem tions of Solar System objects, as most of the planets’ The ecliptic forms one of the two fundamental planes orbits have small inclinations to the ecliptic, and therefore always appear relatively close to it on the sky. Because Earth’s orbit, and hence the ecliptic, moves very little, it is a relatively fixed reference with respect to the stars.

Inclination of the ecliptic over 200,000 years, from Dziobek (1892).[23] This is the inclination to the ecliptic of 101,800 CE. Note that the ecliptic rotates by only about 7° during this time, whereas the celestial equator makes several complete cycles around the ecliptic. The ecliptic is a relatively stable reference compared to the celestial equator. The apparent motion of the Sun along the ecliptic (red) as seen on the inside of the celestial sphere. Ecliptic coordinates appear in (red). The celestial equator (blue) and the equatorial coordinates (blue), being inclined to the ecliptic, appear to wobble as the Sun advances.

Because of the precessional motion of the equinox, the ecliptic coordinates of objects on the celestial sphere are continuously changing. Specifying a position in ecliptic coordinates requires specifying a particular equinox,


32.9. ASTROLOGY that is, the equinox of a particular date, known as an epoch; the coordinates are referred to the direction of the equinox at that date. For instance, the Astronomical Almanac[24] lists the heliocentric position of Mars at 0h Terrestrial Time, 4 Jan 2010 as: longitude 118° 09' 15”.8, latitude +1° 43' 16”.7, true heliocentric distance 1.6302454 AU, mean equinox and ecliptic of date. This specifies the mean equinox of 4 Jan 2010 0h TT as above, without the addition of nutation.

357 • Libra • Scorpius • Ophiuchus[27] • Sagittarius • Capricornus • Aquarius

32.6 Eclipses

32.9 Astrology

Main article: Eclipse

Main article: Astrology The ecliptic forms the center of a band about 20° wide

32.7 Equinoxes and solstices Main articles: Equinox and Solstice The exact instants of equinoxes or solstices are the times when the apparent ecliptic longitude (including the effects of aberration and nutation) of the Sun is 0°, 90°, 180°, or 270°. Because of perturbations of Earth’s orbit and peculiarities of the calendar, the dates of these are not fixed. [26]

32.8 In the constellations The ecliptic currently passes through the following constellations: • Pisces • Aries • Taurus • Gemini • Cancer • Leo • Virgo

Apparent magnitude: Constellation family: +90° Cepheus Cepheus

0 1 Zodiac

2 3 4 Ursa Major Perseus Ursa Minor β UMi

Spectral type: Hercules Orion

O B A F Heavenly Waters

G K Bayer α UMi Polaris

Kochab

M W La Caille Cepheus Cepheus γ Cas β Cas Tsih Caph

α UMa Camelopardalis Dubhe Cassiopeia α Per β Aur α Aur LynxMenkalinan Capella Mirfak β UMaUrsa γ And α Cas MerakMajor PerseusAlmach Schedar Boötes Canes γ UMa Vega α Gem Auriga Andromeda Andromeda γ Cyg Leo Castor β And Phad β Gem ε Cyg β Per Venatici Corona Sadr β Peg β Tau Minor Gienah Pollux Lyra Triangulum Mirach Borealis Elnath Algol +30° Scheat γ Leo β Cyg A Gemini Taurus Aries ε Boo VulpeculaAlbireo Algieba Coma α And Cancer Izar α Tau ♈ Pegasus Alpheratz Berenices Leo γ Gem ♊ Sagitta Hercules Serpens γ Ori α Ari Aldebaran β Leo ♉ ε Peg Alhena Bellatrix Hamal ♋ Canis α Ori Delphinus α Oph (Caput) ♌ Denebola Enif Pisces α Peg Pisces α Boo Orion Rasalhague α Leo Betelgeuse δ Ori ♓ Markab ♓ Arcturus Virgo ♍ Equuleus Regulus Mintaka Minor ζ Ori Serpens α Aql ο Cet 0° TIC ε Ori Sextans η Oph α Vir Mira Alnitak α CMi Altair Aquila (Cauda) Sabik α Hya LIP β Ori Alnilam Spica Alphard ProcyonMonoceros EC Aquarius Aquarius

Cassiopeia +60°

α Cep Alderamin

α Dra Thuban

Draco

γ Dra α Cyg Deneb Cygnus Etamin α Lyr Lacerta

μ Cep Herschel's Garnet Star

α CrB Alphecca

80 UMa Alcor

η UMa Alkaid

δ UMa ε UMa Megrez Alioth

ζ UMa Mizar

Declination

Because the orbit of the Moon is inclined only about 5.145° to the ecliptic and the Sun is always very near the ecliptic, eclipses always occur on or near it. Because of the inclination of the Moon's orbit, eclipses do not occur at every conjunction and opposition of the Sun and Moon, but only when the Moon is near an ascending or descending node at the same time it is at conjunction or opposition. The ecliptic is so named because the ancients noted that eclipses only occurred when the Moon crossed it.[25]

ε Eri Scutum Cetus Libra α CMa Lepus Rigel Sadira Crater ♒ α PsA δ Sco Corvus Eridanus CMa Sirius Ophiuchus Capricornus HydraδWezen β Cet Canis β CMa κ Ori τ Cet Fomalhaut ♑ σ SgrSagittarius ♎ Dschubba λ Sco Durre Menthor Deneb Kaitos η Cen θ Cen Nunki Pyxisη CMa Major Mirzam Saiph ♐ Piscis α Sco Marfikent Shaula Menkent ε Sgr Antares Austrinus Antliaζ Pup Aludra Fornax Sculptor Kaus AustralisCoronaScorpius Lupus Centaurus Naos λ Vel Columba ♏ Microscopium Puppis ε CMaCaelum ε Cen γ Cen Suhail ε Sco Phoenix Phoenix Austrina Birdun Muhlifein α Gru Wei Adhara Velaδ Vel γ Vel β Gru Alnair α Phe Ara Norma α Lup Pictor Horologium Koo She Suhail Gruid Grus Indus Telescopium Ankaa θ Sco Men κ Sco Crux α Pav Sargas Carina Girtab Circinus -60° ε Car Peacock Triangulum Tucana Tucana Tucana Tucana DoradoReticulum β Cen Australe ι Car Avior Cru δ Pav Pavo α Eri α Car κ Vel Aspidiske α Cen B HadarMusca γGacrux α TrA Apus Hydrus Achernar best SETI target star ε Tuc Markab VolansCanopus Atria last star in Rigil Kentaurusβ Cru Hipparcos Chamaeleonβ Car Mensa Becrux α Cru Catalogue α Cen A Miaplacidus Octans Acrux Rigil Kentaurus -90° 21 h 18 h 15 h 12 h 9h 6h 3h 0h Right ascension

-30° Sculptor

Equirectangular plot of declination vs right ascension of the ecliptic, modern constellations (including the zodiac, shaded light grey), Milky Way (fuzzy band) and stars brighter than apparent magnitude 5

called the zodiac, on which the Sun, Moon, and planets are seen always to move.[28] Traditionally, this region is divided into 12 signs of 30° longitude, each of which approximates the Sun’s motion through one month.[29] In ancient times the signs corresponded roughly to 12 of the constellations that straddle the ecliptic.[30] These signs give us some of the terminology used today. The first point of Aries was named when the vernal equinox was actually in the constellation Aries; it has since moved into Pisces.[31]

32.10 See also • Formation and evolution of the Solar System • Invariable plane • Protoplanetary disk • Celestial coordinate system

32.11 Notes and references [1] U.S. Naval Observatory Nautical Almanac Office, Nautical Almanac Office; U.K. Hydrographic Office, H.M.


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Nautical Almanac Office (2008). The Astronomical Almanac for the Year 2010. U.S. Govt. Printing Office. p. M5. ISBN 978-0-7077-4082-9. [2] U.S. Naval Observatory Nautical Almanac Office (1992). P. Kenneth Seidelmann, ed. Explanatory Supplement to the Astronomical Almanac. University Science Books, Mill Valley, CA. ISBN 0-935702-68-7., p. 11 [3] The directions north and south on the celestial sphere are in the sense toward the north celestial pole and toward the south celestial pole. East is the direction toward which Earth rotates, west is opposite that. [4] Astronomical Almanac 2010, sec. C [5] Explanatory Supplement (1992), sec. 1.233

[23] Dziobek, Otto (1892). Mathematical Theories of Planetary Motions. Register Publishing Co., Ann Arbor, Michigan., p. 294, at Google books [24] Astronomical Almanac 2010, p. E14 [25] Ball, Robert S. (1908). A Treatise on Spherical Astronomy. Cambridge University Press. p. 83., at Google books [26] Meeus (1991), chap. 26 [27] Serviss, Garrett P. (1908). Astronomy With the Naked Eye. Harper & Brothers, New York and London. pp. 105, 106. at Google books [28] Bryant, Walter W. (1907). A History of Astronomy. p. 3., at Google books

[6] Explanatory Supplement (1992), p. 733 [29] Bryant (1907), p. 4 [7] Astronomical Almanac 2010, p. M2 and M6 [8] Explanatory Supplement (1992), sec. 1.322 and 3.21 [9] U.S. Naval Observatory Nautical Almanac Office; H.M. Nautical Almanac Office (1961). Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac. H.M. Stationery Office, London. , sec. 2C [10] Explanatory Supplement (1992), p. 731 and 737 [11] Chauvenet, William (1906). A Manual of Spherical and Practical Astronomy. I. J.B. Lippincott Co., Philadelphia. , art. 365-367, p. 694-695, at Google books [12] Laskar, J. (1986). “Secular Terms of Classical Planetary Theories Using the Results of General Relativity”. , table 8, at SAO/NASA ADS [13] Explanatory Supplement (1961), sec. 2B

[30] see, for instance, Leo, Alan (1899). Astrology for All. , p. 8, at Google books [31] Vallado, David A. (2001). Fundamentals of Astrodynamics and Applications (second ed.). Microcosm Press, El Segundo, CA. ISBN 1-881883-12-4. , p. 153

32.12 External links • The Ecliptic: the Sun’s Annual Path on the Celestial Sphere Durham University Department of Physics • Seasons and Ecliptic Simulator University of Nebraska-Lincoln • MEASURING THE SKY A Quick Guide to the Celestial Sphere James B. Kaler, University of Illinois

[14] U.S. Naval Observatory, Nautical Almanac Office; H.M. Nautical Almanac Office (1989). The Astronomical Almanac for the Year 1990. U.S. Govt. Printing Office. ISBN 0-11-886934-5. , p. B18

• Earth’s Seasons U.S. Naval Observatory

[15] Astronomical Almanac 2010, p. B52

• Kinoshita, H.; Aoki, S. (1983). “The definition of the ecliptic”. Celestial Mechanics. 31: 329–338. Bibcode:1983CeMec..31..329K. doi:10.1007/BF01230290.; comparison of the definitions of LeVerrier, Newcomb, and Standish.

[16] Newcomb, Simon (1906). A Compendium of Spherical Astronomy. MacMillan Co., New York. , p. 226-227, at Google books [17] Meeus, Jean (1991). Astronomical Algorithms. Willmann-Bell, Inc., Richmond, VA. ISBN 0-94339635-2. , chap. 21 [18] Danby, J.M.A. (1988). Fundamentals of Celestial Mechanics. Willmann-Bell, Inc., Richmond, VA. ISBN 0943396-20-4. , sec. 9.1 [19] Roy, A.E. (1988). Orbital Motion (third ed.). Institute of Physics Publishing. ISBN 0-85274-229-0. , sec. 5.3 [20] Montenbruck, Oliver (1989). Practical Ephemeris Calculations. Springer-Verlag. ISBN 0-387-50704-3. , sec 1.4 [21] Explanatory Supplement (1961), sec. 2A [22] Explanatory Supplement (1961), sec. 1G

• The Basics - the Ecliptic, the Equator, and Coordinate Systems AstrologyClub.Org


Chapter 33

Orbital eccentricity This article is about eccentricity in astrodynamics. For 33.1 Definition other uses, see Eccentricity (disambiguation). The orbital eccentricity of an astronomical object is a In a two-body problem with inverse-square-law force, every orbit is a Kepler orbit. The eccentricity of this Kepler orbit is a non-negative number that defines its shape. The eccentricity may take the following values: • circular orbit: e = 0 • elliptic orbit: 0 < e < 1 (see ellipse) • parabolic trajectory: e = 1 (see parabola) • hyperbolic trajectory: e > 1 (see hyperbola) The eccentricity e is given by Theta

Focal point

e=

1+

2EL2 mred α2

where E is the total orbital energy, L is the angular momentum, mᵣₑ is the reduced mass, and α the coefficient of the inverse-square law central force such as gravity or electrostatics in classical physics: F =

α r2

(α is negative for an attractive force, positive for a repulsive one; see also Kepler problem)

An elliptic, parabolic and hyperbolic Kepler orbit: elliptic (eccentricity = 0.7) parabolic (eccentricity = 1) hyperbolic orbit (eccentricity = 1.3)

or in the case of a gravitational force: √

parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptical orbit, 1 is a parabolic escape orbit, and greater than 1 is a hyperbola. The term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section. It is normally used for the isolated twobody problem, but extensions exist for objects following a rosette orbit through the galaxy.

e=

1+

2εh2 µ2

where ε is the specific orbital energy (total energy divided by the reduced mass), μ the standard gravitational parameter based on the total mass, and h the specific relative angular momentum (angular momentum divided by the reduced mass). For values of e from 0 to 1 the orbit’s shape is an increasingly elongated (or flatter) ellipse; for values of e from 1

359


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to infinity the orbit is a hyperbola branch making a to- where: tal turn of 2 arccsc e, decreasing from 180 to 0 degrees. The limit case between an ellipse and a hyperbola, when • rₐ is the radius at apoapsis (i.e., the farthest distance e equals 1, is parabola. of the orbit to the center of mass of the system, which is a focus of the ellipse). Radial trajectories are classified as elliptic, parabolic, or hyperbolic based on the energy of the orbit, not the ec• r is the radius at periapsis (the closest distance). centricity. Radial orbits have zero angular momentum and hence eccentricity equal to one. Keeping the energy constant and reducing the angular momentum, elliptic, The eccentricity of an elliptical orbit can also be used to parabolic, and hyperbolic orbits each tend to the corre- obtain the ratio of the periapsis to the apoapsis: sponding type of radial trajectory while e tends to 1 (or in the parabolic case, remains 1). rp 1−e For a repulsive force only the hyperbolic trajectory, in= ra 1+e cluding the radial version, is applicable. For elliptical orbits, a simple proof shows that arcsin( e ) yields the projection angle of a perfect circle to an ellipse of eccentricity e. For example, to view the eccentricity of the planet Mercury (e = 0.2056), one must simply calculate the inverse sine to find the projection angle of 11.86 degrees. Next, tilt any circular object (such as a coffee mug viewed from the top) by that angle and the apparent ellipse projected to your eye will be of that same eccentricity.

33.4 Examples

33.2 Etymology From Medieval Latin eccentricus, derived from Greek ἔκκεντρος ekkentros “out of the center”, from ἐκ- ek-, “out of” + κέντρον kentron “center”. Eccentric first appeared in English in 1551, with the definition “a circle in which the earth, sun. etc. deviates from its center.” Five years later, in 1556, an adjective form of the word was added.

33.3 Calculation

Gravity Simulator plot of the changing orbital eccentricity of Mercury, Venus, Earth, and Mars over the next 50,000 years. The arrows indicate the different scales used. The 0 point on this plot is the year 2007.

The eccentricity of the Earth's orbit is currently about 0.0167; the Earth’s orbit is nearly circular. Over hundreds of thousands of years, the eccentricity of the Earth’s orbit varies from nearly 0.0034 to almost 0.058 as a result of gravitational attractions among the planets (see graph).[1]

The eccentricity of an orbit can be calculated from the Mercury has the greatest orbital eccentricity of any planet orbital state vectors as the magnitude of the eccentricity in the Solar System (e = 0.2056). Before its demotion vector: from planet status in 2006, Pluto was considered to be the planet with the most eccentric orbit (e = 0.248). The Moon's value is 0.0549. Sedna, the most distant known e = |e| trans-Neptunian object in the Solar System, has an exwhere: tremely high eccentricity of 0.85491 due to its estimated aphelion of 937 AU and perihelion of about 76 AU. For • e is the eccentricity vector. the values for all planets and other celestial bodies in one table, see List of gravitationally rounded objects of the SoFor elliptical orbits it can also be calculated from the lar System. periapsis and apoapsis since r = a(1 − e) and rₐ = a(1 Most of the Solar System’s asteroids have orbital eccen+ e), where a is the semimajor axis. tricities between 0 and 0.35 with an average value of 0.17.[2] Their comparatively high eccentricities are probra − rp ably due to the influence of Jupiter and to past collisions. e= ra + rp Comets have very different values of eccentricity. 2 Periodic comets have eccentricities mostly between 0.2 = 1 − ra + 1 and 0.7,[3] but some of them have highly eccentric rp


33.7. EXOPLANETS elliptical orbits with eccentricities just below 1, for example, Halley’s Comet has a value of 0.967. Non-periodic comets follow near-parabolic orbits and thus have eccentricities even closer to 1. Examples include Comet Hale– Bopp with a value of 0.995[4] and comet C/2006 P1 (McNaught) with a value of 1.000019.[5] As Hale–Bopp’s value is less than 1, its orbit is elliptical and it will in fact return.[4] Comet McNaught has a hyperbolic orbit while within the influence of the planets, but is still bound to the Sun with an orbital period of about 105 years.[6] As of a 2010 Epoch, Comet C/1980 E1 has the largest eccentricity of any known hyperbolic comet with an eccentricity of 1.057,[7] and will leave the Solar System indefinitely. Neptune's largest moon Triton has an eccentricity of 1.6×10−5 (0.000016),[8] the smallest eccentricity of any known body in the Solar System; its orbit is as close to a perfect circle as can be currently measured.

33.5 Mean eccentricity The mean eccentricity of an object is the average eccentricity as a result of perturbations over a given time period. Neptune currently has an instant (current Epoch) eccentricity of 0.0113,[9] but from 1800 to 2050 has a mean eccentricity of 0.00859.[10]

361

33.7 Exoplanets Of the many exoplanets discovered, most exoplanets have a higher orbital eccentricity than our solar system. Exoplanets found with low orbital eccentricity, near circular orbits, are very close to its star and are tidal locked to the star, like planet Mercury. All eight planets in the Solar System have near-circular orbits. The exoplanets discovered show that the solar system, with its unusually low eccentricity, is rare and unique.[14] One theory attributes this low eccentricity to the high number of planets in the Solar System; another suggests it arose because of its unique asteroid belts. A few other multiplanetary systems have been found, but none resemble the solar system. The solar system has unique planetesimal systems, which led the planets to have nearcircular orbits. Solar planetesimal systems include the asteroid belt, Hilda family, Kuiper belt, Hills cloud, and the Oort cloud. The exoplanet solar systems discovered have either no planetesimal systems or one very large planetesimal system. Low eccentricity is needed for habitability, especially advanced life. High multiplicity planet systems are much more likely to have habitable exoplanets.[15][16] The Grand tack hypothesis of the solar system also helps understand the near-circular orbits of the solar system and the other unique features of the solar system.[17][18][19][20][21][22][23] [24] [25]

33.8 See also 33.6 Climatic effect Orbital mechanics require that the duration of the seasons be proportional to the area of the Earth’s orbit swept between the solstices and equinoxes, so when the orbital eccentricity is extreme, the seasons that occur on the far side of the orbit (aphelion) can be substantially longer in duration. Today, northern hemisphere fall and winter occur at closest approach (perihelion), when the earth is moving at its maximum velocity—while the opposite occurs in the southern hemisphere. As a result, in the northern hemisphere, fall and winter are slightly shorter than spring and summer—but in global terms this is balanced with them being longer below the equator. In 2006, the northern hemisphere summer was 4.66 days longer than winter and spring was 2.9 days longer than fall due to the Milankovitch cycles.[11][12] Apsidal precession slowly changes the place in the Earth’s orbit where the solstices and equinoxes occur (this is not the precession of the axis). Over the next 10,000 years, northern hemisphere winters will become gradually longer and summers will become shorter. Any cooling effect in one hemisphere is balanced by warming in the other—and any overall change will, however, be counteracted by the fact that the eccentricity of Earth’s orbit will be almost halved,[13] reducing the mean orbital radius and raising temperatures in both hemispheres closer to the mid-interglacial peak.

• Eccentricity (mathematics) • Eccentricity vector • Equation of time • Milankovitch cycles • Orbits

33.9 References [1] A. Berger & M.F. Loutre (1991). “Graph of the eccentricity of the Earth’s orbit”. Illinois State Museum (Insolation values for the climate of the last 10 million years). Retrieved 2009-12-17. [2] Asteroids [3] Lewis, John (2 December 2012). Physics and Chemistry of the Solar System. Academic Press. Retrieved 2015-0329. [4] “JPL Small-Body Database Browser: C/1995 O1 (HaleBopp)" (2007-10-22 last obs). Retrieved 2008-12-05. [5] “JPL Small-Body Database Browser: C/2006 P1 (McNaught)" (2007-07-11 last obs). Retrieved 2009-12-17.


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[6] “Comet C/2006 P1 (McNaught) - facts and figures”. Perth Observatory in Australia. 2007-01-22. Retrieved 201102-01.

[24] Harvard-Smithsonian Center for Astrophysics, “Is Earthly Life Premature from a Cosmic Perspective?”, August 1, 2016

[7] “JPL Small-Body Database Browser: C/1980 E1 (Bowell)" (1986-12-02 last obs). Retrieved 2010-03-22.

[25] Relative Likelihood, by Loeb, Batista, and Sloan

[8] David R. Williams (22 January 2008). “Neptunian Satellite Fact Sheet”. NASA. Retrieved 2009-12-17.

• Prussing, John E., and Bruce A. Conway. Orbital Mechanics. New York: Oxford University Press, 1993.

[9] Williams, David R. (2007-11-29). “Neptune Fact Sheet”. NASA. Retrieved 2009-12-17. [10] “Keplerian elements for 1800 A.D. to 2050 A.D.”. JPL Solar System Dynamics. Retrieved 2009-12-17. External link in |publisher= (help) [11] Data from United States Naval Observatory [12] Berger A.; Loutre M.F.; Mélice J.L. (2006). “Equatorial insolation: from precession harmonics to eccentricity frequencies” (PDF). Clim. Past Discuss. 2 (4): 519–533. doi:10.5194/cpd-2-519-2006. [13] Arizona U., Long Term Climate [14] exoplanets.org, ORBITAL ECCENTRICITES, by G.Marcy, P.Butler, D.Fischer, S.Vogt, 20 Sept 2003 [15] National Academy of Sciences of the United States of America, Astronomy, Exoplanet orbital eccentricity: Multiplicity relation and the Solar System, by Mary Anne Limbacha and Edwin L. Turnera, 2014 Dec 15 [16] Steward Observatory, University of Arizona, Tucson, Planetesimals in Debris Disks, by Andrew N. Youdin an dGeorge H. Rieke, 2015 [17] Zubritsky, Elizabeth. “Jupiter’s Youthful Travels Redefined Solar System”. NASA. Retrieved 4 November 2015. [18] Sanders, Ray. “How Did Jupiter Shape Our Solar System?". Universe Today. Retrieved 4 November 2015. [19] Choi, Charles Q. “Jupiter’s 'Smashing' Migration May Explain Our Oddball Solar System”. Space.com. Retrieved 4 November 2015. [20] Davidsson, Dr. Björn J. R. “Mysteries of the asteroid belt”. The History of the Solar System. Retrieved 7 November 2015. [21] Raymond, Sean. “The Grand Tack”. PlanetPlanet. Retrieved 7 November 2015. [22] O'Brien, David P.; Walsh, Kevin J.; Morbidelli, Alessandro; Raymond, Sean N.; Mandell, Avi M. (2014). “Water delivery and giant impacts in the 'Grand Tack' scenario”. Icarus. 239: 74–84. arXiv:1407.3290 . Bibcode:2014Icar..239...74O. doi:10.1016/j.icarus.2014.05.009. [23] Relative Likelihood for Life as a Function of Cosmic Time, Journal of Cosmology and Astroparticle Physics, by Abraham Loeb, Rafael Batista, and David Sloan, August 2016, doi:10.1088/1475-7516/2016/08/040

33.10 External links • World of Physics: Eccentricity • The NOAA page on Climate Forcing Data includes (calculated) data from Berger (1978), Berger and Loutre (1991). Laskar et al. (2004) on Earth orbital variations, Includes eccentricity over the last 50 million years and for the coming 20 million years. • The orbital simulations by Varadi, Ghil and Runnegar (2003) provides series for Earth orbital eccentricity and orbital inclination. • Kepler’s Second law’s simulation


33.10. EXTERNAL LINKS

363

{{int:Coll-attribution-page| • Jet Propulsion Laboratory Source: https://en.wikipedia.org/wiki/Jet_Propulsion_Laboratory?oldid=743518499 Contributors: Brion VIBBER, Timo Honkasalo, Berek, Andre Engels, XJaM, Nate Silva, William Avery, Gjalexei, Tim Starling, Looxix~enwiki, Ahoerstemeier, BigFatBuddha, ²¹², Lommer, Akira742, Itai, Bevo, Bearcat, Gentgeen, Ke4roh, Zandperl, Modulatum, Roscoe x, Kent Wang, Giftlite, Romanpoet, Curps, Alison, Ryjaz, DO'Neil, Python eggs, Bobblewik, Neutrality, Deglr6328, D6, Lovelac7, FranksValli, User2004, Nabla, Ylee, JustinWick, Kwamikagami, Tom, Spoon!, AllyUnion, Photonique, A2Kafir, Musiphil, Alansohn, RoySmith, Alex '05, Caesura, Gene Nygaard, Woohookitty, Sburke, Alanmak, BlankVerse, Bruce Cabot, Gisling, Emerson7, GoldRingChip, Taestell, BD2412, Amerique, Grammarbot, Rjwilmsi, Rogerd, BlueMoonlet, Bubba73, The wub, DoubleBlue, AySz88, Rangek, Margosbot~enwiki, JYOuyang, Tedder, King of Hearts, Chobot, Gwernol, YurikBot, Ugha, RobotE, Arado, 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MBK004, ClueBot, Jeffreykegler, The Thing That Should Not Be, Mild Bill Hiccup, Easphi, SuperHamster, DragonBot, SJL III, Sun Creator, M.O.X, Rivertown, Mellebga, Nathan Johnson, Dthomsen8, Feinoha, Kbdankbot, Dradler, Addbot, Dudemanfellabra, DocOfSoc, Alessandrina, Mjr162006, Glane23, AnnaFrance, Maddox1, Damonskye, Lightbot, The Bushranger, Legobot, Rretwa, Luckas-bot, Yobot, JJARichardson, THEN WHO WAS PHONE?, BeBoldInEdits, AnomieBOT, Meganfoxx, RadioBroadcast, Ckruschke, Savdrtu, Monfasdu, Xqbot, Clohuigt, Thisgureat, Nasaverve, GrouchoBot, Dwagon3, Glenn.S.Johnson, Jarrok43, SpaceHistory101, CTechie, RightCowLeftCoast, Inputpersona, LucienBOT, VS6507, Britbrit1313, MGA73bot, Steve Quinn, Danielpauldavis, Tom.Reding, RedBot, Asbasb, Tbhotch, PhiberOptik, RjwilmsiBot, , EmausBot, Look2See1, Brian642, JustinTime55, Ducati748, ZéroBot, Cogiati, Sandwirt, UCLA Young Research Library, Brandmeister, Donner60, Tabularasasm, KarlsenBot, Dlu776, ClueBot NG, Jamiemillar, Widr, Helpful Pixie Bot, Island Monkey, John Cummings, Wiki13, Netdetectress, Compfreak7, Soerfm, Xlicolts613, Standard2211, Wer900, MeanMotherJr, Cyberbot II, ChrisGualtieri, Khazar2, Fudgewunkles, Livableworld, Sosthenes12, EMC1965, Nhj78992, Apriestofgix, Elinycman, KasparBot, Jmc76, Petpaw, InternetArchiveBot, GreenC bot, Btehrani2 and Anonymous: 147 • Voyager program Source: https://en.wikipedia.org/wiki/Voyager_program?oldid=744007850 Contributors: Eloquence, Bryan Derksen, Robert Merkel, Zundark, Jeronimo, Css, Alex.tan, Eclecticology, Roadrunner, Ray Van De Walker, TomCerul, Olivier, Nealmcb, Patrick, Tillwe, Michael Hardy, Delirium, Alfio, Glenn, Rotem Dan, Evercat, Crissov, Quux, SEWilco, Joy, Chrisjj, Bshort, Robbot, Puckly, Diderot, Alba, Cyrius, Cat6, Giftlite, Reubenbarton, Brouhaha, Steve Casburn, Jyril, Dinomite, Karn, Bradeos Graphon, Fleminra, JamesHoadley, Xinoph, Keith Edkins, ConradPino, Blankfaze, Hammersfan, Ukexpat, MementoVivere, Deglr6328, Intrigue, Eisnel, Andylkl, JTN, Brianhe, Supercoop, Vsmith, Xezbeth, Mani1, Paul August, Bender235, Loren36, RJHall, El C, Ganesha, Remember, Art LaPella, Bobo192, 23skidoo, Duk, Rje, Gsklee, Supersexyspacemonkey, Wendell, 119, Andrew Gray, TommyBoy, Bart133, RPH, Knowledge Seeker, Psmither, Blaxthos, Kitch, Dan100, Nuno Tavares, OleMaster, Bacteria, BillC, MrWhipple, Pol098, Bricktop, Asdert, Hbdragon88, Eyreland, Alan Canon, Smartech~enwiki, Zooks527, Driftwoodzebulin, BD2412, Drbogdan, Rjwilmsi, Strait, Rillian, Vegaswikian, Krash, JEdward, John Alan Halloran, SchuminWeb, Ground Zero, Leslie Mateus, Geimas5~enwiki, DVdm, Bgwhite, Whosasking, RussBot, Witan, Xihr, Hellbus, Hydrargyrum, Lavenderbunny, Tavilis, DragonHawk, Grafen, Joel7687, CecilWard, Ejl, 7Train, Enfresdezh, Philip Stevens, Serendipodous, Sardanaphalus, SmackBot, Hydrogen Iodide, Onebravemonkey, Lukas.S, Gilliam, Ohnoitsjamie, Aaron of Mpls, Marc Kupper, Chris the speller, Bluebot, TimBentley, ChaosControl, Scwlong, WDGraham, Badger151, OrphanBot, MBlume, OOODDD, Aces lead, Andy120290, SpacemanAfrica, The PIPE, Mostlyharmless, Ged UK, John, CorvetteZ51, Vgy7ujm, J 1982, JorisvS, Camilo Sanchez, Cxk271, Uwe W., Emx~enwiki, Newone, Twas Now, Tawkerbot2, Bubbha, Robyn Gibbard, Patrickwooldridge, HDCase, Capedude2005, CmdrObot, Cumulus Clouds, Johnlogic, Hyperdeath, Gogo Dodo, B, Optimist on the run, Omicronpersei8, Splateagle, JamesAM, Epbr123, Hazmat2, Trappleton, SGGH, Uruiamme, Noclevername, Ricnun, Mack2, Walkersam, JAnDbot, Hypnometal, Airbreather, Acroterion, Magioladitis, WolfmanSF, Secret Squïrrel, Swpb, Faizhaider, BatteryIncluded, MissionControl, Gyroid, MartinBot, Loupizzuti, Salsa man, CommonsDelinker, AlexiusHoratius, Zygimantus, Gah4, J.delanoy, Acalamari, Rod57, Ohfosho, Jer10 95, Spoxjox, NewEnglandYankee, Ohms law, Jorfer, Potatoswatter, Sunderland06, ACSE, Spacehog26, Wolfnix, Sdsds, Philip Trueman, TXiKiBoT, Oshwah, TheresJamInTheHills, Macslacker, Vgranucci, BotKung, Telecineguy, Calixton, Norrico, Spinningspark, Bernstein2291, Chenzw, SieBot, Bizbob, Crash Underride, Rackshea, Flyer22 Reborn, The Evil Spartan, Mimihitam, Thomerow, Oxymoron83, Pac72, Lightmouse, Svick, Dravecky, Anchor Link Bot, Nipsonanomhmata, Bpeps, Explicit, Twinsday, John Doe42, Martarius, MBK004, ClueBot, Hongthay, MikeVitale, Beljin~enwiki, PixelBot, Muhandes, JasonAQuest, Jhonwask, Ex penumbrae, ElChristou, AC+79 3888, HumphreyW, DumZiBoT, SuddenFrost, Nettings, XLinkBot, Dthomsen8, Sinister Stairs, Kajabla, Addbot, Mortense, Roentgenium111, Toyokuni3, Fluffernutter, Download, LinkFA-Bot, Tassedethe, 84user, Seeker alpha806, F Notebook, Lightbot, , Legobot, Luckas-bot, Yobot, Donfbreed, Sarrus, AnomieBOT, A More Perfect Onion, Jabalong, Materialscientist, Danno uk, Savdrtu, LilHelpa, Marshallsumter, Xqbot, Srich32977, Trafford09, Fotaun, RetiredWikipedian789, FrescoBot, Jc3s5h, VS6507, Scythian23, D'ohBot, Ysyoon, Tom.Reding, RedBot, MastiBot, NarSakSasLee, Abc10, Bookbuddi, Diannaa, RjwilmsiBot, TjBot, Spudgfsh, WikitanvirBot, Dewritech, Racerx11, Kral!zec-, Solarra, Dffgd, Redav, SporkBot, Tolly4bolly, Lokpest, Dongennl, ChiZeroOne, Abrahampaul74, 1007D, ClueBot NG, MelbourneStar, This lousy T-shirt, Xession, HonestIntelligence, Snotbot, Frietjes, Moneya, O.Koslowski, Rezabot, Widr, MerlIwBot, Helpful Pixie Bot, Theoldsparkle, VoyagerLJG, Félix Wolf, Trevayne08, Epinedo, Kmcurry, Jaybear, Bjskidmore, Cyberbot II, YFdyh-bot, FoCuSandLeArN, Makecat-bot, Jknight6, Hillbillyholiday, Eyesnore, Jcejhay, The Herald, Anythingcouldhappen, Mariner9, Patriot 1423, Captain Schmetterling, Stacie Croquet, Aledownload, Horned Frogs, Tetra quark, DN-boards1, Tdadamemd sioz, Sir Cumference, Shahen books, WillBo and Anonymous: 284 • Pioneer program Source: https://en.wikipedia.org/wiki/Pioneer_program?oldid=735095443 Contributors: RjLesch, Eloquence, Bryan Derksen, Css, Rmhermen, Imran, Darkwind, Gestumblindi, Maximus Rex, JonathanDP81, Dimadick, Ancheta Wis, Reubenbarton, JamesHoadley, Stereo, JTN, RJHall, Remember, Svdmolen, Storm Rider, Gene Nygaard, Kitch, DonPMitchell, Scriberius, Marudubshinki, Vegaswikian, FlaBot, Chobot, Roboto de Ajvol, YurikBot, Van der Hoorn, DragonHawk, Richardcavell, Knotnic, Allens, GrinBot~enwiki, Cmglee, The Yeti, Sardanaphalus, Bigs slb, Greygh0st, Scwlong, Beatgr, WDGraham, John Hyams, Andy120290, SundarBot, J 1982, Novangelis, Kurtan~enwiki, Necessary Evil, Cydebot, Thijs!bot, Seaphoto, Ricnun, Freddicus, VoABot II, Ling.Nut, BatteryIncluded, 28421u2232nfenfcenc, Nodekeeper, CommonsDelinker, NerdyNSK, Gpetrov, Glossologist, Sdsds, Imasleepviking, Broadbot, Telecineguy, Geanixx, SieBot, WereSpielChequers, BotMultichill, Lightmouse, Tombomp, Murlough23, Moletrouser, Randy Kryn, Martarius, Tomeasy, SoxBot, Rror, MystBot, Addbot, Some jerk on the Internet, FiriBot, SamatBot, Yobot, II MusLiM HyBRiD II, 4th-otaku,


364

CHAPTER 33. ORBITAL ECCENTRICITY

AnomieBOT, Hunnjazal, RadioBroadcast, MauritsBot, Xqbot, GrouchoBot, January2009, FrescoBot, RedBot, Ali Abbasi7, MMS2013, EmausBot, Acather96, AvicBot, ZéroBot, Δ, ClueBot NG, Cgruda, Artman maine, Don2074978 and Anonymous: 51 • Copernican Revolution Source: https://en.wikipedia.org/wiki/Copernican_Revolution?oldid=740663669 Contributors: William Avery, TakuyaMurata, William M. Connolley, Charles Matthews, Guy Peters, Giftlite, Matthead, Andycjp, Antandrus, Piotrus, Grstain, Kwamikagami, Smalljim, Martian, KYPark, Naraht, Jameshfisher, King of Hearts, DVdm, Schlafly, Ragesoss, Finell, SmackBot, InverseHypercube, C.Fred, Skizzik, Silly rabbit, Sadads, Vanished User 0001, Fuhghettaboutit, Ckatz, RekishiEJ, Chris55, ShelfSkewed, Neelix, Slazenger, Alaibot, SteveMcCluskey, TonyTheTiger, Escarbot, Hmrox, KConWiki, MartinBot, R'n'B, J.delanoy, Maurice Carbonaro, Cpiral, Lyonski, Philip Trueman, Madhero88, Q Science, Synthebot, PericlesofAthens, PaddyLeahy, Romuald Wróblewski, Nihil novi, Ergateesuk, Yintan, Dino246, Pinkadelica, Dolphin51, Denisarona, ClueBot, Hult041956, Auntof6, Excirial, Johnuniq, Roxy the dog, Addbot, Blethering Scot, Scientus, Glane23, Kyle1278, Mmnaw, Ssaalon, Bootyy, Bfigura’s puppy, Lightbot, TheSuave, Yobot, Houutata, Clubbota, Placcjata, Apptas, MihalOrela, Coulatssa, Timmorra, AnomieBOT, DemocraticLuntz, ‫מאן דאמר‬, Materialscientist, Citation bot, Noideta, Shogartu, Drosdaf, Unigfjkl, Omnipaedista, Cristianrodenas, SD5, Krinkle, Tkuvho, Cnwilliams, Trappist the monk, Extra999, SeoMac, Jarpup, DARTH SIDIOUS 2, Bluszczokrzew, EmausBot, RA0808, Slightsmile, Solomonfromfinland, ZéroBot, GianniG46, Donner60, Xanchester, ClueBot NG, This lousy T-shirt, Helpful Pixie Bot, ‫בלנק‬, Calabe1992, FullnessOfTime, Klilidiplomus, Anbu121, BattyBot, YFdyh-bot, KeepOptions, William2001, QuantifiedElf, Ginsuloft, Meganjeanne1, IndigoDeberry, Petesimon2, Monkbot, KasparBot, DarGothicus, Wilkinstein, Qzd and Anonymous: 105 • Celestial spheres Source: https://en.wikipedia.org/wiki/Celestial_spheres?oldid=736452805 Contributors: SimonP, Edward, Michael Hardy, Menchi, Minesweeper, Charles Matthews, Lumos3, Matthead, Icairns, D6, Rich Farmbrough, Bender235, Camw, Mlewan, Rjwilmsi, Nihiltres, Gaius Cornelius, Ragesoss, Wiqi55, Moogsi, Finell, SmackBot, Jagged 85, MartinPoulter, Silly rabbit, SchfiftyThree, Lambiam, J 1982, RandomCritic, Gregbard, Logicus, SteveMcCluskey, Headbomb, Magioladitis, Chandlr, GoldenMeadows, David J Wilson, Maurice Carbonaro, Deor, James McBride, Radagast3, PaddyLeahy, WRK, Astrologist, Francvs, Leadwind, Singinglemon~enwiki, Rockfang, Sun Creator, Tyler, Editor2020, Legobot II, Coulatssa, AnomieBOT, Towsdfvui, Omnipaedista, FrescoBot, Paine Ellsworth, Machine Elf 1735, Aldoaldoz, Miracle Pen, RjwilmsiBot, Syncategoremata, L0ngpar1sh, Jacobisq, Helpful Pixie Bot, Bibcode Bot, MrBill3, SethSheppard, Tetra quark and Anonymous: 22 • Firmament Source: https://en.wikipedia.org/wiki/Firmament?oldid=738484711 Contributors: Leandrod, Bueller 007, JamesReyes, Xanzzibar, J heisenberg, Beland, Rich Farmbrough, Bishonen, Dbachmann, Longhair, Interiot, Hq3473, WadeSimMiser, Doric Loon, Ashmoo, Koavf, Kauffner, Anyone7, Finell, That Guy, From That Show!, Bluewave, SmackBot, PiCo, Yamaguchi , Kevinalewis, Tv316, Bluebot, Mr.Z-man, John D. Croft, JohnCub, JoshuaZ, Robert Stevens, NJMauthor, Keahapana, Maestlin, Lenoxus, CmdrObot, Agathman, Cydebot, SteveMcCluskey, Peter Gulutzan, Fayenatic london, Wasell, Jéské Couriano, ***Ria777, Rocinante9x, Simon Peter Hughes, Pomte, Trusilver, Smitty927, TomS TDotO, Byronshock, Jarry1250, Lights, VolkovBot, EnterStanman, Asarlaí, Pjoef, ProfessorUniversity, StAnselm, KebsOne, Vanished user ewfisn2348tui2f8n2fio2utjfeoi210r39jf, Iaroslavvs, Uncle Milty, Megamile, IMSirius, Feline Hymnic, Editor2020, Swift as an Eagle, Ost316, SilvonenBot, MystBot, Kbdankbot, Addbot, Aykantspel, Glane23, FaithF, SpBot, Cesiumfrog, Luckas-bot, Yobot, Jeremiahmccarver, AnomieBOT, Andromeas, FrescoBot, Machine Elf 1735, Kibi78704, Reconsider the static, Susieb78, Hueyha, Cobaltcigs, Brandmeister, Rigley, ClueBot NG, JohnsonL623, Tomerav, Saxophilist, Hillbillyholiday, Shalom.sobaba, Mrwittyguy, Giovannimounir, Jalvarez4Jesus, Rmonchez, Anactaka, ImHere2015, Matjitzu and Anonymous: 84 • Primum Mobile Source: https://en.wikipedia.org/wiki/Primum_Mobile?oldid=731795122 Contributors: Nagelfar, BD2412, Koavf, MZMcBride, BOT-Superzerocool, Andrew Lancaster, SmackBot, Mladifilozof, RandomCritic, Maestlin, Penbat, Cydebot, SteveMcCluskey, Dr. Submillimeter, ***Ria777, Reedy Bot, Deor, Astrologist, Fadesga, Addbot, AnomieBOT, Omnipaedista, Paine Ellsworth, TRBP, Jacobisq, Wbm1058, BG19bot, NukeofEarl and Anonymous: 5 • Geocentric model Source: https://en.wikipedia.org/wiki/Geocentric_model?oldid=743410582 Contributors: Bryan Derksen, Andre Engels, XJaM, Christian List, SJK, Roadrunner, SimonP, Lir, Michael Hardy, Gabbe, Ixfd64, Ahoerstemeier, Muriel Gottrop~enwiki, Theresa knott, Bueller 007, Andres, Evercat, º¡º, Dwo, Tom Peters, Timwi, Dino, Fuzheado, Doradus, Zoicon5, Haukurth, Furrykef, David Shay, Omegatron, Shizhao, Flockmeal, Astronautics~enwiki, Fredrik, Lowellian, Hadal, Modeha, Raeky, Anthony, Decumanus, Art Carlson, Fastfission, Paul Pogonyshev, Peruvianllama, Curps, Jfdwolff, Duncharris, Telso, Antandrus, Beland, Kaldari, JimWae, Tothebarricades.tk, Satori, Icairns, Histrion, Arminius, Brianjd, Jayjg, Discospinster, Dbachmann, Bender235, ESkog, RJHall, El C, Marcok, Shanes, Haxwell, Art LaPella, Kappa, WoKrKmFK3lwz8BKvaB94, Juzeris, Kjkolb, Nk, Mdd, Jumbuck, Truth seeker, Matani2005~enwiki, Anthony Appleyard, Delachatelaine, Wtmitchell, Super-Magician, KingTT, Itschris, RainbowOfLight, Sciurinæ, Oleg Alexandrov, Angr, Boothy443, Professor Ninja, Camw, Gerd Breitenbach, Kokoriko, Dzordzm, Someone42, MarcoTolo, Palica, Graham87, NCdave, Rjwilmsi, Leeyc0, Sbp, The wub, FlaBot, Margosbot~enwiki, Winhunter, RexNL, Gurch, Alvin-cs, Chobot, Antiuser, The Rambling Man, YurikBot, Sceptre, Jimp, Brandmeister (old), Red Slash, Stephenb, NawlinWiki, Ragesoss, Kooky, Historymike, Bota47, FF2010, Wiqi55, 2over0, Chanheigeorge, JoanneB, CWenger, Kubra, Allens, Tarquin Binary, Listowy, Serendipodous, WikiFew, SmackBot, Selfworm, Moeron, Hydrogen Iodide, Pgk, C.Fred, Hu Gadarn, Jagged 85, HeartofaDog, HalfShadow, Villaged, Hmains, Skizzik, Chris the speller, MalafayaBot, SchfiftyThree, Neo-Jay, Baa, DHN-bot~enwiki, Deenoe, Scwlong, Tsca.bot, Can't sleep, clown will eat me, Nick Levine, Leinad-Z, Al95521, TKD, Krich, Decltype, Iblardi, Shadow1, Byelf2007, SashatoBot, Lambiam, BrownHairedGirl, Titus III, J 1982, Cronholm144, Aleator, JoshuaZ, Ckatz, Hypnosifl, Z-Axis, Novangelis, Peyre, T4exanadu, Vanished user, BananaFiend, Maestlin, Lmblackjack21, RekishiEJ, Courcelles, Chris55, Cricketicecream, CmdrObot, Geremia, Insanephantom, Agathman, Calibanu, JohnCD, Dgw, El aprendelenguas, TheTito, Richard Keatinge, Yaris678, Cydebot, Valodzka, Xanthoptica, Alvesgaspar, ST47, Doug Weller, Roberta F., Ameliorate!, Apus~enwiki, SteveMcCluskey, Gimmetrow, Thijs!bot, Qwyrxian, Lupogun, Headbomb, Horologium, Ram4eva, Legend Saber, RichardT, AntiVandalBot, Czj, Tchoutoye, MECU, SkoreKeep, Leuqarte, Res2216firestar, JAnDbot, Dan D. Ric, Matthew Fennell, IanOsgood, Acroterion, SteveSims, Magioladitis, Connormah, VoABot II, Professor marginalia, JamesBWatson, Hendrixjoseph, Brain40, ***Ria777, Nyttend, Lucaas, Catgut, Theroadislong, Crzysdrs, Cgingold, Allstarecho, Rockman-X, Pkrecker, Glen, Gwern, S3000, MartinBot, Coolpm, David J Wilson, R'n'B, Tgeairn, J.delanoy, Hippasus, Yensx89, Ian.thomson, Bot-Schafter, Mottelg, JaxBax5, Chiswick Chap, NewEnglandYankee, Nick Graves, Kraftlos, Wavemaster447, Armedconventicle, KylieTastic, Remember the dot, Suaven, BernardZ, Yehoishophot Oliver, VolkovBot, Cireshoe, Macedonian, JohnBlackburne, Abigailgem, Sdsds, Philip Trueman, TXiKiBoT, A4bot, Miranda, Alphaios~enwiki, Supertask, Wassermann~enwiki, Rjm at sleepers, Ericmaue, Tresiden, VVVBot, Caltas, ConfuciusOrnis, Yintan, Hirohisat, S711, Flyer22 Reborn, Faizaguo, Steven Crossin, Lightmouse, Jonpaulusa, Edwardbains, Anchor Link Bot, Mygerardromance, Astrologist, Denisarona, Twinsday, Martarius, ClueBot, The Thing That Should Not Be, Raborg, Jorge Ianis, Boing! said Zebedee, U5K0, Singinglemon~enwiki, Sun Creator, Executor Tassadar, Razorflame, Thehelpfulone, Versus22, Adriansrfr, Editor2020, Whoelius, PSimeon, Avoided, Aunt Entropy, Addbot, Freakmighty, Fyrael, Non-dropframe, Captain-tucker, Fieldday-sunday, Scientus, Proxima Centauri, Glane23, Favonian, Ehrenkater, Tide rolls, Lightbot, Randomness2, MissAlyx, Luckas-bot, Yobot, WikiDan61, II MusLiM HyBRiD II, Abasass, Keeratura, Timmorra, AnomieBOT, Givbataska, IRP, AdjustShift, Citation bot, Givbatad, Maxis ftw, Obersachsebot, Xqbot, Leabnm, Bandgjl, Drojuas, Nexeuitas, Leadusata, Spiretas, Haputdas, Necirsad, Linburats, Pordaguit, Glafyjk, Voigfdsa, Unigfjkl,


33.10. EXTERNAL LINKS

365

Platewq, Sellyme, Zebra2016, GrouchoBot, Mariotaddei1972, Ftaisdeal, Yellowweasel, FrescoBot, StephenWade, Paine Ellsworth, Furryblobs, Gummer85, Pergamino, Yety75, Pimpeddoll, Machine Elf 1735, Buzgun, Thethingofthething, Louperibot, Javert, Pinethicket, Blubro, Tom.Reding, Reconsider the static, Zbayz, ‫علی ویکی‬, Surprizi, Thepalmhq, Nederlandse Leeuw, RjwilmsiBot, Nmillerche, Skamecrazy123, Esoglou, ImprovingWiki, Spandrel, Nocopernicus, Syncategoremata, RA0808, Dcirovic, Solomonfromfinland, Hhhippo, AvicBot, Misty MH, Knight1993, Bfdogood, H3llBot, WillBildUnion, Jacobisq, Donner60, ChuispastonBot, Forever Dusk, Llightex, ClueBot NG, Historikeren, Dpc89, Braincricket, Noym, Widr, Oddbodz, Helpful Pixie Bot, HMSSolent, Bibcode Bot, DBigXray, Roberticus, Jelly gelo, Arjenvreugd, ElphiBot, MusikAnimal, Davidiad, JohnThorne, Harizotoh9, MrBill3, Minsbot, Carliitaeliza, Richmasterninja, ChrisGualtieri, Dexbot, Cwobeel, Hmainsbot1, Mogism, JeanEva Rose, Hair, Remus Octavian Mocanu~enwiki, Junjunone, FenixFeather, Flat Out, DavidLeighEllis, Decrypt Mystic, Ac262, Jimmyevans333, Meo1048, Monkbot, Jayakumar RG, KH-1, Crystallizedcarbon, Yml1944, Codylamare, Caeciliusinhorto, Supercalufraguespexpialidosus, Isambard Kingdom, Lollipop11032001, DoWhatYouMust69, Wolfbear77, SUPASKUA, N. Yanofsky, ImHere2015, Huritisho, L12122001, InternetArchiveBot, Chesedchai, Fiesty panther, GreenC bot, YYYYAAAAYYYY, Griffen Ray and Anonymous: 512 • Geocentric orbit Source: https://en.wikipedia.org/wiki/Geocentric_orbit?oldid=742382582 Contributors: Patrick, Cherkash, Steinsky, SD6-Agent, Icairns, Rich Farmbrough, Bender235, RJHall, 0.39, John Vandenberg, Melaen, Gene Nygaard, BD2412, Vegaswikian, Nihiltres, Kolbasz, Arado, Gaius Cornelius, Reyk, JPK, SmackBot, W!B:, Yamaguchi , Chris the speller, Bluebot, Colonies Chris, Hongooi, Flyguy649, Fuhghettaboutit, Radagast83, Lloyd Wood, Derek R Bullamore, J 1982, JHunterJ, RekishiEJ, ChrisCork, Neelix, Thijs!bot, Headbomb, Marek69, Dainis, BuffaloChip97, Alphachimpbot, Wayne111, Harryzilber, MartinDK, Swpb, Cardamon, JaGa, Gwern, Atulsnischal, Kf4yfd, Sm8900, R'n'B, RockMFR, Plasticup, VolkovBot, Sdsds, TXiKiBoT, Tavix, Rjm at sleepers, AlleborgoBot, Paolo.dL, LaggyLuke, Paulinho28, Easphi, Blanchardb, AikBkj, Morana, Ashtonstreet01, Addbot, Bob K31416, Lightbot, Luckas-bot, Materialscientist, DirlBot, LilHelpa, Sriram.aeropsn, Cekli829, Wiki User 68, Beaber, D'ohBot, Thethingofthething, DixonDBot, EmausBot, WikitanvirBot, JustinTime55, Christianna1219, Thecheesykid, ZéroBot, H3llBot, Ego White Tray, ChiZeroOne, Teapeat, Sabrinamagers, ClueBot NG, BattyBot, Cyberbot II, Gial Ackbar, Melonkelon, Nathginbn, Transphasic, Frinthruit, Mfb, Gronk Oz, UglowT, InternetArchiveBot and Anonymous: 39 • Goddard Space Flight Center Source: https://en.wikipedia.org/wiki/Goddard_Space_Flight_Center?oldid=729767186 Contributors: Rmhermen, Charles Matthews, Denelson83, Gentgeen, Robbot, Ke4roh, JamesMLane, Wolfkeeper, Jacob1207, D6, Bender235, A2Kafir, MrTree, Simone, Etacar11, Robballan, FlaBot, Naraht, YurikBot, Epolk, RadioFan, Gaius Cornelius, Bovineone, EngineerScotty, Grafen, RFBailey, Jpbowen, Ruhrfisch, LeszekKrupinski, Blurble, Open2universe, N Yo FACE, SmackBot, Chris the speller, Stevage, Dual Freq, WDGraham, Penrithguy, KevM, Joema, Tanyiliang, Gump Stump, RJBurkhart, Andrei Stroe, Redeagle688, Hu12, Michaelbusch, Joseph Solis in Australia, Leebert, Lakee911, RockinRob, Cydebot, Clappingsimon, PKT, Dawnseeker2000, WinBot, Kent Witham, Harryzilber, Yill577, TAnthony, Dream Focus, Jllm06, Swpb, Meodudlye, Ebellii, R'n'B, SimpsonDG, Ohms law, Treisijs, VolkovBot, Philip Trueman, TXiKiBoT, Martin451, Broadbot, Christopher Connor, MDfoo, Nova212avon, AlleborgoBot, GirasoleDE, Millerj1993, Toddst1, Kasos fr, Lightmouse, The Someday, Dravecky, Randy Kryn, Dp67, Martarius, FieldMarine, Enenn, Solar-Wind, Lchappell, Nymf, Alexbot, N p holmes, SchreiberBike, Aprock, Atallcostsky, Jonverve, XLinkBot, MystBot, Addbot, Epicadam, 5 albert square, Lightbot, ‫زرشک‬, Evans1982, AnomieBOT, Vextron, Ulric1313, Cyan22, RadioBroadcast, ArthurBot, MauritsBot, Weather91, DSisyphBot, Kithira, Nasa-verve, Wyndhamkapan41, Mark Schierbecker, Obdoc007, Mnmngb, Thehelpfulbot, Originalwana, Phydocmarko, Airmanedwards, FoxBot, TobeBot, Walkerawiki, EmausBot, Immunize, JustinTime55, Jasonanaggie, ZéroBot, SporkBot, ChiZeroOne, ClueBot NG, Jrice0206, Andyfreeberg, Morgan Riley, Tention12, Cgruda, BG19bot, Rhodesia7, Ninney, Derschueler, BattyBot, Guanaco55, JYBot, Rs wrangler, Sohowsgoing, Archwayh, TWette, KasparBot and Anonymous: 60 • Moon Source: https://en.wikipedia.org/wiki/Moon?oldid=743851406 Contributors: Damian Yerrick, Paul Drye, Joao, Derek Ross, WojPob, Brion VIBBER, Mav, Bryan Derksen, Zundark, Berek, Tarquin, Malcolm Farmer, -- April, Ed Poor, Aidan Elliott-McCrea, Andre Engels, Eclecticology, Eob, Arvindn, Christian List, Enchanter, PierreAbbat, Torfason, SimonP, Ben-Zin~enwiki, Maury Markowitz, Zoe, Heron, Montrealais, Youandme, Bignose, Hephaestos, Tucci528, Olivier, Rickyrab, Clintp, Frecklefoot, Edward, Lorenzarius, Lir, Patrick, Infrogmation, JohnOwens, Michael Hardy, Rhorn, Alan Peakall, Liftarn, MartinHarper, Gabbe, Bobby D. Bryant, Wapcaplet, Ixfd64, Cyde, GTBacchus, Minesweeper, Alfio, Egil, Ihcoyc, Ahoerstemeier, Haakon, Mac, Samuelsen, Marumari, Jniemenmaa, Jebba, Kingturtle, Mark Foskey, Goblin, Glenn, Bogdangiusca, Vzbs34, Andres, Jiang, Evercat, David Stewart, Jacquerie27, BRG, Denny, Pizza Puzzle, Ehn, Vodex, Jerryb1961, Hike395, Emperorbma, Victor Engel, Charles Matthews, Timwi, Janko, LennyWikipedia~enwiki, Dino, Wikiborg, RickK, Ed Cormany, Reddi, Random832, Stone, Dysprosia, Colipon, Dandrake, Fuzheado, Doradus, Wik, Prumpf, DJ Clayworth, Haukurth, Tpbradbury, Maximus Rex, Mrand, Tempshill, Mkfairdpm, Chariot, Paul-L~enwiki, Omegatron, Sabbut, Ed g2s, Head, Bevo, Nickshanks, Indefatigable, Fvw, Stormie, Kenatipo, TravelingDude, Raul654, AnonMoos, Wetman, Gakrivas, Ortonmc, Jerzy, Jusjih, Proteus, Johnleemk, Francs2000, Lumos3, Shantavira, PuzzletChung, Donarreiskoffer, MattSal, Nufy8, Robbot, Rossnixon, Sander123, Fredrik, Eman, Jredmond, Alrasheedan, Sanders muc, ZimZalaBim, Kowey, Forseti, Psychonaut, Naddy, Calmypal, Mirv, Postdlf, Ashley Y, Yosri, Sverdrup, Academic Challenger, Lesonyrra, Rursus, Hemanshu, Andrew Levine, Bkell, Hadal, Saforrest, JackofOz, Wereon, Borislav, Michael Snow, Jor, SoLando, Angilbas, Cutler, Dina, David Gerard, Dave6, Ancheta Wis, The Fellowship of the Troll, Nephelin~enwiki, Alexwcovington, Giftlite, DocWatson42, Christopher Parham, Awolf002, Elconde, Oberiko, Nichalp, Wolfkeeper, Tegla, Cobaltbluetony, Netoholic, Tom harrison, Ferkelparade, Brian Kendig, Fastfission, Zigger, Monedula, Karn, Risk one, Bradeos Graphon, Peruvianllama, Everyking, No Guru, Mayavada, Anville, Curps, Alison, Michael Devore, Wikibob, Ryjaz, LLarson, Lurker, Gareth Wyn, Dsmdgold, Dmmaus, Ptk~enwiki, Eequor, Bobblewik, Golbez, Mooquackwooftweetmeow, Wmahan, Vanished user wdjklasdjskla, Stevietheman, StuartH, Chowbok, Ben Arnold, Andycjp, Patteroast, Jm butler, Seba~enwiki, Zeimusu, Slowking Man, Junuxx, Yath, Antandrus, Beland, MisfitToys, Piotrus, Vanished user 1234567890, Kusunose, Kaldari, Karol Langner, 1297, Tels~enwiki, Rdsmith4, Oneiros, DragonflySixtyseven, Mpiff, Latitude0116, Tomruen, PFHLai, Satori, Brianyee0, Lintu~enwiki, Icairns, Zfr, Sam Hocevar, Gscshoyru, B.d.mills, TonyW, Neutrality, Urhixidur, Jcw69, Imjustmatthew, Neale Monks, Demiurge, Deglr6328, Kaustuv, Chmod007, M1ss1ontomars2k4, Zondor, Canterbury Tail, Gcanyon, Lacrimosus, Esperant, Thorwald, Bluemask, Kmccoy, Freakofnurture, JTN, Ultratomio, A-giau, Moverton, Discospinster, Brianhe, Rich Farmbrough, Guanabot, BlueMars, Qutezuce, Kks862003, Vsmith, Florian Blaschke, User2004, Xezbeth, AlexKepler, Ponder, Arthur Holland, Dbachmann, Paul August, Sergei Frolov, SpookyMulder, Goochelaar, Stbalbach, Bender235, Zaslav, Violetriga, Aranel, RJHall, CanisRufus, Mr. Billion, El C, Lycurgus, Huntster, Mdf, Kwamikagami, QuartierLatin1968, Shanes, Tom, Art LaPella, RoyBoy, Femto, Dalf, Iridia, Jonathan Drain, Alxndr, Gedanken, Bobo192, Army1987, Longhair, Fir0002, Smalljim, Xevious, Cmdrjameson, Spug, .:Ajvol:., AllyUnion, JeR, Timl, Juzeris, Man vyi, La goutte de pluie, Sasquatch, Nk, TheProject, Famousdog, Rje, BillCook, MPerel, Sam Korn, Haham hanuka, Benbread, Juanpabl, Jonathunder, Alphonsus, Supersexyspacemonkey, Batneil, Espoo, Goodwin24, Red Winged Duck, Bob rulz, Alansohn, Anthony Appleyard, Mark Dingemanse, Trollminator, SnowFire, Mo0, Richard Harvey, Golobach, Eric Kvaalen, Wiki-uk, Typhlosion, Ricky81682, Verdlanco, Andrew Gray, AzaToth, Orelstrigo, Lectonar, Hinotori, SlimVirgin, Ferrierd, Cramos05, PAR, Garfield226, Mlm42, Malo, Titanium Dragon, Avenue, Max rspct, TaintedMustard, Saga City, Moonfan, Thomas C., Rebroad, Zantastik, Knowledge Seeker, Suruena, Evil Monkey,


366

CHAPTER 33. ORBITAL ECCENTRICITY

Harej, Simon Dodd, Amorymeltzer, Count Iblis, RainbowOfLight, Dirac1933, Cmapm, R6MaY89, H2g2bob, Skatebiker, Cfrjlr, Itsmine, Foggg, Gene Nygaard, Jgb~enwiki, Brizor, Dan East, Capecodeph, Nick Mks, HenryLi, Kazvorpal, KAleksic, Kay Dekker, Meadowbrook, Adrian.benko, RyanGerbil10, Bruce89, TShilo12, Tom.k, Gatewaycat, Siafu, Garrison Roo, Gmaxwell, Weyes, Thryduulf, Velho, Richard Arthur Norton (1958- ), Rorschach, Jeffrey O. Gustafson, Byron Farrow, OwenX, Woohookitty, Mindmatrix, DonPMitchell, TigerShark, Mu301, Justinlebar, LOL, Yansa, Asteron, PoccilScript, Daniel Case, Uncle G, Borb, Benhocking, Bkkbrad, Barrylb, Miketwo, Jacobolus, Kzollman, Capneb, Mpj17, Benbest, TheoClarke, Moth Lor, JeremyA, Jeff3000, MONGO, -Ril-, AshishG, Nakos2208~enwiki, Apokrif, Eleassar777, Schzmo, Pdn~enwiki, Grika, Bbatsell, Dangerous-Boy, Tysalpha, TotoBaggins, Steinbach, Sengkang, KFan II, GregorB, Philosophicles, Eyreland, Darkoneko, CharlesC, Wdanwatts, , Fxer, Joerg Kurt Wegner, Gallaghp, Rgbea, Jimgawn, Rtcpenguin, Paxsimius, Graham87, Marskell, Magister Mathematicae, A Train, BD2412, Vyse, Seyon, Alanstrohm, Reisio, Icey, Sebastiankessel, Drbogdan, Sjakkalle, Rjwilmsi, Bremen, Nightscream, Саша Стефановић, Nkrosse, Vary, Amire80, Rillian, Linuxbeak, JHMM13, Rschen7754, Sdornan, Salix alba, Tawker, Mike s, ErikHaugen, SMC, Nick R, Mike Peel, Crazynas, HappyCamper, Ligulem, Jehochman, SeanMack, Bubba73, Brighterorange, Bhadani, Mkehrt, DirkvdM, Dbigwood, Yamamoto Ichiro, Algebra, Titoxd, SystemBuilder, CAPS LOCK, SchuminWeb, G Clark, RobertG, Musical Linguist, Jcmurphy, Winhunter, Nihiltres, Crazycomputers, RexNL, Ewlyahoocom, Gurch, ChongDae, Mpradeep, President Rhapsody, TeaDrinker, Codex Sinaiticus, Spriteless, Joedeshon, Alphachimp, Bmicomp, Srleffler, JiVE, Gareth E. Kegg, Boyinabox, Cause of death, CiaPan, Daev, Chobot, DaGizza, Jdhowens90, Nagytibi, Mattgenne, DVdm, 334a, Cactus.man, Whosasking, EamonnPKeane, The Rambling Man, Wavelength, Borgx, Spacepotato, Eraserhead1, Hairy Dude, Jimp, Kafziel, Phantomsteve, Gump~enwiki, RussBot, Crazytales, V Brian Zurita, John Quincy Adding Machine, Hellesfarne, Anonymous editor, Bhny, Lexi Marie, SpuriousQ, Chaser, Hellbus, Shawn81, Lar, Yamara, RadioFan, Stephenb, Lord Voldemort, CambridgeBayWeather, Eleassar, Kimchi.sg, Wimt, MarcK, Purodha, NawlinWiki, Vanished user kjdioejh329io3rksdkj, Fabhcún, Shreshth91, Fizan, Stephen Burnett, SEWilcoBot, Wiki alf, E123, Robertvan1, Grafen, Chick Bowen, Bloodofox, Erielhonan, Trovatore, 7121989, Cognition, Stallions2010, Schroedinger’s Mouse, Journalist, Dureo, Mccready, Lexicon, Cleared as filed, JDoorjam, LuthiX, Mshecket, Banes, Anotheran, Brian Crawford, Matticus78, Padajtsch-kall, PhilipO, Chal7ds, Raven4x4x, Off!, Froth, Nick C, Ragzouken, Emersoni, Tony1, Dbfirs, Roy Brumback, MrBark, Zephalis, DeadEyeArrow, Martinwilke1980, Phenz, Nlu, Tonywalton, Wknight94, Avraham, Tkalayci, Noosfractal, Eurosong, Jkelly, Pawyilee, Daniel C, Sandstein, Advanced, Donbert, Doldrums, Emijrp, Deville, Theodolite, Asnatu wiki, Andrew Lancaster, Ageekgal, Nikkimaria, Theda, Studentne, Besselfunctions, Reyk, JQF, Dspradau, Beaker342, GraemeL, Jecowa, JoanneB, Peyna, Vicarious, Danny-w, Fram, Jdmalouff, Hurricane Devon, ArielGold, AGToth, Nixer, X3210, Kungfuadam, Junglecat, Hagie, Phr en, Airconswitch, Iago Dali, Rscottfree, Ghandir, Roke, Serendipodous, Cmglee, DVD R W, Finell, Chandrasonic, Itprotj, Luk, Rayd8, Danlmark, Deuar, Lviatour, Sardanaphalus, Sintonak.X, KnightRider~enwiki, A bit iffy, SmackBot, Burtonpe, WilliamThweatt, Fireman biff, Stonefield, Jimothyjim, Moeron, David Kernow, Rtc, Tarret, Slashme, The hoodie, Dbalderzak, KnowledgeOfSelf, Royalguard11, Arswann, Pgk, Spiffmedic, Rrius, Jacek Kendysz, Anubis2051, Allixpeeke, Jagged 85, Davewild, Thunderboltz, Mickeym, Stifle, Grey Shadow, EncycloPetey, Jrockley, Renesis, Delldot, Lengis, Miljoshi, Monz, Frymaster, Nick Warren, Avatarcourt, Master Deusoma, WesDecker, Aksi great, Gilliam, Ohnoitsjamie, Betacommand, Skizzik, Desiphral, Rufty, Oldfield~enwiki, Vinsabay, GerardKeating, Saros136, Chris the speller, Jbill, Veloslaw~enwiki, Bluebot, PawełMM, KaragouniS, TimBentley, Audacity, Agateller, Persian Poet Gal, Postoak, Soundslikealotofhooplah, Ag Foghlaim, SeanWillard, Rickyjames, Wousifou7, AndrewBuck, MalafayaBot, Hibernian, Spellchecker, DHN-bot~enwiki, Sbharris, Mkamensek, Konstable, Portnadler, William Allen Simpson, Gracenotes, Mikker, Andrew502502, John Reaves, Scwlong, Royboycrashfan, WDGraham, Salmar, Ron g, Can't sleep, clown will eat me, Ajaxkroon, Valdezlopez, Tamfang, Jinxed, Mrwuggs, OrphanBot, OOODDD, Astrobhadauria~enwiki, Chan Yin Keen, IdahoPotatoFarmer, TheKMan, EvelinaB, Homestarmy, Wiki me, Starexplorer, Aces lead, Kcordina, Edivorce, PrivateWiddle, ChaosSorcerer91, UU, Jmlk17, HeteroZellous, Krich, DavidStern, Cybercobra, Khukri, Decltype, NorseOdin, Nakon, TheLimbicOne, Savidan, Jackhextall, DRLB, IntrplnetSarah, RJN, Benjiem1, RaCha'ar, Dany174, Iblardi, Richard001, Wirbelwind, Tomtom9041, Lcarscad, A19grey, Clean Copy, Weregerbil, Occultations, Adrigon, Adamarthurryan, RichAromas, Jlujan69, Ultraexactzz, MarcymYoung, Terrasidius, Acdx, Sigma 7, Suthers, Rodeosmurf, Pilotguy, Kukini, Wilt, Ohconfucius, Bosola, Hmoul, Jf1288, Nishkid64, LtPowers, Robomaeyhem, Tombadevil, Marcavis, Harryboyles, AAA765, Zero10one, Srikeit, Sophia, Soap, Kuru, RTejedor, John, The idiot, Polaris019, Grumpy444grumpy~enwiki, Vgy7ujm, Mathiasrex, ShadowPuppet, J 1982, Jan.Smolik, AnonEMouse, Heimstern, Loodog, Rajiv13, Korean alpha for knowledge, The Infidel, JohnCub, Sir Nicholas de Mimsy-Porpington, Tktktk, JoshuaZ, JorisvS, Volcycle, Accurizer, Minna Sora no Shita, Mgiganteus1, Zzzzzzzzzzz, Ckatz, The Man in Question, Chrisch, RandomCritic, Volkan Yuksel, Loadmaster, HerrPatrick, Bless sins, HerrPatrick2, Incomplete~enwiki, Special-T, Braverman, Loganlogn, TheHYPO, Booksworm, SQGibbon, Aeluwas, Mr Stephen, Rickert, Piepants, Mortpete3, Dicklyon, Xiaphias, SandyGeorgia, Tobyw87, Spiel496, Whomp, Darkinquirer, Ryulong, Fluppy, Lenzar, Novangelis, H, Jose77, Avant Guard, RHB, PSUMark2006, JohnnyBGood, Squirepants101, Fveraz, Lee Carre, Hu12, PaulGS, ChazYork, Ambadale, Tvjames, Michaelbusch, Hayttom, StuHarris, Chance b, Laurens-af, Paul venter, Joseph Solis in Australia, Newone, Mmmoo, Paultownsend, Tó campos~enwiki, R~enwiki, Tony Fox, Octane, SweetNeo85, Hikui87~enwiki, A. Pichler, IanOfNorwich, Alexisgood, Eluchil404, Oshah, Frank Lofaro Jr., Tauʻolunga, Tawkerbot2, Daniel5127, Voge, Bilanovic, Anthony Arrigo, Cryptic C62, Poolkris, Chris55, Orangutan, Michaelh2001, Angelpeream, Behmod, Joshthejedi3, Alexthe5th, JForget, Vaughan Pratt, Adam Keller, Chickenfeed9, CmdrObot, NKSCF, Charlie Quebec Delta Echo Seven Sierra Foxtrot, Geremia, Mustang6172, Cky haggard, Wafulz, CaspianM, Zarex, Olaf Davis, The Font, Drinibot, Banedon, Gyopi, MiShogun, Ruslik0, GHe, Ltrustno1l, Psdel125, Dwolsten, Ferdiaob, WHATaintNOcountryIeverHEARDofDOtheySPEAKenglishINwhat, Outriggr (2006-2009), MarsRover, Basar, RobertLovesPi, Guyguy818181, Trunks6, RagingR2, Ufviper, Phatom87, Douts, Necessary Evil, Cydebot, Peripitus, ChristTrekker, Reywas92, VAXHeadroom, Steel, Wingchild, Meno25, Goldfritha, Gogo Dodo, JFreeman, Corpx, Llort, ST47, Cole Dalton, XcepticZP, Hmkingroman, Rracecarr, Luckyherb, Eu.stefan, Dancter, EnemyOfTheState, Felinoel, Q43, Tawkerbot4, Juansempere, DumbBOT, Dunzoboy, Cheamikejones, Lee, Marvel3666, Paranoid123, Garik, Idioto, Vladq, NMChico24, Omicronpersei8, JodyB, Robertsteadman, Daniel Olsen, Blakjak, UberScienceNerd, Krylonblue83, Zpenzer, Rainer Bartoldus, Joshrulzz, Malleus Fatuorum, Doct.proloy, Mikebuer, LeeG, Vanished user 06, Ilikelotsofnumbers, Markus Pössel, Ante Aikio, Jpmaffett, Aster2, Kablammo, Keraunos, Andyjsmith, Tmguchi, Halibut Thyme, Headbomb, Moondigger, Bad Astronomer, HammerHeadHuman, Leon7, Philippe, Dgies, CharlotteWebb, Greg L, BlytheG, HappyGod, Big Bird, Dawnseeker2000, Natalie Erin, Rompe, AlefZet, Northumbrian, Escarbot, Pie Man 360, Sbandrews, Dantheman531, Ghinji, KrakatoaKatie, Rickyrpatel, Hires an editor, AntiVandalBot, The Obento Musubi, Majorly, Yonatan, Luna Santin, Widefox, Gopherbone, CodeWeasel, Ricnun, Sion8, Opelio, Grouchy Chris, Ravipkb, Juan Cruz~enwiki, SmokeyTheCat, Jk1987, Mdotley, Helicoptor, Harrissc, Shahid hassan99, Spril4, Naveen Sankar, Farosdaughter, Jhsounds, Dwaymire, Myanw, Wahabijaz, Rjwoer, Topatientlyexplain, PresN, Canadian-Bacon, Ingolfson, Len Raymond, JAnDbot, Husond, Harryzilber, WordSurd, MER-C, Dsp13, Truth4Sale, Inbetweener, Something14, Sheitan, IanOsgood, Mark Rizo, Hello32020, Db099221, Michig, Andrew Swallow, Awien, Andonic, PaleAqua, Yill577, Rentaferret, Smith Jones, Roidroid, Rothorpe, Phahrtknoquer, Joshua, LittleOldMe, SteveSims, Callycrane, Thejamesdixon, Angelofdeath275, Magioladitis, WolfmanSF, Secret Squïrrel, Hroðulf, Pedro, Murgh, Suradasa, Bennybp, Bongwarrior, VoABot II, MiguelMunoz, Ukuser, AuburnPilot, VGer!, All your games are belong to us, Gamesarefun, Wikidudeman, Brandt Luke Zorn, JamesBWatson, Adrian122, Teh videogamer!, Father Goose, Drayku, Eltener, ‫باسم‬, Think outside the box, WagByName, Ling.Nut, Geodoc, Azmanet, Bigdan201, Crazytonyi, Axidos, Flappstermoon-


33.10. EXTERNAL LINKS

367

base, Inertiatic076, Email4mobile, Nyttend, Jatkins, WODUP, Deathstars101, SparrowsWing, Mother.earth, Shanster, CosmicPenguin, Gr1st, Rareboy, Presearch, ErKURITA, Ottokhanal, Indon, DYShock, ForestAngel, Its the videogamer!, SaberScorpX, You can't beat the videogamer!, 128.32.16.64., BatteryIncluded, Videogames r fun, Gameguy1, ArthurWeasley, Loonymonkey, Aviatormd, Ciaccona, Hamiltonstone, Allstarecho, Attack of the videogamer!, Attack of t3h videogamer!, Nords, !RemagoediV, James W., Gennaroc, Jim65537, Spellmaster, Zelretch, Dylang3893, Just James, Glen, DerHexer, The videogamer has just pwned you, Robogirl, Patstuart, Kitler005, Kheider, An Sealgair, NatureA16, Gjd001, Jez9999, Adriaan, `1234567890-=, Brutus79, Hdt83, MartinBot, Technodude, Winkwink, Diabla71588, UnfriendlyFire, Kane Freak8, Lol66~enwiki, Ianeggo, Game time..., Imakefunofstuff, Alexei Kopylov, Uriel8, Pallasathena~enwiki, Bus stop, R'n'B, CommonsDelinker, AlexiusHoratius, CASfan, A10012, Thermidorthelobster, Tomdatom, Eugene Romi, The Anonymous One, Mikaida, LunneyME, Keermalec, Watch37264, Mikek999, J.delanoy, Classicalclarinet, Trademark123, DrKay, Glamourish, Timvireo, AstroHurricane001, Dangoo, Sageofwisdom, Poohead4411, Drie ice, UBeR, Glencharles, Joshua777, Uncle Dick, All Is One, TrueCRaysball, Jerry, PC78, Tdadamemd, Cspan64, Century0, FriendlyRiverOtter, ABTU, Acalamari, SharkD, IdLoveOne, Dispenser, Cats220, Smart.harish, Bigmac31, Smeira, DarkFalls, MikOrg, Lunokhod, Wombat™, KawiRider91, Ignatzmice, Dfoofnik, Robauz, Jonathanvt, Ryan Postlethwaite, Skier Dude, Jayden54, Bob5191, Smartandgeeky, Rossenglish, RHBridges, Richard D. LeCour, NewEnglandYankee, Lygophile, Urzadek, Philipholden, Ohms law, Tatrgel, ThinkBlue, Heyitspeter, JohnnyRush10, Angular, MetsFan76, Pblaauw, Ukt-zero, FOTEMEH, Advaitavedanta, Haljackey, Kalendis, Screenager87, SlightlyMad, Gallion620, Kehanren, Geekdiva, ACBest, DorganBot, Treisijs, Fnx85, Derekhal, RVJ, Marsgirl8675309, Jbhatt, LaughingVulcan, Sao4, Useight, StoptheDatabaseState, Retal, Brianmaersk, DrewHenson, Specter01010, Chip8884, Idioma-bot, Redtigerxyz, Blabd, Jrt224, Goccfalcons, Lrdwhyt, ACSE, Makewater, Black Kite, Lights, Vranak, Gunnerdevil4, Chinneeb, UnicornTapestry, Ezekiel6789, Eratosignis, VolkovBot, IWhisky, Johan1298~enwiki, Fbifriday, Dave Andrew, ColdCase, Science4sail, JohnBlackburne, Katydidit, Kuebi, Itsmekirill, Indianescence, Iatomm, Freewayeric, Barneca, Mattfox22, Philip Trueman, Drunkenmonkey, Charleca, TXiKiBoT, Agha Nader, Sroc, Zamphuor, Waggy boy, Dojarca, Antoni Barau, Myles325a, UlrikOldenburg, Joehall219, GDonato, Miranda, Rei-bot, Larspedia, Afluent Rider, Klamser, Tupolev154, Princessa125, Aholladay, Qxz, Donnadonnadonna, Imasleepviking, Asdfasdfasdfasdfasdfasdfasdfasdf, Gtasa2345, Beyond silence, Lizzie17b, Fizzackerly, The3stars, Martin451, JhsBot, Leafyplant, Macman2, Dronir, Username:45, Trampton, LeaveSleaves, Ripepette, THE MOON RULES, Anthrcer, Seb az86556, Duckman89, Picturef1, Qwert135, Cremepuff222, Zigzag20, Schuyler11dy, Yergizmo, Liberal Classic, Maxim, Selenologist, Saturn star, Cosmos416, Smartguy911, Desai96, 1981willy, Colin stuart, Coolotter88, Mwilso24, Rune Kock, Eubulides, Tri400, SheffieldSteel, Pious7, Blurpeace, Lerdthenerd, MacTire, Omulazimoglu, Happyme22, RayNorris, Synthebot, Youridhere, Richtom80, Vchimpanzee, Neilnat, Patyoda, Dpleibovitz, Thanatos666, WatermelonPotion, Insanity Incarnate, Tsuchi Kokoro, Jobberone, Brianga, Hinomaru kun, Sealman, Rep07, WikiGlory, Soulzangel, Dan52192, AlleborgoBot, Darkkujah, K-dawg69, Mrgr, PericlesofAthens, Vanilla Fire, Blondeditz10880, Mmaaxx123, Oklabama, EmxBot, Todonchus, Tedstryk, Okay exclaim, Steven Weston, Arjun024, SimonPQ, SieBot, Flamingott, StAnselm, Cattails~enwiki, Rambo’s Revenge, Rjk1541, Waldhorn, Jim77742, Codylinleyishot, LarsHolmberg, YonaBot, Spartan, Tiddly Tom, That girl over there, BotMultichill, Jack Merridew, Sakkura, Mortarion666, Su huynh, Dawn Bard, Livezero711, Redhookesb, Charlesburg, Happysailor, Exert, Oda Mari, Arbor to SJ, Mirkoruckels, Shaheenjim, Jamiepgs, SPACKlick, Mike Shepherd, Beaupedia, Oxymoron83, Lightmouse, Mus640, Jimmyup, Iain99, Murlough23, RSStockdale, Yamaka122, BenoniBot~enwiki, Hamochik4300, Camo17, Antfrisby, Kingcon999, Correogsk, LonelyMarble, HokieJC, James AL Williams, Paulinho28, WikiLaurent, Ken123BOT, Dabomb87, Pskeidere, Superbeecat, Jscorp, Neo., Archtransit, Aceman91, Illinois2011, Lord Opeth, Nergaal, DRTllbrg, Lloydpick, Escape Orbit, Into The Fray, TracySurya, Randy Kryn, Tuntable, Hibsch, Asher196, Velvetron, Gis-team, The sunder king, Invertzoo, Animorphswes, Francis Hoar, Soporaeternus, Kanesue, Martarius, MBK004, Gratedparmesan, ClueBot, Jbening, VanishedUser sdu9aya9f213ws, Wildie, QueenofBattle, WurmWoode, Irwade, Hustvedt, PipepBot, Deanlaw, Dobermanji, Sammmttt, ArdClose, Edited by you, Roga Danar, ZenCopian, Wwheaton, 1redrun, Sakai26, Hxckid0018, FileMaster, Gregcaletta, Meekywiki, Mr sean meers, Franamax, WDavis1911, Itsadiel, Cp111, NikoTooCool, Wet flame20, MichaelWhi~enwiki, Lostweston09864, Full Moon Acorah, Half Moon Acorah, Ahhatungz, Sosoor, High on meth, ToddT91, Duskateteam, Adamg1996, Shamusmagee, Kiia1511019, Laffy1992, Tu2snpointeshz, J.30-06, Created Accounts, Shaye12345, J8079s, Wak3y, SuperHamster, Hmrz, Hot1-no.972623244, JTBX, Bangkokbetty, Regibox, Vezii, Irish hunta, Gordo1717, Niceguyedc, Lold666, Pj6hall, Polizzt, Camo19, Neverquick, Heflinator, ManiaclexXxDevil, Adampantha, Dades4-0, Solar-Wind, Lotsofxoxluv, Gusyo, N00bz0r123324234234, DragonBot, Rodney420, Littleperson, Opkong5, Awickert, Rdelehunt, Jusdafax, Allyluvspink, Hargitai, Tgmonkeyman, Halo 87, Sun Creator, Brews ohare, NuclearWarfare, Hamfan, PhySusie, 7&6=thirteen, Sweetieepie7, Kacey60, Gciriani, Dj manton, Askahrc, Leroyinc, JasonAQuest, Mud dog, Stepheng3, Salon Essahj, Kingkong23832, Sakurausumaki, Poor people, Care bear count down halo 2, Galifokerr, Nissansunny2007, Wearethemoon, Thingg, Jtle515, Aitias, Ch3atah, ApostleJoe, Dana boomer, Akaszynski, Johnuniq, SoxBot III, Wnt, Mirboj, DumZiBoT, Darkicebot, Harold.k.rogers, Caldwell malt, Skunkboy74, Sorurou, AlanM1, Spitfire, Kaustubh, Terry0051, Stickee, Jopparn, Jacob jordan, Emma mcfly, Rreagan007, TFOWR, Onetreehill1215, SilvonenBot, ScoutingforGirls, Topherus54321, Subversive.sound, JinJian, D.M. from Ukraine, Errolhunt, Yaik9a, Hammie423, Roentgenium111, Mohamed Osama AlNagdy, DOI bot, Xe Cahzytr Ryz, Ncc1701a, Tcncv, JJ606, Betterusername, CycloneGU, PahaOlo, Dgroseth, Fgnievinski, AkhtaBot, Iceblock, Lionoso, Ronhjones, Butcher1234, SpillingBot, Harrymph, Modþryð, LaaknorBot, Ccacsmss, 37ophiuchi, Chzz, Paris 16, Kyle1278, SecretIdentityNumber26, LinkFA-Bot, Jasper Deng, Xev lexx, Tahmmo, 84user, Numbo3-bot, Prim Ethics, Ehrenkater, Tide rolls, Lightbot, Kiril Simeonovski, AHbot, Bro0010, Greyhood, CountryBot, HerculeBot, Spiritualism, Coviepresb1647, Luckas-bot, Yobot, Ptbotgourou, TaBOT-zerem, Legobot II, Kan8eDie, The Earwig, KamikazeBot, YngNorman, Ayrton Prost, Szajci, Breenchris72, AnomieBOT, Archon 2488, 1exec1, Rjanag, Kosmicwizard, JackieBot, BK520, LlywelynII, Copytopic1, Kingpin13, Jo3sampl, Jedikid5, EryZ, Materialscientist, Jtmorgan, RadioBroadcast, Citation bot, Eumolpo, ArthurBot, LilHelpa, MauritsBot, Xqbot, Lily20, Timir2, Denyerl, Engineering Guy, TechBot, Fol de rol troll, Watermelon21, Timmyshin, The Rogue Leader, Loveless, Tyrol5, Gap9551, Almabot, Crzer07, GrouchoBot, Abce2, Aashrith, Earlypsychosis, Mark Schierbecker, RibotBOT, Nedim Ardoğa, Charvest, Ejrubio, The Wiki ghost, Fobos92, Bigger digger, Eugene-elgato, A. di M., Erik9, Fotaun, Thehelpfulbot, Basketballdood14, Casteres, FrescoBot, Gwideman, LucienBOT, Paine Ellsworth, Originalwana, Tobby72, Pepper, Altg20April2nd, Sky Attacker, Jc3s5h, , Masz, MathFacts, Mfwitten, Worldrimroamer, Bambuway, BenzolBot, Greggydude, Orion 8, HamburgerRadio, OgreBot, Citation bot 1, Galmicmi, Arsareth, Cmiych, Osprey9713, JIK1975, Gautier lebon, ChrisJBenson, Monkeyfox, HRoestBot, WaveRunner85, 10metreh, Rameshngbot, Tom.Reding, Cax17, Valkyrie Red, Heyheyheyelmohere, Ejvind, Shadowwalker93, Achim1999, Semjlb, Manwell123, Lazy Sk8, Jody4180, Ryanblanck, Reporter2009, RedBot, Ezhuttukari, Plasticspork, Fartherred, SkyMachine, IVAN3MAN, Hanakabutchii, Soccerisawesome, Kgrad, Gryllida, FoxBot, Thrissel, Double sharp, TobeBot, Trappist the monk, Fama Clamosa, Dinamik-bot, Raama, NunthorpeSchool, Lollypopliam, Oisteadman, Aiken drum, Diannaa, Earthandmoon, Saprissy, Tbhotch, SeanBrockest, RjwilmsiBot, TjBot, Indypapi, Yaush, Wintonian, Polylepsis, DASHBot, EmausBot, Dolescum, WikitanvirBot, Qurq, Ka2uya2ep, Grrow, Benichan, Syncategoremata, GoingBatty, JustinTime55, Sdicastro, Gwillhickers, Dcirovic, Theurgist, Oceans and oceans, Werieth, Destroyer4115454, ZOMG.co, Misty MH, A2soup, Rppeabody, R. J. Mathar, Nicolas Eynaud, AvicAWB, Battoe19, Pankazunleashed, H3llBot, SporkBot, Jackstephenbuchanan, L1A1 FAL, Rcsprinter123, Arnaugir, Sbmeirow, Jchelios, Fjbabbitt95, DOwenWilliams, Brandmeister, Elisabethand, A1b2c3d4e5g6, L Kensington, Ekac23, Jj98, Epicstonemason, ChuispastonBot, RockMagnetist, ChiZeroOne, Leomill, Bobsager112233, ErnestSDavis, ClueBot NG, Kirill Borisenko, C4100,


368

CHAPTER 33. ORBITAL ECCENTRICITY

Xession, Violettsureme, Heaney555z, Frietjes, Stas000D, AlexAndrews, Dalekcan, Hlm Z., North Atlanticist Usonian, Bstephens393, Flendersnod, Helpful Pixie Bot, Akbarmohammadzade, Unbal3, Bibcode Bot, Will123321, BG19bot, Deepblue1, Qwerty1219, Wiki13, Raybob95, Snow Rise, Michael Barera, Cadiomals, Pocketthis, Soerfm, SundanceXP, Colinmartin74, Zedshort, CAWylie, Strz4life, PattiCakes91, Jfkduihv, MeanMotherJr, BattyBot, Jake.edu, Njaohnt, GoShow, Kelvinsong, Smalleditor, Dexbot, Bioisme, Br'er Rabbit, CuriousMind01, TwoTwoHello, Sidelight12, Corn cheese, JustAMuggle, Hillbillyholiday, Reatlas, Anixx1, Joeinwiki, Rfassbind, Epicgenius, F6Zman, Maddit, CamV8, Hanamanteo, Reaper-NG, GutiGuys, Bardbom, RaphaelQS, CensoredScribe, Ugog Nizdast, JeanLucMargot, Exoplanetaryscience, Kind Tennis Fan, Shrees1234, Anrnusna, Tara.lemieux, Abitslow, Lbattersby0, *thing goes, Monkbot, Filedelinkerbot, The Original Filfi, Themulticaster, Saurusaurus, ElkoGraf, Cynulliad, ThePenultimateOne, MacMorrow Mór, GoldCoastPrior, Tetra quark, Isambard Kingdom, Human3015, For12for11aa, Jason.nlw, SdfaDFg, DN-boards1, , Inyouchuu shoku, Tdadamemd sioz, Supdiop, Tiger7253, Ocdgrammarian, KasparBot, Gothaparduskerialldrapolatkh, Dilidor, Deepanshu1707, Champ 7FC, Yogee23, Edulovers, SHOBHADIVYA, MartinZ02, InternetArchiveBot, Colonel Wilhelm Klink, Rfl0216, Motivação, Zwifree, Handthrown and Anonymous: 1505 • Space Network Source: https://en.wikipedia.org/wiki/Space_Network?oldid=618266978 Contributors: Vegaswikian, N2e, Ohms law, Gekritzl, Dravecky, ImageRemovalBot, Jonverve, Yobot, ChildofMidnight, Nasa-verve, Locobot, DrilBot, EdoBot, Monkbot and Anonymous: 2 • NASA Source: https://en.wikipedia.org/wiki/NASA?oldid=742501857 Contributors: Magnus Manske, WojPob, Brion VIBBER, Eloquence, Mav, Wesley, Bryan Derksen, Berek, Tarquin, Koyaanis Qatsi, Alex.tan, Rmhermen, William Avery, SimonP, DavidLevinson, Ben-Zin~enwiki, Camembert, Icarus~enwiki, Montrealais, Netesq, Hephaestos, Edward, Patrick, Kaijan, Norm, Tompagenet, Wapcaplet, Ixfd64, TakuyaMurata, Tangentier, Karada, Arpingstone, Minesweeper, Tregoweth, Looxix~enwiki, Ahoerstemeier, Pjamescowie, Mac, Erzengel, Rlandmann, Andres, Jiang, Astudent, Mxn, Hashar, Daniel Quinlan, Audin, WhisperToMe, Zoicon5, DJ Clayworth, Maximus Rex, Saltine, Taxman, SEWilco, Thue, Bevo, Nickshanks, Wetman, Jusjih, Proteus, Finlay McWalter, Frazzydee, Francs2000, Cncs wikipedia, RadicalBender, AlexPlank, Robbot, Ke4roh, Palnu, Mustang dvs, Sander123, AlainV, Zandperl, Benwing, Moondyne, ZimZalaBim, Arkuat, Postdlf, Spike, Rursus, Hemanshu, Caknuck, Rasmus Faber, Hadal, Wikibot, LX, Wereon, Michael Snow, Profoss, Mushroom, Davidcannon, Giftlite, Reubenbarton, Christopher Parham, Gtrmp, Fennec, 0x0077BE, Kim Bruning, Tom harrison, Lupin, Rbs, Peruvianllama, Wwoods, Everyking, Capitalistroadster, Curps, Alison, Michael Devore, Ssd, Guanaco, Ceejayoz, Yekrats, AlistairMcMillan, Python eggs, Bobblewik, Golbez, Peter Ellis, Erich gasboy, Kums, GeneralPatton, Antandrus, Beland, OverlordQ, Jossi, CaribDigita, Oneiros, Mzajac, JimWae, DragonflySixtyseven, Mike Storm, Husnock, Icairns, Howardjp, Neutrality, Sam, Joyous!, Oknazevad, Jh51681, Syvanen, Trevor MacInnis, JamesTeterenko, Canterbury Tail, Jimaginator, Mike Rosoft, Chris Howard, Alkivar, Freakofnurture, N328KF, AliveFreeHappy, O'Dea, Imroy, CALR, JTN, Indosauros, Yossarian4010, Moverton, Diagonalfish, Discospinster, Steve Farrell, Guanabot, Supercoop, GrantHenninger, Marsian~enwiki, Vsmith, Aris Katsaris, Cromis, SpookyMulder, Bender235, Loren36, Hapsiainen, Violetriga, Fenice, Pedant, Eric Forste, Brian0918, PatrickDunfordNZ, MBisanz, Huntster, Joanjoc~enwiki, Kwamikagami, Kross, The bellman, Chairboy, Tom, Art LaPella, RoyBoy, EurekaLott, Thunderbrand, Atraxani, Bobo192, Dralwik, Yonghokim, Longhair, Hurricane111, Mike Schwartz, Smalljim, Clawson, John Vandenberg, Walkiped, BrokenSegue, Mtruch, Viriditas, Blakkandekka, Dpaajones, Elipongo, Angie Y., JW1805, Bijal d g, WoKrKmFK3lwz8BKvaB94, Alexanderpas, Giraffedata, ScottM, Kjkolb, Nk, CoolGuy, Thewayforward, Pschemp, Jvanvelden, Pharos, C-squared, HasharBot~enwiki, Danski14, Alansohn, Gary, PaulHanson, Anthony Appleyard, Hektor, Sheehan, Borisblue, Silver86, Doopokko, Andrewpmk, Andrew Gray, Lectonar, Fat pig73, Mlm42, Hu, Katefan0, LearnMore, Snowolf, Jblake, Velella, Knowledge Seeker, Suruena, Garzo, Evil Monkey, Xyrrus, Max Naylor, Jon Cates, Dirac1933, TenOfAllTrades, Mikeo, Henry W. Schmitt, Pauli133, Seth Goldin, Johntex, RickDeNatale, HenryLi, Kitch, Dan100, Ceyockey, SmthManly, Kbolino, TShilo12, Brookie, KUsam, Bobrayner, Kelly Martin, OwenX, Scriberius, Simon Shek, Whitehorse1, Yansa, PoccilScript, StradivariusTV, Bratsche, Clemmentine, WadeSimMiser, SergeyLitvinov, Jeff3000, MONGO, Jok2000, Cbustapeck, GregorB, Eyreland, Mb1000, Kralizec!, , Prashanthns, Palica, Driftwoodzebulin, Dysepsion, Mandarax, MassGalactusUniversum, Graham87, GoldRingChip, Edison, Crzrussian, Drbogdan, Saperaud~enwiki, Rjwilmsi, Joe Decker, Wahoofive, Koavf, Rogerd, Саша Стефановић, AllanHainey, Bill37212, XP1, Rillian, BlueMoonlet, Linuxbeak, Tangotango, Bruce1ee, Mike Peel, Crazynas, NeonMerlin, Wingover, Ghepeu, Boccobrock, Bhadani, Ttwaring, Yamamoto Ichiro, N0YKG, Marsbound2024, FayssalF, Titoxd, FlaBot, SchuminWeb, Ground Zero, The ARK, Mishuletz, Crazycomputers, Brianreading, Nivix, Themanwithoutapast, Maire, Gurch, Ayla, TheDJ, Nationalseries, ViriiK, Fsguitarist, Srleffler, Stephantom, Coolhawks88, Startaq, King of Hearts, Chobot, Frappyjohn, Lightsup55, DVdm, Imikem, Digitalme, Gwernol, Wjfox2005, Samwaltz, The Rambling Man, Rmbyoung, YurikBot, Wavelength, Angus Lepper, Radishes, RobotE, Hairy Dude, Jimp, Retodon8, Kafziel, Phantomsteve, RussBot, Arado, Me and, Splash, Epolk, LordBleen, RadioFan, Hydrargyrum, Stephenb, Centurion328, Shell Kinney, CambridgeBayWeather, Pseudomonas, Member, Bovineone, RadioKirk, MarcK, NawlinWiki, Vanished user kjdioejh329io3rksdkj, Wiki alf, Grafen, NickBush24, Jaxl, DarthVader, Korny O'Near, RazorICE, The Obfuscator, Lexicon, Cosworth~enwiki, Renata3, CecilWard, Mikeblas, RUL3R, RattBoy, Voidxor, Misza13, Tony1, Syrthiss, San taunk, Polpo, DeadEyeArrow, Bota47, Evrik, TimK MSI, Pierpontpaul2351, Zer0fighta, Light current, Zzuuzz, Lt-wiki-bot, Bayerischermann, Ageekgal, Theda, Closedmouth, Jwissick, E Wing, Jesushaces, GraemeL, Red Jay, JLaTondre, ArielGold, Johnpseudo, Argo Navis, Katieh5584, Junglecat, Jonathan.s.kt, Roke, Sam Weber, DVD R W, CIreland, Kf4bdy, Tom Morris, Luk, Johnmarkh, Sardanaphalus, Veinor, Crystallina, FearTec, AndersL, RupertMillard, SmackBot, Classicfilms, MorrisS, Renegadeviking, Cdogsimmons, Prodego, CompuHacker, Jared555, Unyoyega, WSpaceport, Jacek Kendysz, Thunderboltz, Marauder62, Chairman S., RedSpruce, Michael Dorosh, Delldot, TypoDotOrg, Cuddlyopedia, Ohnoitsjamie, DividedByNegativeZero, Oscarthecat, Skizzik, Fetofs, Poulsen, Saros136, Chris the speller, Bluebot, Kurykh, Joefaust, Persian Poet Gal, Chalkdusted, Postoak, MK8, Achmelvic, Jnelson09, Jordan.Kreiger, Raymond arritt, Rogerhc, MidgleyDJ, SchfiftyThree, Krous~enwiki, I7s, George Church, JoeCool59, Lodev, DHN-bot~enwiki, Kabri, Firetrap9254, Yanksox, Meltingwax, Royboycrashfan, Chendy, WDGraham, Salmar, Zsinj, Can't sleep, clown will eat me, Jahiegel, Kelvin Case, Kirk Surber, Skidude9950, Nima Baghaei, TheKMan, AttackingHobo, Aces lead, Andy120290, Addshore, Wine Guy, Celarnor, SundarBot, Zirconscot, Meson537, Check-Six, Ghiraddje, Cybercobra, Nakon, Savidan, Ne0Freedom, Umbra4, EVula, Silveroblivion, Paroxysm, John oh, AndreasSchreiber, Aafm, Lessthanthree, Tactik, Junyor, Mwtoews, Salamurai, TheVikingRaider, Tankred, Sayden, Mion, Vinaiwbot~enwiki, Fireswordfight, Pilotguy, Kukini, Mikejmu, Wilt, Ohconfucius, SalopianJames, Deepred6502, Ali 786, The undertow, SashatoBot, Nishkid64, Rory096, AThing, Kuru, John, AmiDaniel, Demicx, UberCryxic, Scientizzle, J 1982, Jaffer, Curtholr, Gobonobo, Tim bates, The Inundator, Mbeychok, Tim Q. Wells, Minna Sora no Shita, Mgiganteus1, NYCJosh, Tlesher, Aleenf1, CrimsonDragon90, EnthusiastFRANCE, Jess Mars, Babygrand1, WikiRichard, Ckatz, RandomCritic, Stupid Corn, Stwalkerster, Shangrilaista, Tac2z, Mr Stephen, Teridon, Rglovejoy, Saveben, AxG, Rwboa22, Tomgibbens, Meco, Waggers, Geologyguy, Midnightblueowl, Ryulong, Isenstein, AEMoreira042281, Caiaffa, Andreworkney, DaveG12345, Paleolith, BranStark, DouglasCalvert, Nehrams2020, Iridescent, Clayclayclay, Michaelbusch, Craigboy, Gualtieri, IworkforNASA, Joseph Solis in Australia, Dolly123, Newone, J Di, Philip ea, Cbrown1023, Tony Fox, ChadyWady, CapitalR, EfrenIII, Ytny, Az1568, Courcelles, Cheeesemonger, Fdp, Tawkerbot2, Dlohcierekim, Andy120, George100, RockinRob, Orangutan, Eastlaw, Jtowns, SkyWalker, HDCase, INkubusse, Cyrusc, JForget, PageantUpdater, Vargklo, CRGreathouse, Ale jrb, Geremia, Van helsing, The ed17, Hucz, Ninetyone, Picaroon, JohnCD, ZsinjBot, Runningonbrains,


33.10. EXTERNAL LINKS

369

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Drewza.Collins, Music is math101, DirectEdge, Bob98133, Oxymoron83, Antonio Lopez, Galactus91, Faradayplank, C1AStewart, AngelOfSadness, Nuttycoconut, Fotty, Lightmouse, TrufflesTheLamb, Boromir123, Bucksportmainerocks, Nskillen, TopGUN71691, Arnoldmartin, Int21h, PbBot, Lax237, Gtadoc, Smartguy8307, StaticGull, Adam Cuerden, Legendgirl12345, TaerkastUA, Sphilbrick, Fishnet37222, Nn123645, Florentino floro, Laser813, Pinkadelica, TubularWorld, Randy Kryn, Fordzii, Nbrobnjrel, Cslashb, Mr. Granger, Loren.wilton, Martarius, Tanvir Ahmmed, FlamingSilmaril, MBK004, ClueBot, LAX, GorillaWarfare, GrandDrake, Raymondokoro, The Thing That Should Not Be, Brian Cooke is A God, Nickbirdeagle, Mattkrass, Darklord1307, Supertouch, Wysprgr2005, Theskrobot, Pairadox, Radiodata111, UserDoe, Drmies, Cp111, Mild Bill Hiccup, Jath143, C6758, ClivePIA, CounterVandalismBot, Baseball102, Niceguyedc, Frankypiama, Neverquick, Cirt, Ironb777, Uberthong537, Jeremiestrother, Senthil g j, Nemesis131, Mightyms, Samsee, Donnnni, Albanian012, Loserxaxa, Mimimimimimimim, Nimbus227, Kanishafa, Ben ross.ross, Samhaney, DragonBot, Excirial, Quercus basaseachicensis, Jusdafax, WMidyette, JohnTechno, Reesiemoto, OMGOMGOMGOMGOMGOMGstrawberryshortcake, JIBLETS, Vivio Testarossa, Lartoven, The Founders Intent, Alejandrocaro35, Sun Creator, Tyler, KubenP1234567, Questmagazine, Cenarium, Arjayay, Promethean, Matr91, Mr. Met 13, JamieS93, Lbrun12415, Ndsrulz1, Dekisugi, Tienwilliam, Doberman1560, 0northm, ChrisHodgesUK, La Pianista, Allers95, Poor people, C628, Thingg, Aitias, Jonverve, MarkBrooke, Sasquatch7, MelonBot, Nikki1991, ClanCC, DumZiBoT, Capitalwiki, Erjohnst2, LightAnkh, 123suthan, BarretB, XLinkBot, Amiralia, BOBMANJRBOY, Wikkipeidamesserupper2, Theguyguyguy, Asfasfd, Rolandscholten, Astrofreak92, Motown1665, Avoided, Rreagan007, WikHead, PhoenixMourning, SilvonenBot, Suppermarioman, Mifter, MustafaeneS, Alexius08, Rbsis, Raso mk, Jamespitts89, Thatguyflint, Bababadger, Osarius, Themanz0r, Addbot, Doglover64, Willking1979, AVand, Some jerk on the Internet, Mad Mills, Davedroc, Rthjargjkabbrgjharbg, Dragonkiller33454, Thedemonsouldeath, Tcncv, Pwnwiki, Adamrocks22, AndrewHZ, Klipatov, Laser Razor, NicholasSThompson, 15lsoucy, Nvnv, Ronhjones, Ixireveng3ixi, Gcpioneers, Hatashe, Fieldday-sunday, Julian1234~enwiki, CanadianLinuxUser, Leszek Jańczuk, Ederiel, Bail bonze, Nevgaz181993, NjardarBot, G0T0, Cst17, Messin with heads, Morning277, Macbethmoot, Glane23, Sulmues, Dpwiki~enwiki, Chzz, Favonian, Maddox1, LinkFA-Bot, Jasper Deng, Tyw7, Fiddle4199, Bobsmother123, Numbo3-bot, Ssmercedes18, Bmattioli, St166, Tide rolls, Gail, Zorrobot, MuZemike, TeH nOmInAtOr, Schmiddr2, Nedron12, LuK3, Gameseeker, Swarm, Rrmsjp, Blackjesus11, Luckas-bot, TheSuave, Yobot, Symmerhill, Blckhawk1234, Andreasmperu, Ptbotgourou, TaBOT-zerem, Cleric Yacorah, Trainwreck in the corner, MarcoSaarela, Dufus00, Rsquire3, Evans1982, WikiPiki2, Aelatico, Megan Reyes, Norris the Borris, Eemme1, Laserforce, JohneyAmerica, Vrinan, Againme, Spacestationshuttle, MacTire02, Sk8rbluscat, Harsha850, AnomieBOT, Whiterook6, Jim1138, Chuckiesdad, Kingpin13, RandomAct, Materialscientist, RadioBroadcast, The High Fin Sperm Whale, Danno uk, Citation bot, Ewikdjmco, E2eamon, Felyza, Experting, Xqbot, Wikidushyant, Engineering Guy, Pocketnife43, Loveless, Tyrol5, Nasa-verve, GrouchoBot, Armbrust, Ute in DC, Dextrovix, RibotBOT, Mathonius, Vistasurfdude, Chaheel Riens, Misortie, Žiedas, Fotaun, Green Cardamom, Tktru, Weatherdude2, FrescoBot, Originalwana, Tobby72, Wstrwald, Vinceouca, Sahmejil, HJ Mitchell, Steve Quinn, Finalius, Evalowyn, HamburgerRadio, OgreBot, Citation bot 1, SUL, DrilBot, Biker Biker, Pinethicket, Adlerbot, Tom.Reding, Jackrace, Calmer Waters, A8UDI, CHawc, NorthnBound, MastiBot, Brian Everlasting, Σ, Ras67, Vikalp.kadre, Abw1987, Ravit, Double sharp, Fox Wilson, Rmochinski, Sol-nemisis, Vrenator, DividedFrame, Extra999, Lilbrotherboo, Defender of torch, Dontrell04, Ajfd11111, Pot-Cat*, Tristangeorgethomas, Diannaa, Sts128, Mattahelz, Eagle cole, JV Smithy, Earthandmoon, Toppro, Tbhotch, Chappie5, Minimac, Firecrotch69, OptoMechEngineer, Ironnickel, DARTH SIDIOUS 2, Freysauce, Nemixis, The Utahraptor, RjwilmsiBot, Carrotsarefun12, TjBot, Havea1234, Geräusch, Jadbad, Regancy42, Dobat, Shermanh, Noommos, Dreemteem, Slon02, Steve03Mills, EmausBot, John of Reading, ASeverin, Tubsalot303, Katherine, Dewritech, Orphan beater, Killer kaor, Diamondbaxfan2, Djtrollshard, JustinTime55, Acgrogans17, MartinThoma, Bull Market, Gwillhickers, Sp33dyphil, TJ994, Tommy2010, Challisrussia, Mussermaster, Kingkluk1234, ThorX13, Crissangelmindfreak2, C16sh, Lordgarz, Googar123, Kkm010, ZéroBot, Illegitimate Barrister, Brickbrown, Ghost9420, ElationAviation, Claritas, Stovl, KuduIO, AvicAWB, Everard Proudfoot, Drcjel, Feralhamsterjustin, Aeonx,


370

CHAPTER 33. ORBITAL ECCENTRICITY

H3llBot, Netknowle, Thisguy75, Makecat, Wayne Slam, LukeGallagher, Tompoole247, Sbmeirow, Δ, Alvez3, L Kensington, Yang988, Jakebob88, Gsarwa, Bribo3, Bulwersator, Herzensgut, Gooblah, Cmind123, ChuispastonBot, ChiZeroOne, Marioluigi98, Sean Quixote, Username uses wiki, TexasTerror, Robo77671, Rocketrod1960, Dchicago, ClueBot NG, Terrencegorebach, CRJ200flyer, Gareth GriffithJones, Punyasavatsut, Snow32100100, El Roih, Jeff Song, MelbourneStar, Inkdragon2, Gilderien, JimsMaher, Z-1411, Baseball Watcher, Dtank97, Theimmaculatechemist, Donghyuncoconut, O.Koslowski, Tazandsim, Widr, Tpstick, DeFy18, Penyulap, Fgsak, Pcjstl, Trotterbilly06, HHH-13times, Bobmarley96, Vibhijain, NNNNIIIICCCCHHHH, Pluma, Headline123, Diyar se, Bnash108, Helpful Pixie Bot, Connortoohey, Bokbokchicken, Nikhil naidu2021, ATR94, පසිඳු කාවින්ද, BG19bot, Krenair, Pine, Jab7842, Dr meetsingh, Soerenfm, Bumblezellio, Mark Arsten, Havefunchangingmyedits, Ninney, Metallicavery, Atomician, Dipankan001, Cadiomals, Drift chambers, Gorthian, Soerfm, Zanucktv, Ding612, Xenoma, Agood25, Luckymeister, Hanboan, Shannonsayshi, Raddy5, Zedtwitz, Saumiss, I8urneighbor, Shaun, Wer900, Anbu121, WebTV3, BattyBot, Sam geek, Sadsaque, DarafshBot, Cyberbot II, Rcw258, Adnan bogi, Khazar2, MadGuy7023, Hridith Sudev Nambiar, Jssteil, Dexbot, Rezonansowy, Dissident93, Isaiah lowe, Igotoschool2917, SoledadKabocha, Alckwc, Nathangarg, Mogism, BScMScMD, Rs wrangler, Poopstain47, Ilikeracing, Rachelaine, Euroflux, ਰਾਜੇਨ੍ਦ੍ਰ ਸਿੰਘ, Broken Spine, Jamesx12345, Redalert2fan, Manyakonana1996, Confuciusay, Zziccardi, USA Friends, 19aineshl, The Anonymouse, Robstar1998, Reatlas, Rfassbind, E emma0306, Buckaroofuss, Cawhee, Trollface64, Eehahn12, Ksj2k9, Forgot to put name, Jupiter-4, Epicgenius, Slasher212, The4thPope, AwesomeNinja1337, Lukekfreeman, Awesome girl 123\madi, Kogmaw, Tammy guding, Alkoller, Dustin V. S., Lindenhurst Liberty, Ugog Nizdast, Raphael.concorde, Extremecoopster, PrivateMasterHD, Finnusertop, TheGreenJohn, Skynorth, Kind Tennis Fan, Rustynail127, Human., Rpbedayos, Frenzie23, Robevans123, W.carter, Engr. Mohiuddin Ahmed Rajon, Jack.belk, ColRad85, Monkbot, MakeItSoNumber1, TheQ Editor, Lukeyhano, Backreach, Saurusaurus, SkaterLife, Omnific One, ChamithN, Cynulliad, PRIYANKA SAHU PS, Mnethercutt, I am. furhan., Tetra quark, Isambard Kingdom, Shuvoraj, FerJox, DbivansMCMLXXXVI, Mattster3517, KasparBot, JamusDoore, Anarchyte, Skyllfully, Huritisho, UnitTwo, HalloweenNight, Eurocus47, JJMC89 bot, Imamhosein, Motivação and Anonymous: 1533 • Solar System Source: https://en.wikipedia.org/wiki/Solar_System?oldid=741915062 Contributors: AxelBoldt, Peter Winnberg, Derek Ross, Brion VIBBER, Vicki Rosenzweig, Mav, Bryan Derksen, The Anome, Berek, Tarquin, Jeronimo, -- April, Andre Engels, Eob, Scipius, XJaM, JeLuF, DavidLevinson, Mjb, Heron, Dwheeler, Rickyrab, Patrick, Kchishol1970, Oliver Pereira, Liftarn, Ixfd64, Cyde, Frank Shearar, (, Minesweeper, Lemming, Looxix~enwiki, Ahoerstemeier, KAMiKAZOW, Stan Shebs, Caid Raspa, JWSchmidt, Kingturtle, Mark Foskey, Julesd, Glenn, Kyokpae~enwiki, Stefan-S, Poor Yorick, Nikai, Kwekubo, Jeandré du Toit, Evercat, Ghewgill, Mxn, BRG, Denny, Pizza Puzzle, Schneelocke, Hike395, The Tom, Ec5618, Vanished user 5zariu3jisj0j4irj, Timwi, Andrewman327, Evgeni Sergeev, Doradus, Selket, Markhurd, Tpbradbury, Dragons flight, Saltine, Whcernan, Paul-L~enwiki, Ed g2s, Thomasedavis, Traroth, Topbanana, Nickshanks, Olathe, Bcorr, Jerzy, Jusjih, Lumos3, PuzzletChung, Robbot, The Phoenix, Fredrik, Tlogmer, Jredmond, Altenmann, Yelyos, Nurg, Naddy, Babbage, Merovingian, Academic Challenger, Rursus, Joelwest, Diderot, Roscoe x, Gnomon Kelemen, Rasmus Faber, Davodd, Bkell, Hadal, JackofOz, Borislav, Umlautbob, Carlj7, Rizzoj, Xanzzibar, Mattflaschen, Dina, Carnildo, Decumanus, Nephelin~enwiki, Connelly, Centrx, Giftlite, DocWatson42, Vasi, Jao, Jyril, Laudaka, Elf, Sj, Kim Bruning, Wolfkeeper, Ævar Arnfjörð Bjarmason, Lethe, Lupin, Monedula, Ausir, Peruvianllama, Everyking, Curps, Rick Block, Sundar, Mboverload, Siroxo, Solipsist, Matthead, Foobar, Matt Crypto, Python eggs, Bobblewik, Kmsiever, Golbez, Christopherlin, Wmahan, Ato, Masterhomer, Gadfium, Nova77, Geni, Antandrus, The Singing Badger, HorsePunchKid, BozMo, Beland, Onco p53, Eroica, Phe, MisfitToys, Kaldari, 1297, Mzajac, Samy Merchi, Anythingyouwant, DragonflySixtyseven, Latitude0116, Tothebarricades.tk, Bumm13, Tomruen, PFHLai, Icairns, DenisMoskowitz, Atulsohan, Gscshoyru, Iantresman, Neutrality, Urhixidur, Fanghong~enwiki, Zondor, Adashiel, Grunt, Lacrimosus, DmitryKo, Jfpierce, Grstain, Mormegil, Zowie, Freakofnurture, ClockworkTroll, Sparky the Seventh Chaos, A-giau, Moverton, Discospinster, Vsmith, Jpk, ArnoldReinhold, Adam850, Notinasnaid, Ibagli, MuDavid, Paul August, SpookyMulder, Night Gyr, Bender235, Crevaner, Rubicon, Cyclopia, Neurophyre, Kjoonlee, A purple wikiuser, Limbo socrates, Kelvinc, Nabla, Eric Forste, Brian0918, Tompw, RJHall, MisterSheik, Ben Webber, Sfahey, El C, Mdf, Kwamikagami, Surachit, Pilatus, Worldtraveller, Shanes, Tom, Sietse Snel, Art LaPella, RoyBoy, Thunderbrand, Jonathan Drain, Bobo192, Iamunknown, Longhair, 23skidoo, Jeffmedkeff, Jpallan, Adraeus, Dreish, Chessphoon, Unquietwiki, Maurreen, Geoff.green, Badmonkey0001, Sampo Torgo, The shaggy one, Nesnad, Amyrlin, Scott Ritchie, Mark Musante, Dennis Valeev, La goutte de pluie, Jojit fb, Kjkolb, Microtony, Hi332211, Ardric47, Saluyot, Sam Korn, (aeropagitica), Gsklee, QuantumEleven, Mdd, Luckyluke, Peter Shearan, HasharBot~enwiki, Jason One, Jumbuck, Danski14, Bob rulz, Gary, Gt, Enirac Sum, Etxrge, Prometheus7Unbound, Halsteadk, Neonumbers, Moanzhu, Andrew Gray, Atanamir, Riana, AzaToth, Lectonar, Viridian, Flata, Wdfarmer, Spangineer, Mlm42, Malo, Titanium Dragon, Bootstoots, Hohum, Snowolf, Blobglob, Burwellian, Shinjiman, Melaen, Knowledge Seeker, Drat, Dirac1933, Sciurinæ, Cmapm, H2g2bob, Woodstone, Computerjoe, Ianblair23, DV8 2XL, Gene Nygaard, LukeSurl, Blaxthos, Kitch, Voldemort, Dismas, Tariqabjotu, Hojimachong, Zanaq, Weyes, Batintherain, Rorschach, Mr Tan, Cimex, Georgia guy, LOL, Jason Palpatine, PoccilScript, Thorpe, Benhocking, Aaron McDaid, Oliphaunt, Scjessey, JFG, SPKP, Ruud Koot, MONGO, Mpatel, Pi@k~enwiki, Schzmo, Grika, Dzordzm, Bbatsell, Will.i.am, StephenDawson, Sengkang, GregorB, Meneth, Eilthireach, CharlesC, Zzyzx11, Pictureuploader, Noetica, Wayward, Gimboid13, Smartech~enwiki, Wisq, Megabyte73, Gerbrant, Tslocum, Rnt20, Ashmoo, Chupon, Magister Mathematicae, Siniset, FreplySpang, CarbonUnit, Plau, Dwaipayanc, Josh Parris, Canderson7, Dlimeb, Drbogdan, Sjakkalle, Rjwilmsi, Mayumashu, Erebus555, Syndicate, WingZero, Panoptical, Joffan, Vary, Bill37212, Tangotango, Bruce1ee, Feydey, Reedbraden, Mike s, Mred64, Meidosemme, Ems57fcva, N-Man, Brighterorange, Krash, Bhadani, DarApe, AySz88, Sango123, Yamamoto Ichiro, JohnDBuell, Roo60, FayssalF, Dinosaurdarrell, Titoxd, ColinJF, Roerlepel, FlaBot, Emarsee, SchuminWeb, RobertG, Ground Zero, Nihiltres, Crazycomputers, Who, Nivix, James D. McBride, Shadow007, Rune.welsh, RexNL, Gurch, Nimur, Pcj, Arctic.gnome, DannyZ, OrbitOne, Drumguy8800, TeaDrinker, Steveo2, Sennaista, Silivrenion, Glenn L, Idaltu, Acefitt, Jfiling, Mstroeck, Chobot, Lord Patrick, Sherool, Jinma, E Pluribus Anthony, Algebraist, The Rambling Man, Equal, Wavelength, TexasAndroid, Spacepotato, Vedranf, Wink wink, Deeptrivia, Jimp, Zaphodthewise, Michael Slone, Hyad, John Quincy Adding Machine, Gregconquest, NorCalHistory, Zafiroblue05, Fluorhydric, Admiral Roo, Bergsten, SpuriousQ, JBG, CanadianCaesar, Gateman1997, Shawn81, Stephenb, Sikon, Gaius Cornelius, Sacre, Wimt, Ergzay, Anomalocaris, NawlinWiki, Burrito, SEWilcoBot, Dat789, Wiki alf, The Merciful, Msikma, GenestealerUK, Alpertron, Tkbwik, NickBush24, Cquan, Phoenix79, RazorICE, Michalis Famelis, Lexicon, Irishguy, Cholmes75, Rmky87, Raven4x4x, Emilio floris, AdiJapan, Lomn, Tony1, Deckiller, BOT-Superzerocool, DeadEyeArrow, Jeremy Visser, Brisvegas, Wknight94, LifeStar, Noosfractal, Jkelly, FF2010, Joshua368, Manjithkaini, Serendipitous, Zzuuzz, Wikicheng, Chesnok, Bayerischermann, Ageekgal, ChrisGriswold, Theda, E Wing, Pb30, Redgolpe, Th1rt3en, JQF, De Administrando Imperio, Ed de Jonge, BorgQueen, GraemeL, Aeon1006, JoanneB, Peter, Hurricane Devon, Manipe, Nelson50, Jrethorst, RenamedUser jaskldjslak904, Liyster, Nixer, Hmartin, Bob Hu, Tarquin Binary, Kungfuadam, Hayter, Gone999, Zvika, SkerHawx, Serendipodous, Elliskev, Cmglee, One, Krótki, Phil 1970, Isoxyl, DocendoDiscimus, Deuar, Sardanaphalus, SmackBot, Nfitz, Thierry Caro, Ashill, Haza-w, Prodego, Anarchist42, KnowledgeOfSelf, Martin.Budden, K-UNIT, Primetime, Pgk, AndyZ, Roofus, Leki, Bomac, Jagged 85, Davewild, Chairman S., Jrockley, Renesis, Delldot, Parachnidox, Monz, Rachel Pearce, Fnfd, Edgar181, HalfShadow, Apers0n, Gilliam, Skizzik, BenAveling, Saros136, Master Jay, Qwasty, I know about this, Tigah, Dreg743, Emufarmers, Elagatis, MalafayaBot, Domthedude001, Ryan Paddy, Hibernian, Tianxiaozhang~enwiki, Fredvanner, No-Bullet, Michael Patrick, Piper2000ca, Farry, Kunguni, Tyr Anasazi, Scienz Guy, Colonies Chris,


33.10. EXTERNAL LINKS

371

Gracenotes, KojieroSaske, Rama’s Arrow, Scwlong, Sgt Pinback, Zsinj, Can't sleep, clown will eat me, AntiVan, Tamfang, Ajdz, The Placebo Effect, OrphanBot, Onorem, Blakut, Run!, Starexplorer, Andy120290, Squigish, Addshore, Kcordina, Edivorce, Midnightcomm, Krich, Flyguy649, NoIdeaNick, David31584, Tinctorius, Bowlhover, Nakon, Aelffin, Monotonehell, Rake~enwiki, Jan.Kamenicek, Polonium, BryanG, Mwtoews, DMacks, J P, Salamurai, Er Komandante, DDima, Pilotguy, Kukini, Desmond71, Qmwne235, Beyazid, Ceoil, Cuttycuttiercuttiest, GoldenTorc, Weatherman1126, Caravaca, Robomaeyhem, Erimus, Acebrock, Harryboyles, 711groove, Kuru, John, Philolexica, Iliev, J 1982, AnonEMouse, Ibroadbent, The Infidel, JohnCub, Soumyasch, Sir Nicholas de Mimsy-Porpington, Tktktk, Linnell, Stattouk, JorisvS, 2nd Piston Honda, Minna Sora no Shita, Goodnightmush, Diverman, Redsully, DarthCat, Ph89~enwiki, Mr. Lefty, IronGargoyle, Deviathan~enwiki, Morshem, Ckatz, Mr. Vernon, RandomCritic, A. Parrot, JHunterJ, MarkSutton, Slakr, Werdan7, Stwalkerster, Kirbytime, Dicklyon, Rwboa22, Clq, Astrolog~enwiki, Mets501, Geologyguy, Ryulong, RichardF, Novangelis, AEMoreira042281, H, Terminal157, JDAWiseman, Pjrm, Mike Doughney, Keith-264, Deaþe gecweald, Iridescent, K, Michaelbusch, Dekaels~enwiki, Clarityfiend, Joseph Solis in Australia, Scooter20, Lottamiata, Cyril715, Shoeofdeath, Newone, R~enwiki, Anitanorm, Cityside Seraph, Blehfu, Alienkishore, Cyber boy~enwiki, Ewulp, Shehee, Civil Engineer III, Raj Fra, Fullerene~enwiki, Tawkerbot2, Alegoo92, Dlohcierekim, Ouishoebean, Anthony Arrigo, Xammer, Geckodude92, Orangutan, Patrickwooldridge, Dia^, Sleeping123, Phillip J, CmdrObot, Ale jrb, Hermitage17, Rhuaridh, Zarex, Myrrhlin, Tuvas, KyraVixen, Vyznev Xnebara, Leevanjackson, Harperska, Drinibot, Ruslik0, Aquirata, Michaelbarreto, NickW557, Ferdiaob, MarsRover, Pgr94, Cracker017, Karozoa, Trunks6, Shanew2, JStarStar, Matt. P, AndrewHowse, Cydebot, Derek Balsam, Nbound, MeowMedia, Kanags, Mikebrand, Treybien, Mike Christie, Uniqueuponhim, CovenantD, UncleBubba, Meno25, Michaelas10, Gogo Dodo, Travelbird, JFreeman, Alanbly, Corpx, Bazzargh, ST47, Alexdw, Tdvance, Tawkerbot4, DumbBOT, Wilsjrwinners, Madgeek09, FastLizard4, Bryan Seecrets, Lee, Kozuch, Blindman shady, Arbitrary username, SteveMcCluskey, TxMCJ, Omicronpersei8, JodyB, Daniel Olsen, Lo2u, UberScienceNerd, BetacommandBot, MastaIroh, Epbr123, Parsa, Kubanczyk, Coelacan, Qwyrxian, Felix Portier~enwiki, Janviermichelle, Aster2, Sry85, Keraunos, Andyjsmith, Aslvrstn, TransistorsGoneWild, CynicalMe, Mojo Hand, Oliver202, Headbomb, Ushionna, WillMak050389, HammerHeadHuman, Lars Lindberg Christensen, JustAGal, PJtP, Cogito ergo sumo, Leon7, Sinn, Ideogram, Ajo Mama, BirdKr, AgentPeppermint, BlytheG, Big Bird, DeusMP, Paliosun, Elert, Raditzu, Northumbrian, Dendoi, Sbandrews, LachlanA, ILHI, KrakatoaKatie, Sidasta, AntiVandalBot, Yupik, RobotG, Majorly, Fedayee, Luna Santin, Puntori, Opelio, EarthPerson, Erwin85Bot, Quintote, Voortle, Gnixon, Svdragunov, Smartse, Dvandersluis, Dr. Submillimeter, Farosdaughter, Cymruman, Yuya takeuchi, Gdo01, Once in a Blue Moon, Leevclarke, Tails Soda, Myanw, Ashleyy osaurus, PresN, Canadian-Bacon, JAnDbot, Osmaston, Husond, MER-C, Planetary, The Transhumanist, Stellmach, Bookworm2002, Something14, Sanchom, Legolost, KuwarOnline, Andonic, Hut 8.5, Aubadaurada, RobHolbert, Time3000, Makron1n, Savant13, Rothorpe, Samjohnson, Acroterion, RadicalPi, Penubag, TheTruth2, WolfmanSF, Pedro, Murgh, VoABot II, Lulujannings, Dekimasu, Frip1000, Swpb, ‫باسم‬, Robby, BudMann9, The Enlightened, SparrowsWing, Midgrid, Myles Trundle, Ahadland1234, Catgut, Giggy, Animum, Cyktsui, Mr. Garrison, MetsBot, Arce, Ciaccona, Allstarecho, Scottosborne, Morelanj, Martin benettis@hotmail.com, Glen, DerHexer, Esanchez7587, Bambuush~enwiki, Khalid Mahmood, Laserfire, Figures&Puck, IcePuckScore, Patstuart, Madonna Can, Kayau, Wikianon, Kheider, NatureA16, Oren0, Chantelle2004, Hdt83, MartinBot, RP88, Dwarfplanets.org.uk, Rettetast, Anaxial, Cosumel, Bruin69, MaraNeo127, Mschel, CommonsDelinker, Tulkolahten, Gah4, PrestonH, Werothegreat, RockMFR, Watch37264, Pharaoh of the Wizards, Multifinder17, DrKay, Trusilver, Asqwce, Bharathivdevi, Raistlin11325, Abuk78, Nigholith, Extransit, Cocoaguy, Jerry, Nemrac2, Tdadamemd, Q2op, Q3op, Acalamari, Rc3784, Textangel, Soumya11, IdLoveOne, Medium69, Bot-Schafter, Gman124, Lunokhod, Tarotcards, Gurchzilla, Samojari, Johnismyboo, Chriswiki, AntiSpamBot, Bennymgradz, Comp25, HiLo48, Belovedfreak, Richard D. LeCour, Raichu Trainer, Fountains of Bryn Mawr, Sd31415, Teh Xilian, Hello i am a guy, Ohms law, SJP, Mfrontz, Jorfer, Mufka, Student7, Supermat, Cue the Strings, Sanderling, MetsFan76, Cometstyles, Josh Tumath, Hakkahakkabazoom, Spiral Wave, VoidLurker, U.S.A.U.S.A.U.S.A., Asteroidz R not planetz, Mike V, Guyzero, Bonadea, StoptheDatabaseState, Henhellen, Joeborder, Darklich14, Jevans14, Xiahou, Liop666, Misheru~enwiki, Idioma-bot, Spellcast, Ottershrew, Xenonice, Lights, Japak, Vranak, King Lopez, Michael Hinrichs, VolkovBot, CWii, Thedjatclubrock, Lordmontu, RingtailedFox, Hersfold, Katydidit, Sdsds, Philip Trueman, PNG crusade bot, Sweetness46, Amos Han, TXiKiBoT, Crevox, Tricky Victoria, Vowlesy, Hqb, GDonato, DarrynJ, Nxavar, McLarenJAB, HarryAlffa, Norn Guy, Sean D Martin, Papajfd, Michael riber jorgensen, Qxz, Someguy1221, Dipper3, Steven J. Anderson, Lradrama, MasterSci, Symo85, Gian-2, Leafyplant, Slysplace, LuckyBob76, Raymondwinn, Psyche825, PDFbot, UnitedStatesian, Coleflinn, Cremepuff222, Gloern, Maxim, Damërung, Wikiwatchers, Tipou, Clownrobot, Gene Mocoletlet, Wenli, SheffieldSteel, Pious7, Complex (de), MacTire, Madhav krishnan, BankingBum, Enviroboy, Dragostanasie, Iron knife, Bethy12, Insanity Incarnate, Brianga, HiDrNick, AlleborgoBot, Cderoose, Tonic123, Salamander44, LuigiManiac, Dodo von den Bergen, Costalotta, Delfindakila, FlyingLeopard2014, D. Recorder, Ratsbew, Futuristcorporation, Turok 5, Turok 12, Turok 11, Turok 16, Ringmaster56, Peterfwhyte, Thw1309, SuperExpress, Heals33, Demmy100, SMC89, SieBot, Grandrek, Daman numba23, PlanetStar, Coastside, Yodaroxmysox, Kumpees gay, I'm supah awesome, Poiu555, Love fass, Smarty Pants786, Billie Pipier, Speed Air Man, Turnteeth, Nadav12, Dummyacc, WereSpielChequers, Mrexxx, Ttsenis, Gorillaman0321, Tyler148, Perrysweitzer, Anusface2000, Antiestablishment, MoonshineOHNO, Computer user786, Hertz1888, Mode11bob9, Mbz1, Caltas, Yintan, Crash Underride, Gilsinan, Lukaigeneration, Soler97, Amreatsf4620, Jerryobject, Keilana, Oboebasson, Saramae101, Exert, JD554, Scarvie, Trottaman471, Mimihitam, SOCCERchic2134, Oxymoron83, Antonio Lopez, Nuttycoconut, Beast of traal, Lightmouse, Murlough23, KathrynLybarger, LonelyMarble, BeardedBob, Anchor Link Bot, Randomblue, Anyeverybody, Tommi Ronkainen, Dipa1965, Dabomb87, Kortaggio, Nergaal, DRTllbrg, Emokid0987654321234567890, Sherz~enwiki, C0nanPayne, Chem-awb, AutoFire, Freewayguy, Explicit, Athenean, Twinsday, Martarius, ClueBot, LAX, Bond81895, Potatoedrink, Statalyzer, Nacnud298, Wenny888, Snigbrook, The Thing That Should Not Be, Eric Wester, Postmortemjapan, Pgecaj, Franamax, Drmies, Mild Bill Hiccup, Kush2, Boing! said Zebedee, Niceguyedc, Dazza anderson1, Stylteralmaldo, Neverquick, Fatladi, Ima van Daal, Bkdafkup, Spaceman8815, Sean higgy2007, Paulcmnt, Jim bob jr, Paulkondratuklovesny, AlexanderHaas, Cwill19, Cohenna, Myguy123, Alexbot, Robbie098, Geob42, Pyrokitsune777, Supabanakid, Abrech, Darkkid24, Rhododendrites, Sun Creator, Coinmanj, Dean Harper, Cenarium, Aurora2698, Τις, PhySusie, Ember of Light, Smige30, Leigui, Polly, Cmann100, Chaosdruid, Wise1990, Aitias, Cryptk, Johnuniq, HumphreyW, Ahsasin8, Mooseman927, Kiensvay, Simple implication, ManCreamy, InternetMeme, Dynamite12321, Kaustubh, Salamander724, Rror, Feyrauth, Karaku, Rreagan007, DarthSwim, Real editor, Facts707, WikHead, SilvonenBot, Egyptianboy15223, Eiaschool, CapnZapp, Garycompugeek, Noctibus, Editer in disguise cool, Menthaxpiperita, Vy0123, Chipskip, NobodysPerfect312, Andrewlaneyboi93, Munchynik, PMP126, Greentsunami, Aragupta, Erikhansson1, Poplard, Jfullerw, Boopolo, Summabrian, TheCodeman4, Roentgenium111, Don'tknowenough, Blaz5678, Manisero399, DOI bot, Jojhutton, JonWee, Evanspahr5, Rashaani, Ben261994, Bajibble, Ronhjones, TutterMouse, Gwaldo, Matty456789, Ederiel, Ashanda, Delfman, G0T0, Proxima Centauri, Gifðas, Delaszk, Glass Sword, Debresser, LinkFA-Bot, Tassedethe, Numbo3-bot, Ehrenkater, Miden, Gota 93, Gameseeker, Whatismetric, Coviepresb1647, Yobot, Ptbotgourou, TaBOT-zerem, Adi, Amirobot, KamikazeBot, Azcolvin429, Szajci, Tbayboy, AnomieBOT, Galoubet, Materialscientist, The High Fin Sperm Whale, Citation bot, Marshallsumter, Enok, MauritsBot, Xqbot, Timir2, Baseballdude12321, TechBot, DSisyphBot, Br77rino, Mlpearc, Dogyo, Gap9551, Montana’s Defender, GrouchoBot, Alumnum, Supernova0, Mark Schierbecker, RibotBOT, Enceladusgeysers, Nedim Ardoğa, Sabrebd, Bigger digger, Shadowjams, Silbad, Us441, Fotaun, Constructive editor, Spazturtle, FrescoBot, Voxii, LucienBOT, Paine Ellsworth, Lookang, Pergamino, Citation bot 1, Pinethicket, HRoestBot, Rameshngbot, Tom.Reding, BRUTE, RedBot, Tanzania, Jim Fitzgerald, SkyMachine, Cnwilliams, Zbayz, FoxBot, Dou-


372

CHAPTER 33. ORBITAL ECCENTRICITY

ble sharp, TobeBot, Trappist the monk, ‫ئاراس نوری‬, Cocu, Vrenator, Extra999, Pbrower2a, Duoduoduo, Greenmage801, Товарищ, Memaster3, Jhenderson777, Earthandmoon, Tastycheeze, DARTH SIDIOUS 2, RjwilmsiBot, Thiridaz, NerdyScienceDude, Keyboard mouse, Salvio giuliano, DASHBot, Steve03Mills, EmausBot, Acather96, WikitanvirBot, Qurq, Peash, Dexeillic, AbbaIkea2010, Nations United, GoingBatty, Chermundy, Gwillhickers, JBlover23, Dcirovic, P. S. F. Freitas, ZéroBot, Westley Turner, Kevin29303, AvicAWB, Hevron1998, Aeonx, H3llBot, Confession0791, Carultch, AutoGeek, Sam12321, Brandmeister, L Kensington, Sachinvenga, Bugliarisi, Samoojas, Mobiusorg, Hypercephalic, Danielboerman, , PJS102, Dry., Whoop whoop pull up, Mjbmrbot, Fjörgynn, Raghith, Sleddog116, Xession, Tideflat, Lanthanum-138, Frietjes, Freiza667, Theopolisme, Mightymights, Helpful Pixie Bot, The Gaon, Gob Lofa, Bibcode Bot, Technical 13, MKar, Vagobot, RoflSloth, AvocatoBot, Cooldude5298, Ushio01, Cadiomals, Glevum, Tycho Magnetic Anomaly-1, Colinmartin74, Zedshort, ImhotepBallZ, Eguinto, Cliff12345, Roozitaa, Chompzone, 4Jays1034, BattyBot, Justincheng12345-bot, Cyberbot II, WOtP, ChrisGualtieri, GoShow, JYBot, Harsh 2580, BrightStarSky, Dexbot, Rezonansowy, Anti-Quasar, 134340Goat, Buddy777, JustAMuggle, Hillbillyholiday, Reatlas, Joeinwiki, C5st4wr6ch, Rfassbind, NanzB11, Praemonitus, Lindenhurst Liberty, Nestrs, MortenZdk, The Herald, Prokaryotes, W. P. Uzer, Vikasjariyal, Impregnable, Monkbot, MarioProtIV, Tdadamemd dbmb, Alskoj, Trackteur, İnternion, Jbitz743, SweetCanadianMullet, I am. furhan., Tetra quark, Isambard Kingdom, LL221W, Craftwerker, DN-boards1, Tdadamemd sioz, Radeachar, KasparBot, Sir Cumference, Norma.jean, Fdfexoex, Huritisho, MartinZ02, Outedexits, HalloweenNight, Jonathan Chone, PlanetUser, GreenC bot, Meddling meddler, Fdmjiv, Adrian20083, WikipediaMaster4049 and Anonymous: 1525 • Sun Source: https://en.wikipedia.org/wiki/Sun?oldid=741331559 Contributors: AxelBoldt, Magnus Manske, Vicki Rosenzweig, Mav, Bryan Derksen, Robert Merkel, Berek, Tarquin, Malcolm Farmer, -- April, Ed Poor, Xaonon, Eob, Danny, XJaM, Chrislintott, Rmhermen, DavidLevinson, Caltrop, David spector, Heron, Fonzy, Montrealais, Rickyrab, Spiff~enwiki, Edward, K.lee, Lir, Patrick, JohnOwens, Michael Hardy, Palnatoke, Lexor, Liftarn, Jketola, Ixfd64, Cyde, GTBacchus, Delirium, Loisel, Minesweeper, Kosebamse, Dgrant, Egil, Looxix~enwiki, Ihcoyc, Ahoerstemeier, KAMiKAZOW, Snoyes, Kingturtle, Mark Foskey, Amcaja, Glenn, Poor Yorick, Nikai, Samw, Jedidan747, Jonik, Mxn, Pizza Puzzle, Schneelocke, Hike395, Emperorbma, Crusadeonilliteracy, Charles Matthews, Vanished user 5zariu3jisj0j4irj, Timwi, RickK, Stone, Kbk, Fuzheado, Doradus, Mjklin, Timc, Haukurth, Tpbradbury, Maximus Rex, Dragons flight, Morwen, VeryVerily, SEWilco, Rnbc, Phoebe, Thue, Raul654, Jusjih, Johnleemk, Jamesday, Anjouli, Dmytro, RadicalBender, Jni, Twang, Phil Boswell, Donarreiskoffer, Vt-aoe, EdwinHJ, Robbot, Hankwang, The Phoenix, Astronautics~enwiki, Schutz, Akajune, Moncrief, Netizen, Psychonaut, Stephan Schulz, Nurg, Naddy, Modulatum, Arkuat, Postdlf, Flauto Dolce, Lesonyrra, Spike, Rursus, Rhombus, Sunray, Mervyn, Hadal, Saforrest, Robinh, Borislav, Mushroom, Witbrock, Diberri, Dina, StefanosKozanis~enwiki, Cedars, Stirling Newberry, Parasite, Nephelin~enwiki, Giftlite, DocWatson42, Christopher Parham, Awolf002, Fennec, Jyril, Gene Ward Smith, Isam, Barbara Shack, ShaunMacPherson, Wiglaf, Netoholic, Tom harrison, Fastfission, Karn, Bradeos Graphon, Xerxes314, Peruvianllama, Everyking, No Guru, Moyogo, Dratman, Maha ts, Curps, Michael Devore, Markus Kuhn, Bensaccount, Cantus, Rpyle731, DO'Neil, Gilgamesh~enwiki, Saaga, Siroxo, Solipsist, Iceberg3k, Tweenk, Darrien, Jackol, Bobblewik, WikiFan04, ChicXulub, Utcursch, Pgan002, Andycjp, Alexf, Mike R, Zeimusu, Yath, Quadell, Antandrus, HorsePunchKid, OverlordQ, ClockworkLunch, MisfitToys, Piotrus, Kusunose, Melikamp, Jossi, Karol Langner, MacGyverMagic, Rdsmith4, Samy Merchi, DragonflySixtyseven, Rubik-wuerfel, Latitude0116, Jokestress, RetiredUser2, Kevin B12, Satori, Icairns, Clarknova, Marcos, Gscshoyru, Nickptar, HunterX, Iantresman, Urhixidur, Joyous!, Fermion, Clemwang, Subsume, Deglr6328, Trevor MacInnis, Bluemask, Zowie, O'Dea, DanielCD, JTN, Discospinster, Rich Farmbrough, Guanabot, Kenj0418, FT2, Vsmith, Doogee, URMEL~enwiki, Ponder, Dbachmann, MarkS, SpookyMulder, MJSS, Bender235, Swid, Hapsiainen, Violetriga, Nabla, Eric Forste, Commonbrick, Brian0918, RJHall, Maclean25, E Pluribus Anthony redux, Ben Webber, Lycurgus, Huntster, Kwamikagami, QuartierLatin1968, Vinsci, Worldtraveller, Aude, Shanes, Tom, Sietse Snel, RoyBoy, Bookofjude, Spoon!, Femto, Wareh, Madler, Causa sui, Noren, Bobo192, Dralwik, Circeus, Chan Han Xiang, Func, Malafaya, SpeedyGonsales, Vystrix Nexoth, Man vyi, Darwinek, Raja99, Opspin, Ardric47, Apostrophe, Obradovic Goran, Sam Korn, Pearle, Juanpabl, Bijee~enwiki, Mareino, Matthewcieplak, Liberty Miller, Stephen G. Brown, Danski14, AviGilChaitovsky, Alansohn, JYolkowski, Tablizer, Nik42, LtNOWIS, Kjetil, Halsteadk, Eric Kvaalen, Neonumbers, Keenan Pepper, Babajobu, Andrew Gray, Monado, Riana, AzaToth, Lectonar, Axl, Lightdarkness, PAR, Batmanand, Cdc, Fkbreitl, Spangineer, Alinor, Bart133, DreamGuy, Snowolf, GeorgeStepanek, Radical Mallard, Angelic Wraith, Velella, TaintedMustard, Evil Monkey, Tony Sidaway, RJFJR, Gpvos, Amorymeltzer, Jon Cates, RainbowOfLight, Rapscallion, Cmapm, Skatebiker, DV8 2XL, SteinbDJ, Allen McC.~enwiki, Gene Nygaard, Klparrot, Nick Mks, Sturmde, Kitch, Alex.g, Stephen, Flying fish, Dejvid, Feezo, Gmaxwell, WilliamKF, Sterio, Rorschach, Jeffrey O. Gustafson, CygnusPius, OwenX, Woohookitty, CioDu~enwiki, FeanorStar7, Stefannk, Spamguy, TigerShark, Ataru, LOL, Yansa, PoccilScript, Rocastelo, Jersyko, Daniel Case, Mark K. Jensen, Bkkbrad, Benbest, Robert K S, Pol098, Commander Keane, Urod, WadeSimMiser, JeremyA, MONGO, Eleassar777, Schzmo, Jleon, I64s, Aristotle Pagaltzis, Sengkang, KFan II, CharlesC, Wayward, Funhistory, Sam Ellens, ZephyrAnycon, Smartech~enwiki, Wisq, Turnstep, Gerbrant, Mattd4u2nv, RichardWeiss, Rnt20, Ashmoo, Graham87, Marskell, Magister Mathematicae, Descendall, BD2412, Qwertyus, Chun-hian, Seb-Gibbs, FreplySpang, Ando228, The Disco King, Seyon, Icey, Ciroa, Canderson7, Ketiltrout, Sjö, Drbogdan, Sjakkalle, Rjwilmsi, Kstraka, Mayumashu, Coemgenus, IanMcGreene, Fieari, Nightscream, Koavf, Zbxgscqf, NatusRoma, Jake Wartenberg, Vary, Strait, Avia, Amire80, Hiberniantears, Scott Johnson, JHMM13, Rschen7754, Jmcc150, HandyAndy, Kazrak, Thangalin, Ligulem, Sohmc, SeanMack, Brighterorange, Krash, Dar-Ape, Hermione1980, Zimbabwe~enwiki, Sango123, Antimatt, Ghalas, Javalizard, Titoxd, Ace-o-aces, RobertG, Immortal Synn, Latka, Lipis, Crazycomputers, Alhutch, Harmil, Gark, Nivix, Elmer Clark, RexNL, Gurch, Leslie Mateus, Arctic.gnome, DannyZ, OrbitOne, Krun, TeaDrinker, Codex Sinaiticus, Ysw1987, Goudzovski, Alphachimp, Malhonen, Srleffler, Mastorrent, Gareth E. Kegg, MoRsE, CJLL Wright, Chobot, Lord Patrick, ScottAlanHill, DVdm, JesseGarrett, 334a, Ahpook, WriterHound, Therefore, Gwernol, Albrozdude, The Rambling Man, Satanael, YurikBot, Wavelength, TexasAndroid, Spacepotato, Vedranf, JJB, JWB, Hairy Dude, Jachin, Jimp, Alethiareg, Brandmeister (old), Barron64, RussBot, Arado, John Quincy Adding Machine, Anonymous editor, Supasheep, Pigman, GLaDOS, Bergsten, Netscott, SpuriousQ, Chaser, Fabricationary, GusF, CanadianCaesar, BillMasen, Zelmerszoetrop, Subsurd, Stephenb, Mithridates, CambridgeBayWeather, Eleassar, Alex Bakharev, Cryptic, Wimt, Ergzay, Sjb90, NawlinWiki, Wiki alf, The Merciful, Robertvan1, Test-tools~enwiki, Bloodofox, Cquan, Trovatore, Rjensen, Howcheng, Devein, Dureo, Lexicon, Mshecket, Sir48, Lykaestria, Banes, Peter Delmonte, CecilWard, Padajtsch-kall, Ashantii, Raven4x4x, Moe Epsilon, Orbframe, David Pierce, Killdevil, PonyToast, Tony1, Ospalh, Occono, Bucketsofg, Syrthiss, Dbfirs, Elizabeyth, Adreamsoul, Lockesdonkey, Samir, BOT-Superzerocool, Mysid, Gadget850, DeadEyeArrow, Jeh, Elkman, Brisvegas, TUSHANT JHA, Martinwilke1980, Dna-webmaster, Nick123, Wknight94, Tkalayci, Tetracube, WAS 4.250, FF2010, Sandstein, PrincessJO, Donbert, Light current, Show no mercy, Enormousdude, Theodolite, Zzuuzz, TheKoG, Dast, Chesnok, Mopcwiki, Theda, Fang Aili, MikePursifull, Xaxafrad, Reyk, Beaker342, CharlesHBennett, Exodio, Petri Krohn, Black-Velvet, GraemeL, Aeon1006, TBadger, Le sacre, Alias Flood, CWenger, LeonardoRob0t, Kier07, Geoffrey.landis, ArielGold, Tim R, Curpsbot-unicodify, Garion96, Ilmari Karonen, Ybbor, Kungfuadam, Jthebeatles, Gator1, GrinBot~enwiki, Airconswitch, Joshronsen, Serendipodous, Groyolo, DVD R W, Knowledgeum, Xtraeme, That Guy, From That Show!, Luk, Akrabbim, Deuar, Sardanaphalus, Twilight Realm, Jayant412, Crystallina, SmackBot, Dissembly, Unschool, Ashill, Saravask, Hux, Mr A Pinder, Johnpaxton, Jeppesn, CelticJobber, Olorin28, Hydrogen Iodide, Pgk, C.Fred, AndyZ, Bomac, Kilo-Lima, Allixpeeke, Jagged 85, Thunderboltz, Jedikaiti, Jrockley, Renesis, Eaglizard, Delldot, Cdcon, Hardyplants, Frymaster, Dak is back, Josephprymak, AnOddName, Vilerage, K8TEK, Man with two legs, Info lover, Srnec, Tzsch, WesDecker, Xaosflux, Rotemliss, Gilliam, Jdfoote, Madjaxter, Ohnoitsjamie, Divid-


33.10. EXTERNAL LINKS

373

edByNegativeZero, Hmains, Oscarthecat, Skizzik, Desiphral, TRosenbaum, ERcheck, Oldfield~enwiki, Grokmoo, Saros136, Amatulic, Chris the speller, Master Jay, Keegan, SlimJim, KiloByte, Jprg1966, Sirex98, Master of Puppets, Soundslikealotofhooplah, Raymond arritt, Oli Filth, TheScurvyEye, Miquonranger03, MalafayaBot, SchfiftyThree, Hibernian, Fredvanner, StrangerInParadise, Hmich176, Redd Dragon, U-235~enwiki, Oni Ookami Alfador, Kungming2, Sbharris, Colonies Chris, William Allen Simpson, Darth Panda, Bil1, Reaper X, Lewis007, Scwlong, Zsinj, Can't sleep, clown will eat me, Njál, Jinxed, Mourn, Chlewbot, Shibo77, Astrobhadauria~enwiki, Yidisheryid, TonySt, Tuxley, Rubber soul, Aces lead, Addshore, SundarBot, Jmnbatista, Ctifumdope, King Vegita, Chrisd0687, Krich, Wen D House, Flyguy649, Iapetus, Shrine of Fire, Daqu, Makemi, Nakon, Savidan, Duckbill, VegaDark, John D. Croft, Blake-, SnappingTurtle, Iblardi, Invincible Ninja, ShaunES, Akriasas, Chibiabos, Clean Copy, Last Avenue, Henning Makholm, Terrasidius, Daniel.Cardenas, Schgooda, Kukini, Zeneky, Mattwhiteski, Thor Dockweiler, CIS, The Pelican, SashatoBot, Twigge, Nishkid64, ArglebargleIV, Rory096, Robomaeyhem, Weeksy, Agradman, JzG, Sophia, Sambot, Dbtfz, Soap, Kuru, Richard L. Peterson, John, AmiDaniel, N3bulous, Scientizzle, Swlenz, J 1982, Heimstern, FR Soliloquy, Mattw998, Korean alpha for knowledge, Cpom, Shadowlynk, Blinkismyfave, JorisvS, Minna Sora no Shita, Niczar, Moop stick, Majorclanger, Mr. Lefty, Joshua Scott, PseudoSudo, Deviathan~enwiki, Ckatz, Beefy SAFC, The Man in Question, RandomCritic, A. Parrot, Across.The.Synapse, Brent williams, MarkSutton, Stupid Corn, Duke of Kent, Yvesnimmo, SQGibbon, Mr Stephen, Vendetta411, Ferhengvan, Waggers, Mets501, Spiel496, Funnybunny, Special12321, Ryulong, Jarany, Novangelis, H, Jose77, Blindmonkey, Cerealkiller13, Michael Dinolfo, Dean1970, JDAWiseman, Keith-264, Levineps, Swotboy2000, JMK, Michaelbusch, John Mash, Dekaels~enwiki, Clarityfiend, Maestlin, Paul venter, Joseph Solis in Australia, Newone, Pegasus1138, Sam Clark, Cbrown1023, Abdaal, Soapthgr8, Civil Engineer III, Jdb1729, Courcelles, Piccor, WakiMiko, Thricecube, Tawkerbot2, Godlikemammal, The Letter J, Yosef 52, Dc3~enwiki, Orangutan, Harold f, The Haunted Angel, Tifego, Piggysrcute123, Paul Matthews, Stifynsemons, KNM, Thedemonhog, Sakurambo, Friendly Neighbour, Nehushtan, VoxLuna, Markjoseph125, Tanthalas39, PorthosBot, Shanejohnson, Myrrhlin, Iced Kola, Ossanha, Scirocco6, Chimsta, DSachan, Vyznev Xnebara, Rwflammang, MFlet1, Ruslik0, Lmcelhiney, Schweiwikist, GHe, Benwildeboer, N2e, El aprendelenguas, Eric Le Bigot, Dan 1024, Simply south, Joelholdsworth, WeggeBot, MrFish, Skybon, Flammingo, The Enslaver, Ufviper, TJDay, LunceFordPrefect, Dogman15, HalJor, Cydebot, Squizz48, Peripitus, Abeg92, Dillamond, Subravenkat, Poeticbent, Asknine, Reywas92, ArgentTurquoise, Steel, Gogo Dodo, Jkokavec, Mr.Chocobos, Flowerpotman, Corpx, NewProvidence, Andyroo161, Fifo, Michael C Price, Tawkerbot4, Legend78, Codetiger, DumbBOT, Chrislk02, Rsheridan6, Mallanox, Agge.se, Shortdude2889, Kozuch, Adamlaurie, Bob Stein - VisiBone, Editor at Large, Emmett5, NMChico24, Omicronpersei8, Nol888, Saintrain, Casliber, Poverty~enwiki, Thijs!bot, JAF1970, Epbr123, Barticus88, Forbesb, Fsdfsdfsd~enwiki, KimDabelsteinPetersen, Markus Pössel, Daniel, Kablammo, Headbomb, Newton2, Louis Waweru, Shadowblackfire, Pjvpjv, A3RO, Fenrisulfr, Pciszek, Cverlo, Davidhorman, Rimmo21, Cj67, Son of Somebody, OGRE 2, CielProfond, DaveJ7, Greg L, Nick Number, BlytheG, Theophile490, Big Bird, Pkpat2011, MichaelMaggs, Dawnseeker2000, Natalie Erin, CTZMSC3, AlefZet, Northumbrian, Escarbot, I already forgot, Dantheman531, Baclough, Cyclonenim, Jbrezina, AntiVandalBot, Fiksdal, Majorly, Luna Santin, EdgarCarpenter, Ricnun, Opelio, Bm gub, Erwin85Bot, CobraWiki, Quintote, Mrshaba, Efyoo, Edokter, Bequinta, SmokeyTheCat, Helicoptor, Mojohaza1, Chuchunezumi, Shahid hassan99, MECU, Spencer, Asgrrr, Nuttyisms, G Rose, Togarida41, Mike741, Ghmyrtle, Kothari.sagar, Gökhan, Kierco0619, Canadian-Bacon, Squidgyegg, Bogger, JAnDbot, Darthjarek, Krishvanth, Deflective, Davewho2, Barek, WordSurd, MER-C, Nthep, Mcorazao, Supertheman, IanOsgood, Stonnman, Hello32020, Db099221, Flaminkight, Legolost, Ikanreed, Mwarren us, Roleplayer, Hut 8.5, Noface1, TallulahBelle, Smith Jones, Rothorpe, Denimadept, Maias, LittleOldMe, Acroterion, Robertburke2003, Pablothegreat85, WolfmanSF, Secret Squïrrel, Murgh, Bongwarrior, VoABot II, Sushant gupta, Mrld, JNW, Brandt Luke Zorn, Obluis, Blue william, Mbc362, Father Goose, Akronnick, ‫باسم‬, WagByName, LafinJack, Eno-Etile, Brewhaha@edmc.net, Brain40, Hypergeek14, Nyttend, Justice for All, WODUP, Kharri1073, SparrowsWing, Avicennasis, Wikiwhat?, Midgrid, GroovySandwich, Couki, Catgut, Thisisdeansusername, Animum, Cyktsui, Jump off duck, ArthurWeasley, Torchiest, Remi81992, Mkdw, Allstarecho, PYMontpetit, Tins128, SpaceGuide, Siddharthsk2000, Spellmaster, ArmadilloFromHell, Shijualex, Just James, Talon Artaine, DerHexer, Alastan, Khalid Mahmood, TheRanger, Wayne Miller, Patstuart, Thestick, Eschnett, DinoBot, Kheider, G.A.S, NatureA16, Gjd001, September 11 suicide bomber, Jerem43, Hdt83, MartinBot, Eternal Pink, Xdef, Arjun01, Kiore, Whoiam55, Anaxial, TechnoFaye, Richardhenwood, R'n'B, Mycroft7, CommonsDelinker, Pbroks13, Nono64, Organics (usurped), Smokizzy, Lilac Soul, Werothegreat, Cyrus Andiron, Slugger, Watch37264, J.delanoy, Kimse, DrKay, Trusilver, Mr Ernie, EscapingLife, Kulshrax, Bogey97, Numbo3, Theinternetsoify, Hans Dunkelberg, Squallish, Maurice Carbonaro, SpartanVIII, MrBell, Ginsengbomb, Eliz81, Markhayward, Jreferee, WarthogDemon, NerdyNSK, MatheoDJ, OfficeGirl, Fishyghost, Q2op, Cpiral, Gzkn, Acalamari, IdLoveOne, Katalaveno, Peppergrower, Kyonkyon, Lunokhod, Ignatzmice, Dfoofnik, Vac cutter, Nalumc, RTBoyce, Ryan Postlethwaite, Coppertwig, Chriswiki, Spinach Dip, Eoin5s, TomasBat, NewEnglandYankee, Rominandreu, Sd31415, Nwbeeson, Fly101, The Snakemaster, Touch Of Light, 83d40m, Pejmany, LeighvsOptimvsMaximvs, Toon05, Mwmt1, Madhava 1947, MetsFan76, Filam-Man, BrettAllen, Donmarkdixon, KylieTastic, Blueblib, Mantosh1980, Foofighter20x, Kerms, Gwen Gale, LordCo Centre, DorganBot, Equivocal, Treisijs, Jim Swenson, Mike V, HiEv, Xcindydollx, Torf74, Izno, Gamecockfan1001, Martial75, Dkreisst, Scewing, Dvyjones, Idioma-bot, Lrdwhyt, Wikieditor06, CyberForte, Black Kite, Lights, Sam Blacketer, Inn0mmable, 28bytes, VolkovBot, Part Deux, Stevesysum, DagnyB, The Duke of Waltham, Roger M.E. Lightly, Jeff G., Indubitably, Humps, JohnBlackburne, James Callahan, LokiClock, Cadby Waydell Bainbrydge, Rutherfordjigsaw, Haade, Opferman, Katydidit, Landisdesign, QuackGuru, SexyBern, Lidingo, Wugo, Philip Trueman, Tangz22, Guldotarpit, TXiKiBoT, Rambo forever, Brummer Pants, Sagittarian Milky Way, Rakasan, Myles325a, Hqb, Malljaja, Yuma en, Caster23, USferdinand, Ann Stouter, Anonymous Dissident, HarryAlffa, Captain Wikify, Sean D Martin, Rabsak, Qxz, Someguy1221, Dipper3, Matholo1, Piperh, Lambdoid, Christinelaura, Mooverb, Harry sava, Lradrama, PichuUmbreon, Eeron80, MasterSci, Awl, Saibod, 06mkittle, Henrykus, Martin451, Greatparty, Bobblehead2, JhsBot, Choppie3000, Mzmadmike, Fbs. 13, Dalejr.3, Buddhipriya, LeaveSleaves, Macncc, Arcaani, Sakletare, PDFbot, Pleroma, UnitedStatesian, Cremepuff222, Deathsquad53, Quindraco, Jpastelero, Damërung, X3nolith, MearsMan, Sffslibrary, Shane1120, Nishani 1995, Monstrabisne, Rpbreen, Roland Kaufmann, Pious7, Sivani2006, Oliver Manuel, Comrade Tux, Boomervan123, Carinemily, Synthebot, DannyCarl, Speria, Horselover1127, Dragostanasie, CarbonRod85, Heroandgloom, Brianga, Showers, Rida666, Macchess, Palaeovia, AlleborgoBot, Nagy, Planet-man828, PericlesofAthens, EmxBot, LordofPens, D. Recorder, Kbrose, Thw1309, Demmy100, SMC89, Maide, SieBot, MK Dempsey, Jwray, Kfc1864, Timb66, Jim77742, Sonicology, PlanetStar, Tiddly Tom, Scarian, BotMultichill, Hertz1888, Iamthedeus, Krawi, Abc60, Noh Boddy, Su huynh, Caltas, Kylemew, BloodDoll, Rawrthness, Apemanjy, Triwbe, Invadereli94, Arda Xi, Keilana, Flag-Waving American Patriot, Acet0ne, Tiptoety, Wizzard2k, Ireas, Arbor to SJ, Undeadcow66, Nopetro, Travis Evans, Osufitchi, Dhatfield, Will Aaron 6, Wombatcat, Berserkerus, Oxymoron83, SpellingGuru, KPH2293, Steven Crossin, Lightmouse, Wikiwikiwee, Poindexter Propellerhead, Wikiwee~enwiki, Bludevilchief, Murlough23, Alessandroandcharlie, Raihan.mahmud, Roxivus, Disneydude500, Cbennett0811, BenoniBot~enwiki, AMackenzie, Autumn Wind, OKBot, Nymbusfhs, Gunde123456789, LonelyMarble, Andrij Kursetsky, Lapping~enwiki, Iikkoollpp, StaticGull, Jeroen888, Reign atreyu, Jacob.jose, Randomblue, Hamiltondaniel, Realm of Shadows, Ttbya, Paulinho28, Bkumartvm, Dimboukas, Mjpulohanan, Getyourlemondaehere, Nergaal, DRTllbrg, M1n2b3, Escape Orbit, C0nanPayne, Ghetsmith, Budhen, Mesosphere, Freewayguy, Velvetron, Explicit, Squash Racket, ImageRemovalBot, Athenean, ElectronicsEnthusiast, Adoliveira, Martarius, Sfan00 IMG, Dood666, De728631, Elassint, ClueBot, Gladysamuel, Trojancowboy, Binksternet, Artichoker, Feyre, Seazoleta, PipepBot, Agunatak, Fyyer, The Thing That Should Not Be, Fizzixman, Andigk2217, Plastikspork, Hongthay, Dikstr, Nnemo, Ndenison, Arakunem,


374

CHAPTER 33. ORBITAL ECCENTRICITY

Cp111, Razimantv, Dvratnam~enwiki, Dmvward, Boing! said Zebedee, Benito123456789, Timberframe, Hateme666, Emp4eva, Ddunau, Niceguyedc, Jcdw14, XayaneXeX, Gangsters403, Bartholemuel07, Bill3025, Kaage, SaturnCat, Swarm-287, Solar-Wind, Paulcmnt, DragonBot, Awickert, Excirial, H-Vergilius, Jusdafax, Noca2plus, Ontopofthewall, Slntprdtr, Sun Creator, NuclearWarfare, Fire 55, Lunchscale, PhySusie, Awikiwikiwik!!!, Ember of Light, DILNN1, Francisco Albani, Jimmysauce, Doommaster1994, Krazymike, Redthoreau, Bennyvk, Muro Bot, Kmac001, Crbnfan99, Jonverve, Sivakamitvm, RubenGarciaHernandez, Alfonsobernabe, Roberto Mura, Cornerstone77, SoxBot III, Apparition11, Ginbot86, Caldwell malt, Capntek, InternetMeme, PSimeon, Roxy the dog, Blidman, Nathan Johnson, Auslli, Morganbyers, RebirthThom, Ziza123, Gerhardvalentin, Ost316, Facts707, U av probs, JinJian, MystBot, Mbariel~enwiki, Airplaneman, Pokefan098, Lemchesvej, Skeletor 0, Kbdankbot, Maldek, Blanche of King’s Lynn, Yousou, Substar, Willking1979, AolxHangover, DOI bot, Pokathon3000, AAG607, DougsTech, Ocdnctx, C3r4, Older and ... well older, Albot2008, Njaelkies Lea, CharlesChandler, Modþryð, Download, Erudit 78, GeoPopID, LinkFA-Bot, Tassedethe, 84user, Numbo3-bot, Tide rolls, Cordless33, Jarble, Marukh18, Hejsa, Gameseeker, Everyme, Luckas-bot, ZX81, Yobot, 2D, Barry2j, Mech Aaron, Cflm001, Legobot II, Blacklans, Da ninja handyman, Fizyxnrd, I9o0q1, Crispmuncher, Abhinavdhere, Gobbleswoggler, NERVUN, THEN WHO WAS PHONE?, KamikazeBot, Timir Saxa, IW.HG, 8ung3st, South Bay, Squish7, Dickdock, Szajci, AnomieBOT, Travo615, Archon 2488, Kristen Eriksen, Pigs8u3, RJAM1, Hunterevans, Brilliant trees, Piano non troppo, Vextration, Brian1961, Vagmaster69, Emluickyblaju, Rejedef, Copytopic1, Ulric1313, CurtisOrr, Brendanzhang, Materialscientist, The High Fin Sperm Whale, Citation bot, Srinivas, Zahab, Frankenpuppy, Chell and the cake, Marshallsumter, The Firewall, MauritsBot, Xqbot, Tasudrty, BasilRazi, Capricorn42, Emezei, 4twenty42o, Gilo1969, Loveless, BritishWatcher, Wikepediamaniac, Tyrol5, Mlpearc, Gap9551, Lithopsian, Felipe Schenone, GrouchoBot, Armbrust, Jhbdel, Alumnum, Nlilovic, Mark Schierbecker, RibotBOT, Nedim Ardoğa, 78.26, The Wiki ghost, Doulos Christos, The sun is cold, Trafford09, Ganesh J. Acharya, Rainald62, C8sd, Moxy, Letthetruthbetoldforalltobehold, Laelele, Catbob625, MeDrewNotYou, A. di M., Interstellar Man, AJCham, Fotaun, Friedlad, FrescoBot, Originalwana, Tobby72, Pepper, Joshead, Sky Attacker, Hosszuka, KokkaShinto, Martins007, Citation bot 1, Mix Tape Queen, Galmicmi, SL93, Redrose64, AstaBOTh15, Pinethicket, Elockid, HRoestBot, 10metreh, Jonesey95, Tom.Reding, A8UDI, Mutinus, Hoo man, Allthingstoallpeople, NKanngaz, Ezhuttukari, Darktower 12345, Meaghan, Jujutacular, IVAN3MAN, Soccerisawesome, Zbayz, FoxBot, Pdebee, Double sharp, TobeBot, Trappist the monk, Puzl bustr, Cocu, Nicholomothy, Callanecc, Vrenator, David2032, Begoon, Darsie42, Ansumang, GGT, Diannaa, Mvnvinaykumar, Earthandmoon, Tbhotch, Sideways713, DARTH SIDIOUS 2, Mean as custard, The Utahraptor, RjwilmsiBot, TjBot, Bento00, Ripchip Bot, DEagleBot, Jamesshliu, DASHBot, Steve03Mills, DiogenesTCP, EmausBot, John of Reading, WikitanvirBot, Sadalsuud, Syncategoremata, Chermundy, Torturella, CoincidentalBystander, Hive001, ThorX13, Hhhippo, Mz7, AvicBot, Rerumirf, John Cline, Cogiati, Brothernight, A2soup, DeWaine, AvicAWB, Green Lane, Everard Proudfoot, Ridwan93, H3llBot, GianniG46, Wagner, David J Johnson, Ironnail, JoeSperrazza, Sbmeirow, PurpleCoolSun, Donkeykongrider, DOwenWilliams, Brandmeister, Coasterlover1994, Igivefakeinfo, L Kensington, MAN3212, ChrisWenzel, Usernamewhocares, WikiRigaou, Donner60, Andy 3015, The Sumo, Tritoncis101, R1r1f2, Bulwersator, Lawstubes, Oneill05 oneill, Megaguy4, ChuispastonBot, Ihardlythinkso, BigbigbigGIANTY, Pigduckmeatshroom, Aduda, Natalie Hasselriis, Sdjgjhsdrhfgdfjagihdasg, LikeLakers2, Whoop whoop pull up, ClueBot NG, Pokem0n0mekop, Ulflund, GioGziro95, Lepota, Ritabetta, Tyler Lavhey, RocketLauncher2, Hazhk, MasterMind225, Duckshoot, Marechal Ney, Tafoyad12, Amyleigh47, JohnnyStJohn, HappyLogolover2011, Jam000qaz, North Atlanticist Usonian, Flendersnod, Helpful Pixie Bot, Helvitica Bold, Bibcode Bot, Jeraphine Gryphon, Regulov, Jazdisney, Lowercase sigmabot, MKar, AvocatoBot, Bigdon128, Dancindazed, DrNortonWhite, Safiredx, BillTheBunny, Dipankan001, Prokillz21, Cadiomals, Drift chambers, Pocketthis, ZuluKing, Dongod95, Neptuul, Tycho Magnetic Anomaly-1, Colinmartin74, Zedshort, Eguinto, Cliff12345, 4Jays1034, Szczureq, BattyBot, Rachelpacinda, Pendragon5, Tutelary, Mdann52, Stigmatella aurantiaca, Cyberbot II, U-95, DoctorKubla, MadGuy7023, Kelvinsong, Soni, BrightStarSky, Dexbot, Blobbie244, Inayity, Makecat-bot, Cerabot~enwiki, CuriousMind01, BeaumontTaz, MattSucci, Sidelight12, 1,000,000,005k, Jo-Jo Eumerus, Downthehollow, Unknownheror, Awesomechase999, Monsterblarg, EvilQueen16, JustAMuggle, Hillbillyholiday, Reatlas, TrentFlash, Jcpag2012, Praemonitus, Rolf h nelson, The Herald, CarrickB, Batyu, Exoplanetaryscience, Kind Tennis Fan, Stamptrader, Brmb101, Monkbot, Davidbuddy9, Bobtulle, DSCrowned, Miko367, XXboxAddictx, BrentHar, Luciusdevilman, Troll54326, Daxfile, Dhhdhdheyeuwopamsndbdhdueiwkzm, Poddarmanoj33, Streborsattelav, Poo1053, Felix179793, İnternion, Skeletoroforange, I am. furhan., Tetra quark, ‫محمد مجیب‬, Isambard Kingdom, Sol2y, Inyouchuu shoku, KasparBot, Sir Cumference, BU Rob13, SSTflyer, Yogee23, MartinZ02, HalloweenNight, PlanetUser, Judist, WiKaffiN, L4tybj, GreenC bot, Fmadd, Motivação and Anonymous: 1477 • Nicolaus Copernicus Source: https://en.wikipedia.org/wiki/Nicolaus_Copernicus?oldid=743921848 Contributors: AxelBoldt, Magnus Manske, MichaelTinkler, Marj Tiefert, JHK, Brion VIBBER, Eloquence, H.J., Mav, Bryan Derksen, Szopen, AstroNomer, Taw, Slrubenstein, Gareth Owen, Rjstott, Ed Poor, Amillar, Andre Engels, Danny, XJaM, Rmhermen, Gianfranco, William Avery, Space Cadet, Drew Hodge~enwiki, Drbug, Zoe, Tirid Tirid, Arno, DW, Someone else, Lir, Nealmcb, Wapcaplet, Dcljr, Delirium, CesarB, Looxix~enwiki, Ronabop, Ellywa, Ahoerstemeier, William M. Connolley, Suisui, Angela, Den fjättrade ankan~enwiki, Jebba, Kingturtle, Александър, Djnjwd, Eirik (usurped), Pizza Puzzle, Charles Matthews, Adam Bishop, Przepla, RickK, Reddi, Stone, Dandrake, The Anomebot, Wik, Zoicon5, Vancouverguy, Tpbradbury, Maximus Rex, Furrykef, Justin Bacon, LMB, Omegatron, Bevo, Topbanana, Fvw, Stormie, Farshadrbn, Secretlondon, Flockmeal, Pollinator, Francs2000, Lumos3, InanimateCarbonRod, Jni, Dimadick, Kommiec, Gentgeen, Robbot, Adamahill, Astronautics~enwiki, Nico~enwiki, Fredrik, Chris 73, RedWolf, Altenmann, Rübezahl~enwiki, Calmypal, Chris Roy, WolfgangPeters, Tirmie, Academic Challenger, Der Eberswalder, Rholton, Rursus, Halibutt, Caknuck, Hadal, Michael Snow, Mushroom, Cautious, Guy Peters, Xanzzibar, Dina, Alan Liefting, Lysy, Snobot, Giftlite, Yeti~enwiki, Paul Richter, Wizzy, Gdansk, Fastfission, HangingCurve, Zigger, Monedula, Ausir, Rj, Peruvianllama, Average Earthman, Everyking, Curps, Rpyle731, Maroux, Kpalion, Matthead, Jrdioko, Golbez, ChicXulub, Gadfium, Sca, Alexf, J. 'mach' wust, Knutux, Abu badali, Antandrus, Elizabeth A, Piotrus, Domino theory, Kaldari, Jossi, Emax, MacGyverMagic, JimWae, Xandar, Balcer, Macmaxbh, Pmanderson, PolishPoliticians, Gscshoyru, Neutrality, Thorsten1, Burschenschafter, Jewbacca, Schwartz und Weiss, M1ss1ontomars2k4, Trevor MacInnis, Eisnel, Flex, Gazpacho, D6, Rfl, Freakofnurture, Poccil, EugeneZelenko, EBL, Discospinster, Zaheen, Rich Farmbrough, Rhobite, Brutannica, Ex caelo, Vsmith, Naive cynic, Jpk, Freestylefrappe, Ovvldc, HeikoEvermann, Smyth, Bishonen, Dbachmann, Pavel Vozenilek, Uppland, SpookyMulder, Bender235, MattTM, Kbh3rd, Mateo SA, Kaisershatner, Mashford, RJHall, BenjBot, Sfahey, MarvinMonroe, Shanes, Haxwell, Bill Thayer, Noren, Bobo192, Ruszewski, Adraeus, Shenme, Elipongo, Jung dalglish, Jguk 2, Pokrajac, Chirag, Jojit fb, Darwinek, WikiLeon, Ral315, Polylerus, Jonathunder, HasharBot~enwiki, Jumbuck, Danski14, MCiura, Gary, Ocean57, TheParanoidOne, Mo0, Rosenzweig, Babajobu, Mc6809e, Logologist, Riana, AzaToth, Lightdarkness, Sligocki, Bart133, Hohum, Paul Martin, Deacon of Pndapetzim, Garzo, Uffish, Tony Sidaway, Sciurinæ, Kusma, TShilo12, Spartacus007, OwenX, Woohookitty, FeanorStar7, TigerShark, Yansa, Daniel Case, Carcharoth, Kzollman, WadeSimMiser, Dodiad, MONGO, Tabletop, Wikiklrsc, Bbatsell, Damicatz, I64s, EvilOverlordX, , Alec Connors, Rtcpenguin, Siqbal, Graham87, Noit, Magister Mathematicae, Chun-hian, Sjakkalle, Rjwilmsi, Koavf, Srs, Authr, Collard, MZMcBride, Mentality, Vegaswikian, Ligulem, Sferrier, Bhadani, Olessi, Yamamoto Ichiro, FlaBot, RobertG, Old Moonraker, CalJW, Mathbot, Master Thief Garrett, Jak123, Nihiltres, JYOuyang, Gparker, RexNL, Gurch, Witkacy, ApprenticeFan, Krun, Ek8~enwiki, TeaDrinker, Nick81, Alphachimp, Acefitt, Never~enwiki, CJLL Wright, Chobot, Visor, DVdm, Volunteer Marek, Bgwhite, Hall Monitor, Digitalme, Gwernol, Whosasking, Tdoyle, YurikBot, Wavelength, RobotE, Bambaiah, Crotalus horridus, Kinneyboy90, Sceptre, Wester, Huw Powell, Jimp,


33.10. EXTERNAL LINKS

375

Family Guy Guy, Brandmeister (old), RussBot, Luis Fernández García, Splash, Vanillasky, Tresckow, SylwiaS, Rodasmith, Lar, Gaius Cornelius, CambridgeBayWeather, Ugur Basak, Big Brother 1984, Burek, NawlinWiki, Swollib, Wiki alf, Pandries~enwiki, Johann Wolfgang, Schlafly, Uberjivy, Ziel, Devein, Ragesoss, Aaron Brenneman, Robdurbar, Dmoss, PhilipO, Aldux, Jbourj, Mlouns, Molobo, Misza13, Histprof, Lockesdonkey, Mieciu K, DeadEyeArrow, Psy guy, Tachs, Evrik, Wolfling, RustySpear, Igiffin, FF2010, Sandstein, Superdude99, Laszlo Panaflex, Womble, Lt-wiki-bot, Malekhanif, Silverhorse, Chase me ladies, I'm the Cavalry, Rms125a@hotmail.com, GraemeL, JoanneB, Mike1024, Fram, Palthrow, T. Anthony, Curpsbot-unicodify, Che829, Katieh5584, Listowy, Kungfuadam, Appleseed, James Hannam, RG2, Ish warsaw, Zvika, Kgf0, Mejor Los Indios, DVD R W, Finell, Luk, Sardanaphalus, Attilios, SmackBot, AndreniW, FocalPoint, YellowMonkey, Selfworm, Zerocannon, Phil79, Moeron, David Kernow, Lestrade, KnowledgeOfSelf, TestPilot, Royalguard11, Olorin28, CRKingston, Pgk, C.Fred, Blue520, Jacek Kendysz, Jagged 85, Clpo13, WookieInHeat, Delldot, Eskimbot, Srnec, Antidote, Gary2863, Commander Keane bot, Gilliam, Chris the speller, Kurykh, JCSantos, Audacity, NCurse, MK8, Ksenon, Stubblyhead, B00P, Oli Filth, Cadmasteradam, MalafayaBot, Silly rabbit, SchfiftyThree, BrendelSignature, Ctbolt, DHN-bot~enwiki, Jadger, AKMask, Gracenotes, Yanksox, Dr. Dan, Veggies, Trekphiler, Macic7, Can't sleep, clown will eat me, John Hyams, Leinad-Z, Scray, Koscio, Nixeagle, Neilanderson, Leoboudv, JesseRafe, SundarBot, Stevenmitchell, Jmlk17, Weirdy, Mikedow, AntonBryl, Iapetus, Andie142105, Savidan, Theodore7, Dreadstar, Alexandra lb, Robertsussell, DMacks, Informationguy, Wizardman, Kotjze, Sayden, Risker, Vina-iwbot~enwiki, Pilotguy, Nasz, Ohconfucius, Will Beback, Cyberevil, The undertow, SashatoBot, Grommel~enwiki, Txensen, Rory096, Alexjustdoit, Kuru, John, Aeronauticus, Zapptastic, Mathiasrex, Kipala, Vumba, Soumyasch, Sir Nicholas de Mimsy-Porpington, Coredesat, Merchbow, Hemmingsen, Mgiganteus1, Weatherlawyer, IronGargoyle, Ckatz, Otend, Chrisch, RandomCritic, Showcase, Anatopism, Androl, Rofl, Maksim L., Mets501, Ryulong, MTSbot~enwiki, Caiaffa, Udibi, Dl2000, Warmiak~enwiki, Hu12, Ginkgo100, Iridescent, Pipedreambomb, Clarityfiend, Maestlin, Craigboy, Lakers, Dagox, Cyon, Saturday, Matcreg, Noman953, Dpeters11, KonradWallenrod, Tawkerbot2, Chris55, LessHeard vanU, Kurtan~enwiki, INkubusse, SK6, Pugs Malone, EAJoe~enwiki, Starfox Pilot, AlbertSM, CBM, Kowalmistrz~enwiki, Rwflammang, Syrenab, R9tgokunks, N2e, Pseudo-Richard, ShelfSkewed, Moyerjax, Evilhairyhamster, Outriggr (2006-2009), Moreschi, Katya0133, NE Ent, Tex, Cydebot, Future Perfect at Sunrise, Poeticbent, Steel, HokieRNB, Astrochemist, Clayoquot, Gogo Dodo, Cult-p, Siberian Husky, ST47, M.K, Doug Weller, Colorprobe, DumbBOT, Chrislk02, DBaba, Vtcrusade, Dinnerbone, Ward3001, Danogo, SteveMcCluskey, Blah2000, Gimmetrow, Dartharias, Rbanzai, ThevikasIN, Mamalujo, PKT, Thijs!bot, Biruitorul, Bot-maru, Pajz, Lupogun, Smartgirl158, CSvBibra, Nerderer, Andyjsmith, Mpallen, Lopakhin, Oliver202, Simeon H, Marek69, John254, His Ryanness, Wikimoder, K. Lastochka, Dfrg.msc, Bethpage89, Natalie Erin, Porqin, AntiVandalBot, RobotG, Abu-Fool Danyal ibn Amir al-Makhiri, Luna Santin, Prolog, Mrshaba, Smith2006, Jayron32, Nine9s, Dr who1975, TimVickers, Fayenatic london, Dr. Submillimeter, Science History, LawfulGoodThief, Pawel z Niepolomic, JAnDbot, Narssarssuaq, Dan D. Ric, Husond, Kaobear, MER-C, Olaf, Sanchom, OhanaUnited, Jondw, Acroterion, Anna Q~enwiki, Meeples, ArthurianLegend, Connormah, Canjth, VoABot II, Wikidudeman, Umix, Boomcoach, MastCell, Piast~enwiki, Mbc362, Singularity, Nyttend, Mattbray, Avicennasis, Oberer, KConWiki, Catgut, KirinX, Will ward, Arbeiter, Dirac66, DerHexer, Khalid Mahmood, Johnbrownsbody, Jsusky, Gun Powder Ma, Gwern, MartinBot, Lockerop, Danaccuster, Tamerd, Pupster21, Pwnz0r1377, Wowaconia, Mike6271, David J Wilson, R'n'B, CommonsDelinker, Johnpacklambert, Nono64, Footballstar07, Tulkolahten, KnightGun0, Lilac Soul, Evilfrog, Dante51, J.delanoy, Captain panda, Filll, Funny4life, SuperGirl, 63·161·169·137, MoogleEXE, Dbiel, Vanished user 342562, SU Linguist, L337 kybldmstr, Tomensnaben, Dkendr, It Is Me Here, Smeira, Victuallers, Vador4, Daniele.tampieri, Gurchzilla, AntiSpamBot, LittleHow, Krasniy, NewEnglandYankee, Cadwaladr, Poonagewoofy, SJP, Malerin, Mufka, FJPB, Pcarter7, Jc4p, 12345 lewis, SmallPotatoes, Thomaspca, Agrofe, Dsarker, Sodaplayer, Pdcook, Ronbo76, KGV, Scewing, CrZTgR, Idioma-bot, MikeEMCBB, Alan U. Kennington, Lights, Deor, MCBOB, VolkovBot, Leebo, Hersfold, The Duke of Waltham, Davidwr, Jacroe, TXiKiBoT, Dawidbernard, Mahal11, Skoranka, Jokeswell great, Arudra, Wiatr, John Carter, Corvus cornix, Szlam, ColonelKernel, Patyk, Dlugopis, JhsBot, Guldenat, Seb az86556, Pleroma, Brockle, Nicholas.goder, Maxim, Tar-Elenion, Katimawan2005, FrankSanMiguel, Mplungjan, Eldredo, Olowek, Noz1, Gumka, Orestek, AgentCDE, Stuffyyo, I Q('.'Q I, Enghv, Zerged, Why Not A Duck, MurderWatcher1, Citymovement, AlleborgoBot, Symane, Otwieracz, Patka~enwiki, EmxBot, Steven Weston, PaddyLeahy, Romuald Wróblewski, Wumingzi, SieBot, Kmasters0, Zatorade, Coffee, Lodz1, Fixer1234, JohnWarnock, Tiddly Tom, Nihil novi, Sanos1, Vistu, Buggo1, Oddre, Wartt, Lobby1, Koppa3, Toolsbadly, Basedview22, Caltas, Yintan, Chetos, Zbvhs, TR, The Evil Spartan, Juhd, StepPol, Wilson44691, Monegasque, Dans, Markcheli, Oxymoron83, Mankar Camoran, Sokkiejol, Zharradan.angelfire, Nickki xx, Kieszon, Amcwis, BenoniBot~enwiki, QIrus, Vojvodaen, Cosmo0, The Four Deuces, Firefly322, PerryTachett, Nergaal, Faithlessthewonderboy, Martarius, Elassint, Walkee, ClueBot, Zachariel, Fyyer, Kotniski, The Thing That Should Not Be, All Hallow’s Wraith, Goethicus, Kafka Liz, Wysprgr2005, Astronomer28, Jaensky, Jacurek, Polaco77, Cyanothus, J8079s, Skäpperöd, Blanchardb, Altone, Efgab, Okular, Kijakul, Tasmara, Clamare, Kapsule, Bulata, Paddab, Boloniare, Jattala, Kabdaraf, Pernambuko, Masterpiece2000, Metalsheep, Alexbot, Jusdafax, HeWasCalledYClept, Sun Creator, Smeloin, Millionsandbillions, Cenarium, Jotterbot, 8800GTX, M.O.X, Jonathan316, Wolfgang975, Audaciter, Hobohutman, Nafis ru, Al-Andalusi, Unmerklich, Wintersira, Thingg, Xmathx, BurgererSF~enwiki, Wkboonec, DumZiBoT, Bletchley, Shpakovich, Divius, Kunas, Kukuryku2, Mamal-33, Matusalem-78, Alala-333, Avoided, HerkusMonte, Majan, MystBot, Good Olfactory, Draganparis, Thedoctor98, Kbdankbot, Super-stargazer², Emerica52992, Habbabuba91, Narayansg, AVand, Some jerk on the Internet, Dillybob101, Yoenit, Fyrael, OttRider, CanadianLinuxUser, Boearo, Boureo, Cuoato, Couero, Dooreo, Duuruu, NjardarBot, CarsracBot, PranksterTurtle, Valve45, Maladata, Kareaa, Adadasu, Karanata, Barautata, Debresser, Favonian, Jalatas, Mutsu58, Buussola, Huulaa, Oomaat, Muulaa, Vvisla, Mutususu, Maatee~enwiki, Byytar, Kddsaw, Zzazzenn, Ppole, Oota~enwiki, Numbo3-bot, Ttassr, Sseedaf, Nnedass, VASANTH S.N., Koliri, Tide rolls, Lightbot, Luckas Blade, Bbeest, Lrrasd, Hhaarty, Bbggae, Vrrad, Wweert, Aavviof, Bbisdo, Mmuusda, Ccaarft, Wwannsda, Teysz Kamieński, Piotr967, Rretwa, Hhaster, Rradulak, Ttasterul, Luckas-bot, TheSuave, Yobot, Themfromspace, Ptbotgourou, Amirobot, Mmonne, Cclawara, Abasass, Rrokkedd, Ccraccnam, DisillusionedBitterAndKnackered, Washburnmav, Houutata, Teammoto, Clubbota, Placcjata, KamikazeBot, Apptas, Bliduta, Smmalut, Wheenguta, Keeratura, Tempodivalse, Coulatssa, Helatsson, Staggeratto, Limttado, Wrotterasso, Timmorra, AnomieBOT, Plannatas, Rocckoleta, Burssdola, Drootopula, Nottsadol, Hurratolat, Powwradota, Vittsadaf, Taskualads, Givbataska, Madesfuga, Viewsdakla, JackieBot, Toutafada, Shogatetus, Hurtetusda, Colutowe, Portutusd, Ryhor5, Berlin-George, Citation bot, Vanbas, Noideta, Soldarat, Givbatad, Heastada, Bludyta, Savdrtu, Haidata, Weerasad, Namtiota, LilHelpa, Lobtutu, Awyhuito, Schaengel, Worfasdgi, MauritsBot, Morasdeta, Profanatas, Oftopladb, Xqbot, Clohuigt, Trughioy, Doezxcty, Busvbtydj, Whiyufghj, Coutasji, Chefukija, Imadytu, Civjaty, Poiyiop1, Plastadity, Houtdsya, Vierutasd, Thisgureat, Witguiota, Tasfhkl, Desqwer, Leabnm, Iamcvb, TinucherianBot II, Traqwe, Tripodian, ASchudak, Timir2, Suitawty, Glafyjk, Voigfdsa, Estlandia~enwiki, Towsdfvui, Wyklety, Gap9551, J04n, GrouchoBot, Swd, Omnipaedista, Thecoldmidwest, Miriska, Superlinka, RibotBOT, Nedim Ardoğa, Hmxma, GhalyBot, Sewblon, WebCiteBOT, Green Cardamom, FreeKnowledgeCreator, FrescoBot, Paine Ellsworth, Larkusix, 13afuse, Endofskull, Kaiser von Europa, Eagle4000, Killercrossover, Citation bot 1, Sshas75, Iupolisci, I dream of horses, Jonesey95, Tom.Reding, Winooo, Tomcat7, Bmclaughlin9, Yatzhek, Nkdfun, Biala Gwiazda, Jandalhandler, Henrig, DocYako, FoxBot, Double sharp, TobeBot, Trappist the monk, Podruznik, 700KFF, Shisir 1945, Vrenator, The Catholic Knight, Varsovian, Farhikht, Diannaa, Jbenjos, Claudio Pistilli, MyMoloboaccount, Tbhotch, Reach Out to the Truth, Minimac, Getler, DARTH SIDIOUS 2, Whisky drinker, RjwilmsiBot, TjBot, Saruha, OrthodoxLinguist, Esoglou, EmausBot, Mamalala, John of Reading, Gfoley4, Dominus Vobisdu, Sukumar Ray, Gimmetoo, ZxxZxxZ, Maturion, Tommy2010, Solomonfromfinland, Kkm010, ZéroBot, John Cline, Fæ,


376

CHAPTER 33. ORBITAL ECCENTRICITY

Fredfred1112, Aronlee90, AvicAWB, Everard Proudfoot, H3llBot, Hydriz, IIIraute, Wayne Slam, Ocaasi, Akasseb, LWG, Brandmeister, Dagko, Willthacheerleader18, Chewings72, Ego White Tray, Atwardow, Ihardlythinkso, Jimmymaj, Maximilianklein, DASHBotAV, Maxkingesq, Xanchester, ClueBot NG, Taylorgarcia, Serasuna, Gilderien, Marbolski, Conveyance, Robsuper, Mach240390, Razum2010, Frietjes, Alphasinus, Tom5551, Mannanan51, Danim, Helpful Pixie Bot, Mulhollant, Bibcode Bot, Hadashi Black, Lowercase sigmabot, Carjoyg, BG19bot, Vagobot, Quarkgluonsoup, Frze, Darkness Shines, Nijmeagen, Daedalus&Ikaros, Woody4077, Dontreader, RadicalRedRaccoon, Greenknight dv, Presterct, BattyBot, Klawgor, Top811, Cyberbot II, Khazar2, Dexbot, Webclient101, Cerabot~enwiki, THEWISEOLDTURK, Puisque, VIAFbot, Burham, TheSonoran, PinkAmpersand, Epicgenius, Mieszko 8, Mrsquirrel dh, Unfriend13, Yemote, Matt Zjack, Rewa, Oliszydlowski, Bluffer8, Mralext20, Monkbot, Yikkayaya, Jerry3434, 10FCollier, Piledhighandeep, E-960, Py1905py, Moorrests, Pherosalia22, California Genius, White373737, KasparBot, Anarchyte, BostonB.C., Wouter Maes, Jmaxthorntons, IvanScrooge98, GreenC bot, Charizardmewtwo and Anonymous: 1077 • Ptolemy Source: https://en.wikipedia.org/wiki/Ptolemy?oldid=743958900 Contributors: Magnus Manske, JHK, Brion VIBBER, Dan~enwiki, Andre Engels, XJaM, Diatarn iv~enwiki, William Avery, Ktsquare, Panairjdde~enwiki, Nonenmac, Heron, Tzartzam, Hephaestos, Olivier, Lir, Michael Hardy, Llywrch, Dan Koehl, Nixdorf, Menchi, Dcljr, Yann, Looxix~enwiki, Ihcoyc, Ellywa, Ahoerstemeier, Stan Shebs, Kingturtle, Evercat, Genie, Tom Peters, EmphasisMine, Jmccann~enwiki, Tpbradbury, Furrykef, Hyacinth, Adia~enwiki, Wetman, Jerzy, Eugene van der Pijll, Jni, Dimadick, Robbot, Psychonaut, Naddy, Modeha, Wereon, Ianml, Scythian99, GreatWhiteNortherner, Matt Gies, Giftlite, JamesMLane, Hpc, Tom Radulovich, Everyking, Curps, Duncharris, Gilgamesh~enwiki, Per Honor et Gloria, Eequor, Macrakis, Matthead, Wmahan, Quadell, Antandrus, Beland, MacGyverMagic, 1297, Bumm13, Pmanderson, Icairns, Zfr, Karl-Henner, Cglassey, ShortBus, ELApro, Corti, Mike Rosoft, D6, Discospinster, Rich Farmbrough, Guanabot, Vsmith, Eitheladar, Aonaran, Ioliver, Dbachmann, Paul August, SpookyMulder, Bender235, ESkog, JoeSmack, RJHall, CanisRufus, Pjrich, Kwamikagami, Chairboy, Shanes, Art LaPella, Sajt, Spoon!, Bill Thayer, Bobo192, Yonghokim, Ruszewski, Func, Tronno, Troels Nybo~enwiki, LostLeviathan, Storm Rider, Red Winged Duck, Alansohn, PaulHanson, Neonumbers, Atlant, Keenan Pepper, Riana, AzaToth, Lightdarkness, Kapnisma, Fawcett5, Branlory, DreamGuy, Wtmitchell, Super-Magician, Yuckfoo, Suruena, Uffish, Evil Monkey, Jheald, J Heath, Sciurinæ, W7KyzmJt, Jguk, Siafu, NantonosAedui, Woohookitty, FeanorStar7, Camw, Miaow Miaow, Carcharoth, Pol098, WadeSimMiser, Bkuschel, Chochopk, MONGO, -Ril-, Fred J, Dzordzm, Firien, SCEhardt, John Hill, InitHello, Xiong Chiamiov, Prashanthns, Gimboid13, Tokek, Liface, MarcoTolo, Rgbea, Graham87, Qwertyus, FreplySpang, Sjö, Pittising, Rjwilmsi, Coemgenus, Nightscream, Jake Wartenberg, Bill37212, JHMM13, Bruce1ee, Mike s, Bhadani, Ttwaring, Schaengel89~enwiki, Maurog, Ev, Yamamoto Ichiro, Mahlum~enwiki, Miskin, FlaBot, Musical Linguist, AdnanSa, RexNL, Gurch, TeaDrinker, Simishag, Alphachimp, Peter1219, Thecurran, Chobot, Jared Preston, DVdm, Algebraist, Banaticus, EamonnPKeane, YurikBot, Wavelength, Sceptre, Hairy Dude, Phantomsteve, RussBot, Pigman, Kurt Leyman, Lucinos~enwiki, Kirill Lokshin, FDR, Stephenb, Polluxian, Anomalocaris, Shanel, NawlinWiki, Anchjo, Petrouchka, Jaxl, UDScott, Ryright, JDoorjam, Ragesoss, Aldux, PhilipC, Raven4x4x, Juanpdp, Syrthiss, Xompanthy, Nescio, Botteville, NorVegan, Igiffin, Searchme, Tuckerresearch, 21655, SilentC, Lt-wiki-bot, Fulup, J. Van Meter, Pb30, Modify, Vogelfrei, Chris Brennan, BorgQueen, Red Jay, Curpsbot-unicodify, Kungfuadam, TLSuda, DVD R W, One, Sardanaphalus, Amalthea, SmackBot, Amcbride, Selfworm, Tarret, Prodego, InverseHypercube, KnowledgeOfSelf, Pgk, C.Fred, Blue520, Allixpeeke, Jagged 85, Alksub, Flamarande, Srnec, Yamaguchi , Peter Isotalo, Gilliam, Hmains, MPD01605, Abukaspar, Chris the speller, TimBentley, Jabbi, Master of Puppets, OrangeDog, Silly rabbit, Willardo, Ikiroid, DHN-bot~enwiki, Roy Al Blue, Toughpigs, Nicolas101, Scwlong, Philipvanlidth, Can't sleep, clown will eat me, Ammar shaker, TheGerm, Sumahoy, Snowmanradio, Rrburke, Mhym, Addshore, Mr.Z-man, Allan McInnes, SundarBot, Phaedriel, Stevenmitchell, Downwards, TedE, Theodore7, Funky Monkey, Blake-, NaySay, Kleuske, Jon Awbrey, JLogan, SashatoBot, Nishkid64, ArglebargleIV, Rory096, Kuru, Writtenonsand, J 1982, Hemmingsen, Minna Sora no Shita, Tlesher, Ckatz, Stoa, The Man in Question, Werdan7, Optakeover, Hunadam, Novangelis, Zapvet, Hectorian, Asyndeton, Politepunk, Norm mit, Hetar, Nehrams2020, Paul Koning, Maestlin, Shoeofdeath, Supersquid, Zeusnoos, Courcelles, Tawkerbot2, Connection, Atomobot, Lahiru k, SkyWalker, JForget, CmdrObot, Ale jrb, Geremia, Mattbr, Ninetyone, Picaroon, Rwflammang, Tschel, CWY2190, Basawala, Clay4president, El aprendelenguas, Black and White, Equendil, Cydebot, Jgtl2, Aristophanes68, Gogo Dodo, Catalyst in Society, DangApricot, ST47, JamesLucas, Dancter, Hispalois, Tawkerbot4, Shirulashem, Codetiger, DumbBOT, SteveMcCluskey, Zalgo, Ael 2, FrancoGG, Thijs!bot, Epbr123, Wikid77, Teh tennisman, Rosarinagazo, Woody, Itsmejudith, Bauerja24, Nezzadar, Sturm55, CielProfond, Ludde23, Pruy0001, RoboServien, Mentifisto, AntiVandalBot, RobotG, Rosicrux, Seaphoto, Deeplogic, Just Chilling, HMAccount, Toohool, Dr. Submillimeter, Farosdaughter, Wahabijaz, Gökhan, JAnDbot, Deflective, Husond, MER-C, Tosayit, Instinct, Curious Violet, Hamsterlopithecus, Alastair Haines, Xact, Acroterion, Tikkimann, Connormah, Bongwarrior, VoABot II, Jerome Kohl, Catgut, Indon, Animum, Tuncrypt, ‫الدبوني‬, Allstarecho, David Eppstein, Gomm, DerHexer, Edward321, Purslane, Baristarim, Tercer, Geboy, MartinBot, Jonathan Stokes, Twigletmac, Arjun01, Sigmundg, David J Wilson, R'n'B, AlexiusHoratius, Fconaway, LedgendGamer, Ivan T., AlphaEta, J.delanoy, Nev1, Skeptic2, Nigholith, McSly, Zedmelon, Daniel Earwicker, NewEnglandYankee, Malerin, Kansas Bear, Student7, Potatoswatter, Cmichael, TottyBot, KylieTastic, Juliancolton, Cometstyles, STBotD, Bonadea, MishaPan, Spellcast, Deor, Jman8686, VolkovBot, CWii, ABF, Macedonian, DSRH, Jeff G., NikolaiLobachevsky, VasilievVV, Barneca, Philip Trueman, TXiKiBoT, Oshwah, Jeremy221, GroveGuy, Technopat, Qxz, John Carter, Melsaran, Cerebellum, Jackfork, LeaveSleaves, David in DC, Király-Seth, SwordSmurf, Ian Goggin, Meters, Cantiorix, Synthebot, WatermelonPotion, Insanity Incarnate, Mike4ty4, Scivandal11, Quantpole, PGWG, PericlesofAthens, Hazel77, EmxBot, SieBot, StAnselm, PlanetStar, Tiddly Tom, BAScMASc~enwiki, Dawn Bard, Caltas, Triwbe, Fractain, Keilana, Weresnot, Tiptoety, Radon210, JSpung, Hjmck123, Ayudante, Antonio Lopez, Faradayplank, Zharradan.angelfire, Goustien, Alex.muller, BenoniBot~enwiki, OKBot, Maelgwnbot, Liamdanny2, StaticGull, WikiLaurent, Astrologist, Nn123645, Denisarona, Lloydpick, Escape Orbit, Into The Fray, 3rdAlcove, Eragon is the lord of the rings, Atif.t2, Church, ClueBot, Eilidhrosach, VanishedUser sdu9aya9f213ws, Jgeortsis, Zachariel, The Thing That Should Not Be, Pakaraki, Viramundo, Cp111, Mild Bill Hiccup, Tizeff, TheOldJacobite, J8079s, CounterVandalismBot, LonelyBeacon, Parkwells, Otolemur crassicaudatus, Singinglemon~enwiki, Auntof6, DragonBot, Excirial, Jasontecx 6482, Alexbot, Jusdafax, PixelBot, BobKawanaka, Kuka14, Tyler, Jotterbot, Brizzleness, Razorflame, Bballboysigmasix, JasonAQuest, ChrisHodgesUK, Thehelpfulone, Kakofonous, Catalographer, Aitias, Venera 7, Scalhotrod, SorcererofDM, Egmontaz, Bücherwürmlein, Chronicler~enwiki, XLinkBot, Spitfire, Bilsonius, BodhisattvaBot, Tylor 12, DaL33T, WikHead, Kwjbot, Tratosthefeared, Badgernet, Alexius08, Noctibus, Good Olfactory, Aeverrault, HexaChord, Addbot, Jojhutton, Yolgnu, PaterMcFly, DougsTech, TutterMouse, Elmondo21st, Fieldday-sunday, CanadianLinuxUser, Cst17, Download, Joshtynan, Simeon24601, Favonian, Kyle1278, SpBot, AtheWeatherman, LinkFA-Bot, CuteHappyBrute, Numbo3-bot, Koliri, Newyorkbabe817, Tide rolls, Lightbot, Dcrossfire14, Gail, Zorrobot, MuZemike, David0811, Ccaarft, Randomness2, Frehley, Luckas-bot, ZX81, Yobot, Tohd8BohaithuGh1, Wickedwizardofoz, PMLawrence, KamikazeBot, Keeratura, Hazzagazza, LightingZero, Catiline63, AnomieBOT, DemocraticLuntz, Kristen Eriksen, 1exec1, IRP, Spotsupon, AdjustShift, LlywelynII, Kingpin13, Materialscientist, Cutiegirl28088, BillLoney, Philomathes, Drunkenmonk4, Citation bot, Maxis ftw, Surya31415, Frankenpuppy, FreeRangeFrog, MauritsBot, Xqbot, Capricorn42, Gilo1969, Cyphoidbomb, Gap9551, Dude Of War, Richmonkey19, Omnipaedista, K lindegaard, Rick Cooper, Amaury, Den lange, Krscal, Ghio10, Unknown1183, FrescoBot, Paine Ellsworth, Michael93555, 01shoty01, Briggzi, HJ Mitchell, DivineAlpha, Citation bot 1, Ghghghgh1, B424, Pinethicket, I dream of horses, HRoestBot, Edderso, Kelryn, Jonesey95, Tom.Reding, BRUTE, RedBot, Serols, Kevintampa5, RandomStringOfCharacters, Fumitol, Link0226, Merlion444, Jauhienij, FoxBot,


33.10. EXTERNAL LINKS

377

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CHAPTER 33. ORBITAL ECCENTRICITY

Wolfdog, CmdrObot, Thorax The Impaler, Geremia, Robin Scagell, Dycedarg, BoH, Silversink, Arepo~enwiki, AlbertSM, KyraVixen, RedRollerskate, Vininche, Drinibot, Jsd, NickFr, Calmofthestorm7, WMSwiki, Vvargoal, MrFish, Myasuda, Anthony Bradbury, Gregbard, Nauticashades, CMG, Logicus, Cydebot, Schnarf78, Galassi, Steel, Michaelas10, Clayoquot, Gogo Dodo, Travelbird, Corpx, Chasingsol, Pascal.Tesson, Amandajm, Irendraca, Tawkerbot4, DumbBOT, Chrislk02, Sheilakirbos, Benford R, Ssilvers, Hawesinsky, Srath, Kozuch, SteveMcCluskey, Omicronpersei8, Gimmetrow, Satori Son, Mamalujo, FrancoGG, GxxFORCE, Thijs!bot, Epbr123, Hersheys66, Wikid77, VKemyss, Kablammo, Andyjsmith, Headbomb, Superstuntguy, James086, Catsmoke, Assianir, J. W. 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Ric, Husond, Mngt, Komponisto, MER-C, CyberAnth, Arch dude, Pgleason, Trebor trouble, Space wolf, Arturo 7, Plm209, Hut 8.5, Falkan, Kipholbeck, Makron1n, Savant13, Ironplay, Easchiff, Penubag, Magioladitis, Connormah, WolfmanSF, Kikadue~enwiki, VoABot II, Andrewthomas10, MartinDK, JNW, JamesBWatson, Frip1000, SHCarter, DWIII, Charlesreid1, Sekfetenmet, Plain jack, CaptainP, Leeborkman, Avicennasis, Zanibas, Indon, Rusty Cashman, Animum, Chemical Engineer, Abyss257, ArchStanton69, Just H, MiPe, Arbeiter, Fliegen, Shojeeb, Gerry D, Theallfatherodin, Vssun, Parunach, Chris G, DerHexer, JaGa, Drazil91, Pax:Vobiscum, Wayne Miller, TJohn, Patstuart, Wikianon, Sesler, Phuongyy, Gwern, DancingPenguin, SkePtiKaL, Xxdeus777xx, MartinBot, Physicists, PaulLev, DMJ001, Mysjkin, Setoor, GuidoGer, Witch-King, Edtrokr, Rettetast, Stroudj0, David J Wilson, Fdsfdsafsdff, Threedots dead, Ucpress, Mushroom 652, Johnpacklambert, Zygimantus, Lepidus16, LittleOldMe old, Lilac Soul, Gate28, Ssolbergj, 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Junling, PaulTheDon, Steven Crossin, Lightmouse, JerroldPease-Atlanta, Iain99, Pittsburghmuggle, Miguel.mateo, Jesse-briggs, BenoniBot~enwiki, Bramster, COBot, Cheezarita, OKBot, Sallvio, Mitya1, Vojvodaen, Maelgwnbot, CharlesGillingham, Liamdanny2, Calle Widmann, Duae Quartunciae, Realm of Shadows, Firefly322, Dolphin51, Nergaal, NorthParkAdam, Randy Kryn, RS1900, Sagredo, Tomasz Prochownik, Martarius, Theruteger, ClueBot, PipepBot, Jgeortsis, Eyalmc, Fadesga, Scartboy, QueenAdelaide, Rjd0060, DionysosProteus, VsBot, MikeVitale, Duff man2007, Wysprgr2005, Anatidae, Refunked, Chris Bainbridge, Polyamorph, J8079s, Brandon1000000, Laurarosethomson, CounterVandalismBot, Jmn100, Dan 9111, Richerman, Piledhigheranddeeper, Chyky50, Grandpallama, Broc.burmeister, Jersey emt, DragonBot, Futbolchica246, Alexbot, Theremoney, Zaxster007, Ftgyhu, Andy pyro, Alamoman444, Thispagedoesown, Ludwigs2, NuclearWarfare, A22~enwiki, A1b43789erzsd, Zachmosher, Gciriani, Mickey gfss2007, Audaciter, Thingg, Jonverve, Johnuniq, Hasp~enwiki, Bend2pa, Ambrosius007, Terry0051, Dthomsen8, SilvonenBot, Mifter, Kbdankbot, HexaChord, Vic333, Davitoroth, BenSven, Addbot, Yousou, RogerRoger1, DOI bot, Haydeemarinoitzel, Fultzsie11, Sully123123, Cuaxdon, KitchM, Conjohn, Vishnava, Leszek Jańczuk, Proxima Centauri, Chamal N, Glane23, Svernon19, AndersBot, Favonian, LinkFA-Bot, Dupea, Tassedethe, Numbo3-bot, James Balti, Tide rolls, Cesiumfrog, Totorotroll, Krano, Jlodman, Ketabtoon, Killy mcgee, Luckas-bot, Yobot, Lucas, Legobot II, Rsquire3, Nallimbot, Brougham96, KamikazeBot, Theornamentalist, Tempodivalse, Dmarquard, Kata Markon, Orion11M87, AnomieBOT, IRP, Cavarrone, Billydabomb666, Materialscientist, ImperatorExercitus, Citation bot, Onesius, Rockoprem, Frankenpuppy, Neurolysis, LovesMacs, Omarxxx7, Dickweed123, Xqbot, Tasudrty, Timir2, Intelati, Capricorn42, XZeroBot, Galileo1235, Br77rino, Mlpearc, Gap9551, BrianWren, Markell West, Petropoxy (Lithoderm Proxy), GrouchoBot, JanDeFietser, Nayvik, Omnipaedista, Yugolervan, Nedim Ardoğa, Gruß Tom, Krscal, Jyoung22, Sewblon, Vittuone, Spellage, A. di M., Green Cardamom, SirEbenezer, Neojacob, BoomerAB, MaryBowser, Einsteinino, FrescoBot, StephenWade, Dolly1313, Blackguard SF, Paine Ellsworth, Alan D~enwiki, Tranletuhan, HJ Mitchell, Steve Quinn, Marmzok, Eagle4000, Elocute, Dhtwiki, Citation bot 1, B defelici, Imoretti, Pshent, Tkuvho, AstaBOTh15, WQUlrich, Mphammer, Tom.Reding, RedBot, Wikiain, VenomousConcept, Meaghan, Brblweb, Jandalhandler, Jauhienij, Kgrad, TobeBot, Lotje, Greenleaf547, IYA2010, Begoon, PS3ninja, Dep1701, Stalwart111, Curfewcall, Tbhotch, EyeKnows, DARTH SIDIOUS 2, RjwilmsiBot, Altes2009, TjBot, Saruha, Abspqizax, DASHBot, Steve03Mills, EmausBot, Ajraddatz, Katherine, Sprout333, Faolin42, GoingBatty, John of Lancaster, Solomonfromfinland, Je9671111, Mz7, Chiorbone da Frittole, ZéroBot, John Cline, PBS-AWB, Ida Shaw, Bongoramsey, A2soup, Saint cuthbert, Dondervogel 2, AvicAWB, AndrewOne, SporkBot, Ocaasi, Brandmeister, Coasterlover1994, L Kensington, Vibratorhythm, MonoAV, Hugewang69, Chewings72, ChuispastonBot, JFB80, Xanchester, Schinkelburg, LJosil, DonaldRichardSands, Bakrnl, Frietjes, Anold4, Alphasinus, Hazhk, Castncoot, Mariocrossing1, Andrewjohnbayles, Scotfreegirl, Sammy3434, Helpful Pixie Bot, Qwerb2, Bibcode Bot, Theoldsparkle, BG19bot, Hashem sfarim, Quarkgluonsoup, George Ponderevo, Darouet, Contact '97, Gallina3795, Ramos1990, Rynsaha, Tycho-Is-Great, MrBill3, Brad7777, BattyBot, Vanobamo, Cyberbot II, Danny2579, Bharu12, Zh84, Khazar2, Esszet, Dexbot, Periglio, Siberian Patriot, VIAFbot, New York Resident, Jochen Burghardt, Tasmanian123, Corinne, DoubleBook, Jellyfish987987987, Cubomedusa, Ga78675645, Reatlas, Lgfcd, Lomicmenes, FallingGravity, LimosaCorel, Ruby Murray, Lfdder, Dimzz, Antipeacock123456, Sebfamo, Ugog Nizdast, AntiPOVsleeper, AntiPOVmagnet, D Eaketts, Ephemera1234, Vinny Lam, OccultZone, N0n3up, Sleeperagainstracialism, Barjimoa, Mahusha, Ryusc, Monkbot, Axbaksh, Dayvenkirq, AdventurousMe, JoeHebda, Ephemeratta, Agrcsm987, Arxivbuff, Da1Th2Er3Vs4, Good afternoon, Garfield Garfield, TridiaChaplain, GarretKadeDupre, 115ash, Maxwell Verbeek, Aledownload, Tsuvadefence, MissouriOzark1947, 1900Parma1900, Explodingstar, Cccllleeennn, Py1905py, One1915stone, Orduin, Wipeout10, NONIS STEFANO, Isambard Kingdom, Czech1001Slovak, Bparkhu1, KasparBot, Jwicklatz, Simba541chui, Doors777, 1953Stalin, Dynamicmaths IP, Railwayline777389, HelgeLund793, TheEditor867, Co880Tes, Sir Cumference, Yakut987, FirstSecondThird, C.Gesualdo, 543Demosthenes, Soqotri555, Jmaxthorntons, IvanScrooge98, Kkk532, Blue6767unicorn, J7k7l7, G678sdc, PcPrincipal, Charlotte135, Nossa Bova, WhiteHyrax, Piyr, Gh78cb, 35nmsf, Dth7k, G5hsd, Bon4721, Cats The One Eyed Ghoul, Webaugust, 9d3a556, 7a1130, 4gsds, Ddd7d, Pwolit iets and Anonymous: 1409 • Heliocentrism Source: https://en.wikipedia.org/wiki/Heliocentrism?oldid=743476447 Contributors: Eloquence, Bryan Derksen, XJaM,


33.10. EXTERNAL LINKS

379

Christian List, Roadrunner, SimonP, Patrick, Michael Hardy, Chris-martin, Llywrch, Jrauser, Ahoerstemeier, Theresa knott, Mark Foskey, Andres, Evercat, KayEss, Pizza Puzzle, Charles Matthews, Andrevan, Dandrake, Lord Kenneth, Tpbradbury, AnonMoos, Wetman, Pollinator, Lumos3, Jni, Robbot, Chrism, Modulatum, Lowellian, Hadal, Modeha, Anthony, Alan Liefting, Giftlite, Jyril, Nat Krause, Art Carlson, Everyking, Michael Devore, Solipsist, Matthead, Shibboleth, Geni, Drichardson, Wikimol, JimWae, Pmanderson, Icairns, Neutrality, Grunt, ELApro, Mike Rosoft, Discospinster, Brandonrhodes, Wikiacc, Fleung, Dbachmann, Pavel Vozenilek, Bender235, Kbh3rd, Livajo, El C, Robert P. O'Shea, Kwamikagami, Summer Song, Art LaPella, RoyBoy, Noren, Harley peters, Smalljim, Viriditas, Adrian~enwiki, Aquillion, Nk, Sam Korn, Flitzer, Jumbuck, Truth seeker, JYolkowski, Andrewpmk, Wtmitchell, H2g2bob, Bsadowski1, Ent, Marianika~enwiki, Dejvid, Feezo, Richard Arthur Norton (1958- ), Woohookitty, Xover, TigerShark, Kokoriko, Pol098, WadeSimMiser, MONGO, Kelisi, Bennetto, Nerrin, MarcoTolo, Marudubshinki, Paxsimius, Mandarax, Ashmoo, Magister Mathematicae, Qwertyus, Josh Parris, Sjakkalle, Rjwilmsi, Reinis, Sango123, FlaBot, Margosbot~enwiki, Nihiltres, RexNL, TeaDrinker, Wikcerize, Gareth E. Kegg, King of Hearts, Chobot, Frappyjohn, DVdm, Bgwhite, Dj Capricorn, Gwernol, YurikBot, Kinneyboy90, Deeptrivia, Brandmeister (old), RussBot, Pigman, Wikinick~enwiki, Odysses, NawlinWiki, Wiki alf, Dialectric, Schlafly, Ragesoss, Aldux, Dannyno, Tony1, Gadget850, Bota47, Wiqi55, Lt-wiki-bot, Closedmouth, Arthur Rubin, Chanheigeorge, Jecowa, Listowy, Squell, Moomoomoo, GrinBot~enwiki, DVD R W, Cannin, SmackBot, FocalPoint, Nahald, Selfworm, PiCo, ThreeDee912, Incnis Mrsi, Ma8thew, McGeddon, C.Fred, Jacek Kendysz, Jagged 85, Delldot, CurtisI, Gilliam, Hmains, Grokmoo, Michael003, Rstml, Jayanta Sen, Miquonranger03, Stevage, DHN-bot~enwiki, Konstable, Modest Genius, Can't sleep, clown will eat me, Writtenright, Rrburke, TKD, Harlequinn, Mikedow, TedE, Alexandra lb, Andrei Stroe, Fyver528, Serein (renamed because of SUL), Harryboyles, Molerat, Kuru, Khazar, John, J 1982, Zzapper, Yogesh Khandke, Ckatz, MarkSutton, Kyoko, InedibleHulk, Ryulong, MTSbot~enwiki, Iridescent, Maestlin, Lmblackjack21, Harry Stoteles, Blehfu, Gil Gamesh, Tawkerbot2, Chris55, Kurtan~enwiki, CmdrObot, Logicus, Subravenkat, Nick Wilson, Miguel de Servet, Viscious81, Doug Weller, Christian75, Juansempere, Chrislk02, Kozuch, SteveMcCluskey, Gimmetrow, ‫הסרפד‬, Thijs!bot, Epbr123, HappyInGeneral, Oliver202, Headbomb, James086, Pmrobert49, CarbonX, AntiVandalBot, Nikolang~enwiki, AstroLynx, Ajishg, Lkitrossky, Alcap, David Shankbone, Elaragirl, Myanw, Dreaded Walrus, Ibrian, Kaobear, VoABot II, Ezgirl, ***Ria777, Nyttend, Recurring dreams, Inkan1969, JaGa, TheBusiness, Ekotkie, Gun Powder Ma, Cdecoro, MartinBot, Coolpm, David J Wilson, CommonsDelinker, Beit Or, J.delanoy, Dragon manlol, Uncle Dick, WarthogDemon, DigitalCatalyst, Evb-wiki, SoCalSuperEagle, Funandtrvl, ACSE, 28bytes, VolkovBot, BoogaLouie, Ryan032, Philip Trueman, Maximillion Pegasus, Aymatth2, Qxz, LeaveSleaves, Rjm at sleepers, Pleroma, ARUNKUMAR P.R, Solicitr, Daw923, Isis07, Deconstructhis, EJF, SieBot, Tiddly Tom, Nihil novi, Hertz1888, Dawn Bard, Yintan, Jason Patton, Flyer22 Reborn, AngelOfSadness, Waconer, Steven Crossin, JackSchmidt, Denisarona, 3rdAlcove, Chrisclaudatos, Athenean, IAC-62, ClueBot, Foxj, Jorge Ianis, Skäpperöd, FractalFusion, Mcalhanytrey, Niceguyedc, Singinglemon~enwiki, Alexbot, HHHEB3, Leonard^Bloom, Jonathan316, Ottawa4ever, JasonAQuest, Thehelpfulone, Jimmy Fleischer, Thingg, Aitias, SoxBot III, HumphreyW, Egmontaz, JKeck, XLinkBot, Terry0051, Steelrain6, Jovianeye, Rror, Divius, Mifter, Noctibus, Aunt Entropy, ZooFari, Mayarocks, Addbot, Jw30, Fyrael, Landon1980, Soarandthink, Dvntehn00bz, Mr. Wheely Guy, KorinoChikara, CanadianLinuxUser, Akapellah21, Proxima Centauri, Write123567, Glane23, Jonoikobangali, LemmeyBOT, LinkFA-Bot, Tassedethe, Ppole, Yysa, Oota~enwiki, Uuda, Mmnaw, Richwierd, Ssaalon, Ttassr, Tide rolls, Bfigura’s puppy, Lightbot, HerculeBot, Ccaarft, Alfie66, Legobot, Luckas-bot, Yobot, Cflm001, Houutata, Hansihippi, Setukamal, Apptas, Bliduta, Wheenguta, TestEditBot, Synchronism, AnomieBOT, Plannatas, Burssdola, Jim1138, Graywords, Kingpin13, Materialscientist, Citation bot, Noideta, Zahab, Shogartu, ArthurBot, JmCor, Xqbot, Neswtuop, Motadat, Tasudrty, Random astronomer, Capricorn42, Poetaris, Nasnema, Jmundo, Tyrol5, RadiX, GrouchoBot, Bizso, Omnipaedista, RibotBOT, E0steven, A. di M., Ll1324, BoomerAB, RetiredWikipedian789, FrescoBot, Banool1000, Dilic, LucienBOT, Sensor60, Pergamino, Yety75, Giorgiodelucia, D'ohBot, Gueomme, Kitty1145, Parvons, Mhmmgirl, Uh kick, BenzolBot, Spideyyy, Citation bot 1, Pinethicket, Tom.Reding, Danieltburling, Rushbugled13, Reesorville, Tlhslobus, Jeppiz, Nashpur, Zbayz, The12345inator, TreeToppa, Vrenator, Reaper Eternal, Suffusion of Yellow, Sampathsris, TheMesquito, Uled123, Mean as custard, RjwilmsiBot, Raspberryjam314, Mukogodo, EmausBot, Spandrel, Urwrongimright, Da.bus56, Syncategoremata, KHamsun, Ungomma, Tommy2010, Wikipelli, Knight1993, Sekigaara, Ireebs95, Elektrik Shoos, Unreal7, Akasseb, Rcsprinter123, Efenna, Skunkerskunker, RockMagnetist, Petrb, ClueBot NG, Rich Smith, Superscooterkid, MelbourneStar, This lousy T-shirt, Historikeren, Tideflat, Widr, Mydaddy4412, Helpful Pixie Bot, HMSSolent, Titodutta, Bibcode Bot, BG19bot, 2pem, ElphiBot, Darouet, Chief Beef, Mark Arsten, Michael Barera, Try1572, Polmandc, Glacialfox, Ziggypowe, Mrt3366, Khazar2, EuroCarGT, Goldspotter, Cheewowa, Advlokanath, Lugia2453, Frosty, Tasmanian123, Kevin Corbett, BeanZull, Cadillac000, Kurrykingftw, Epicgenius, Sɛvɪnti faɪv, SucreRouge, Tentinator, Mollyb18, DavidLeighEllis, CensoredScribe, Haminoon, Joemanbro49, Ugog Nizdast, Sam Sailor, 22merlin, Marwankhan118, Monkbot, Trackteur, HMSLavender, 2Mars4$2Billion, GreatTruth112233, Crystallizedcarbon, Spartan - 117, Sheldog100, Bob16bobo, Rubbish computer, Greentee235, Tetra quark, Isambard Kingdom, KasparBot, Tkdboy910, Thesenuts3000, Jmaxthorntons, LelouchEdward, AnirudhKalla77, 22Brett, Socialium, Kirk Leonard, ThescienceguyRS, Bear-rings, Griffen Ray, Daniel.chung123 and Anonymous: 657 • Johannes Kepler Source: https://en.wikipedia.org/wiki/Johannes_Kepler?oldid=744013218 Contributors: Magnus Manske, Matthew Woodcraft, Brion VIBBER, Mav, Bryan Derksen, Ed Poor, Andre Engels, Danny, XJaM, Christian List, Roadrunner, Ben-Zin~enwiki, Olivier, Lir, Patrick, Boud, Michael Hardy, Ezra Wax, Kwertii, Liftarn, Gabbe, Bcrowell, Cyde, Tomi, Tzaquiel, Miciah, GTBacchus, Stw, Looxix~enwiki, Ahoerstemeier, William M. Connolley, Muriel Gottrop~enwiki, Snoyes, Suisui, Jebba, Darkwind, Александър, Victor Gijsbers, Djnjwd, BenKovitz, Big iron, Andres, Pizza Puzzle, Hike395, Hashar, EL Willy, Charles Matthews, Timwi, Lfh, JCarriker, Dtgm, Timc, Tpbradbury, Furrykef, Thue, Bwmodular, JorgeGG, Frish, Dimadick, Robbot, Astronautics~enwiki, Jaredwf, Fredrik, Jenmoa, Chocolateboy, Gandalf61, Merovingian, Gidonb, Diderot, Timrollpickering, Phthoggos, Demerzel~enwiki, Alan Liefting, Ancheta Wis, Giftlite, Inter, Tom harrison, Meursault2004, Brian Kendig, Herbee, Wwoods, Average Earthman, Jacob1207, Curps, Michael Devore, Markus Kuhn, Joconnor, Duncharris, Gilgamesh~enwiki, Solipsist, Matthead, Jerith, Wmahan, JE, ChicXulub, Utcursch, Andycjp, Alexf, Quadell, Antandrus, MisfitToys, Jossi, Richmd, Ruzulo, Sky, Gauss, Bumm13, Tomruen, PFHLai, Joyous!, Ukexpat, Robin klein, ELApro, Thorwald, Corti, Grstain, Mike Rosoft, Pfg, D6, Venu62, Obda, Poccil, DanielCD, JTN, Bornintheguz, Discospinster, Rich Farmbrough, Kevinb, Pak21, Dan Gan, Pjacobi, Vsmith, Bishonen, Mjpieters, Arthur Holland, Dbachmann, Mani1, Wadewitz, Grutter, Paul August, SpookyMulder, Rsp, Bender235, Janderk, Kaisershatner, Mashford, Eestevez, Brian0918, RJHall, CanisRufus, Kwamikagami, Hayabusa future, Aude, Shanes, RoyBoy, Cacophony, Triona, Bill Thayer, Peter Greenwell, Bobo192, Che090572, Shenme, Xevious, AKGhetto, WoKrKmFK3lwz8BKvaB94, La goutte de pluie, Jojit fb, Rajah, MPerel, Hagerman, Mpulier, Nsaa, BSveen, Jumbuck, Alansohn, Gary, Kjetil, Ricky81682, Andrew Gray, Riana, Ashley Pomeroy, Walkerma, Burn, Malo, Bart133, Snowolf, Wtmitchell, Bucephalus, Velella, SidP, Dabbler, VivaEmilyDavies, Staeiou, CloudNine, Sciurinæ, Lerdsuwa, Kusma, Redvers, Kazvorpal, Ceyockey, Tariqabjotu, Spartacus007, Siafu, Velho, Woohookitty, Mindmatrix, Sandius, FeanorStar7, LOL, Jersyko, LoopZilla, Carcharoth, Jacobolus, Kam Solusar, MONGO, Fred J, Al E., Dionyziz, Eilthireach, Prashanthns, Liface, Dysepsion, Paxsimius, RedBLACKandBURN, Magister Mathematicae, Peter Maggs, Canderson7, Sjakkalle, Rjwilmsi, Koavf, Syndicate, Lockley, Sdornan, Salix alba, Mike s, Boccobrock, Brighterorange, Bhadani, Olessi, GregAsche, Yamamoto Ichiro, Kasparov, Titoxd, RobertG, Mathbot, Nihiltres, SouthernNights, Krackpipe, RexNL, Gurch, TeaDrinker, Tomer Ish Shalom, Alphachimp, Piniricc65, Chobot, Deyyaz, DVdm, Bgwhite, Gwernol, Algebraist, YurikBot, Wavelength, Bambaiah, Sceptre, Mukkakukaku, Brandmeister (old), RussBot, Kammy~enwiki, Fabartus, Tresckow, SpuriousQ, Gaius


380

CHAPTER 33. ORBITAL ECCENTRICITY

Cornelius, Wimt, Tavilis, Anomalocaris, Purodha, NawlinWiki, Nahallac Silverwinds, Wiki alf, Grafen, Howcheng, Dureo, JocK, Nick, Ragesoss, PhilipC, Tony1, DeadEyeArrow, Dustinsc, Asarelah, Speedoflight, Werdna, Ms2ger, Crisco 1492, PennaBoy, Theda, Closedmouth, Spondoolicks, Fang Aili, Colin, Chris Brennan, BorgQueen, CWenger, Whobot, Emc2, Willtron, Curpsbot-unicodify, Katieh5584, Mohylek, DVD R W, Finell, Tom Morris, Vulturell, Luk, Attilios, Yakudza, SmackBot, Triggar, Nihonjoe, Reedy, Unyoyega, Jagged 85, WookieInHeat, Gabrielleitao, Nil Einne, Arbadihist, VSquared, SmartGuy Old, Gilliam, Portillo, Duke Ganote, Algont, Hmains, Andy M. Wang, Saros136, Bluebot, Quinsareth, MK8, B00P, Miquonranger03, MalafayaBot, SchfiftyThree, DHN-bot~enwiki, Darth Panda, Can't sleep, clown will eat me, Proofreader, Neo139, Lazar Taxon, Pettefar, Ww2censor, Rrburke, Mhym, Addshore, SundarBot, Stevenmitchell, Aldaron, Flyguy649, Nakon, Theodore7, SnappingTurtle, Dreadstar, Alexandra lb, NaySay, KeithB, Richard0612, Didero, Bejnar, Pilotguy, Qmwne235, Ohconfucius, Thetruthingy, SashatoBot, Nishkid64, ArglebargleIV, Quendus, Harryboyles, Axem Titanium, Mike1901, C.jeynes, Brujo~enwiki, Pat Payne, Hemmingsen, Scetoaux, IronGargoyle, Tal.yaron, Ckatz, RandomCritic, A. Parrot, Noah Salzman, SQGibbon, Mr Stephen, Waggers, SandyGeorgia, Funnybunny, AdultSwim, Ryulong, Jose77, Xionbox, Iridescent, TerryE, Maestlin, Lakers, Shoeofdeath, Delta x, Twas Now, Igoldste, Gspieles, A. Pichler, Lemonman31, Courcelles, Tawkerbot2, ChrisCork, Switchercat, JForget, CmdrObot, DUden, Deon, Hermitage17, Dycedarg, JohnCD, Rwflammang, Nunquam Dormio, DeLarge, KnightLago, MarsRover, Myasuda, Oo7565, Pewwer42, Logicus, Cydebot, Tiphareth, Xanthoptica, Mato, Astrochemist, Meno25, Gogo Dodo, Travelbird, Khatru2, Corpx, Islander, A Softer Answer, Chasingsol, Studerby, Christian75, Fireware, DumbBOT, Chrislk02, Jay32183, Sp, Ssilvers, Kozuch, SteveMcCluskey, WxGopher, Pustelnik, Gimmetrow, Cpaolini, Thijs!bot, Epbr123, Jplvnv, Jmg38, N5iln, Zickzack, Headbomb, Marek69, James086, Peter Gulutzan, TXiKi, Zé da Silva, BehnamFarid, BlytheG, Rotundo, Dawnseeker2000, Qp10qp, Escarbot, LachlanA, AntiVandalBot, Seaphoto, AstroLynx, Prolog, Doc Tropics, Edokter, Julia Rossi, Nine9s, Fayenatic london, Dr. Submillimeter, Modernist, LibLord, Malcolm, Science History, Canadian-Bacon, Steelpillow, MikeLynch, Res2216firestar, Sluzzelin, JAnDbot, Leuko, DuncanHill, MER-C, HenryHRich, Fetchcomms, Arturo 7, Matttheguy, Andonic, Count de Chagny, Hut 8.5, NSR77, Noirceuil~enwiki, East718, SUBZBHARTI, PhilKnight, Christopher Cooper, Savant13, Felix116, Cynwolfe, GoodDamon, Acroterion, Geniac, Pseudothyrum, Magioladitis, Connormah, WolfmanSF, Thasaidon, Bongwarrior, VoABot II, Hasek is the best, JamesBWatson, Farquaadhnchmn, BillDeanCarter, Avicennasis, Cyktsui, Gregly, Silentaria, DerHexer, JaGa, Vorlnax, Dr.khangirl, Salimi, FisherQueen, MartinBot, HERODOTUS, Anaxial, AlexiusHoratius, Nono64, Spaceelve~enwiki, Yjwong, J.delanoy, Pharaoh of the Wizards, Kimse, DrKay, Trusilver, EscapingLife, Ali, Jorge Vila, Numbo3, Uncle Dick, Tommyvercetti101, Eliz81, Arneeast, NerdyNSK, Csato07, Michael Daly, It Is Me Here, Katalaveno, LordAnubisBOT, McSly, Samtheboy, Supuhstar, Plasticup, Chiswick Chap, Teh refrigerator, NewEnglandYankee, Rwessel, SJP, Bobianite, Malerin, Aatomic1, Biglovinb, Pdemoss, Sootyboy, Cometstyles, Gemini1980, Bonadea, Ja 62, Andy Marchbanks, S (usurped also), Jlittlenz, BernardZ, Idioma-bot, Spellcast, BigBlob14, Signalhead, Cactus Guru, Sherljim, PeaceNT, McNoddy~enwiki, VolkovBot, Thedjatclubrock, Johan1298~enwiki, ABF, Thisisborin9, A Macedonian, Kwsn, Tomer T, Omegastar, Vlmastra, Ryan032, Philip Trueman, Joeanded, Nd2010, TXiKiBoT, Oshwah, WatchAndObserve, Lots42, Robbn10, Vipinhari, GDonato, Jjfoerch, GcSwRhIc, Agricola44, Sean D Martin, Sankalpdravid, Packa, Ontoraul, Clarince63, DennyColt, Martin451, Omcnew, LeaveSleaves, Wassermann~enwiki, Rjm at sleepers, Cremepuff222, Nicholas.goder, Ken2400, Maxim, Madhero88, Rusica9231, Gabrielsleitao, Falcon8765, Anna512, GaylordBumBum, Homunculus 2, The Devil’s Advocate, Vegitotakinasa, HiDrNick, AlleborgoBot, Logan, PGWG, Closenplay, Jllaurado, Jackrabbit55, FlyingLeopard2014, Simkid96, EmxBot, Kastrel, The Watchtower, SieBot, StAnselm, Laoris, Æthelwold, Jack Merridew, Caltas, Cwkmail, Bentogoa, Thesavagenorwegian, Happysailor, Toddst1, Flyer22 Reborn, Djmoon66, Radon210, Oysterguitarist, Monegasque, Oxymoron83, Ioverka, Christmas 93, Faradayplank, AngelOfSadness, Steven Crossin, Lightmouse, Hobartimus, Miguel.mateo, Vanished user kijsdion3i4jf, OKBot, G.-M. Cupertino, Mojoworker, StaticGull, Mygerardromance, Firefly322, Westwind2, Antonio J. Reinoso, Richard David Ramsey, Escape Orbit, Remmus4, Tatterfly, ImageRemovalBot, Pie rules, Poopoopants~enwiki, WikipedianMarlith, Ricklaman, WikiBotas, Loren.wilton, Martarius, Sfan00 IMG, ClueBot, Artichoker, Snigbrook, Jgeortsis, Zachariel, Foxj, The Thing That Should Not Be, Srdffg, Icarusgeek, Taquito1, MikeVitale, Idahosurplus, Ndenison, DesertAngel, Jappalang, JuPitEer, Arakunem, 4timmy2turner0, J8079s, CounterVandalismBot, Kevin.py, Richerman, Harland1, Neverquick, Puchiko, Excirial, Alexbot, Jusdafax, John Nevard, Tyler, Terra Xin, RC-0722, Klaus Hünig, Bob21212121, Razorflame, RegalStar, Mormon17, Doprendek, Thingg, Aitias, LTPR22, Versus22, MelonBot, Johnuniq, SoxBot III, Tdslk, EstherLois, Darkicebot, Mithrandir726, XLinkBot, Sashatlhs, BodhisattvaBot, Justme713, Canada6969, Skarebo, WikHead, Npnunda, NellieBly, PL290, MHSINDIANS, Kbdankbot, HexaChord, CalumH93, Addbot, Xp54321, Jojhutton, Guoguo12, Landon1980, Otisjimmy1, DougsTech, Ronhjones, Sarasmiles322, Fieldday-sunday, CanadianLinuxUser, Fluffernutter, Rchard2scout, CarsracBot, Legoman779363, Glane23, AndersBot, Debresser, Favonian, LinkFA-Bot, West.andrew.g, 84user, Numbo3-bot, Tide rolls, Lightbot, Gail, David0811, CountryBot, Legobot, Math Champion, Luckas-bot, Yobot, Themfromspace, JohnnyCalifornia, Ajh16, AnomieBOT, Plannatas, Hairhorn, Rubinbot, 1exec1, Jim1138, IRP, Galoubet, AdjustShift, Kingpin13, Ulric1313, RandomAct, Bluerasberry, Materialscientist, Nightflyer, Citation bot, Noideta, ArthurBot, Gsmgm, Xqbot, Ywaz, Noonehasthisnameithink, Motadat, S h i v a (Visnu), Capricorn42, Nasnema, Mononomic, Darkwaterotter, Tyrol5, Gap9551, Maddie!, GrouchoBot, Ajh1138, Omnipaedista, Trafford09, Catterpillarslashtalkingsack, Imperators II, SchnitzelMannGreek, AJCham, Fotaun, Green Cardamom, Neojacob, Captain-n00dle, MaryBowser, FrescoBot, Amazing Steve, NSH002, Tobby72, Michael93555, Mìthrandir, MathFacts, HJ Mitchell, Louperibot, Magik3000, Charliezhao, Tkuvho, AstaBOTh15, Motorau, Lj822, I dream of horses, Martylex1, 10metreh, Comic freako, Supervincent, Tom.Reding, MJ94, Lithium cyanide, A8UDI, Moonraker, Meaghan, Smf77, Reconsider the static, Jauhienij, White Shadows, Zbayz, FoxBot, TobeBot, Fama Clamosa, Lotje, Vic verca, Extra999, 777sms, Ceharanka, Rattrap777, Jamietw, C.hevka, Stroppolo, Old Man of Storr, Lord of the Pit, Sideways713, Mon.verre, Growinglyons, RjwilmsiBot, SeanRoy612, Puzzlechef, Slon02, DASHBot, EmausBot, John of Reading, Acather96, Rasputin72, Chadthehitmankiller, Dominus Vobisdu, Smah142195, Dewritech, Eskimoman97, Syncategoremata, Western Pines, Vanished user zq46pw21, Tommy2010, Mmeijeri, Wikipelli, K6ka, Kkkdddiii, Solomonfromfinland, Italia2006, Kkm010, John Cline, PBS-AWB, LuzoGraal, Uoppppp, Annonnimus, Ebrambot, Can You Prove That You're Human, Kaka Mughal, Cymru.lass, Wayne Slam, Landyvin, Thine Antique Pen, Rcsprinter123, Pankrator, L Kensington, Flightx52, Donner60, Redactomètre, Puffin, Juanjosegreen2, FurrySings, DASHBotAV, Crbazevedo, WMC, Petrb, Xanchester, ClueBot NG, Chichi0071, Loosa 7, Michaelmas1957, Themaskof history, Matthiaspaul, MelbourneStar, Catlemur, Shinli256, Seancasey00, Frietjes, Escapepea, O.Koslowski, Widr, Alexio1000, Bunnies6947, Helpful Pixie Bot, Sceptic1954, Gob Lofa, Bibcode Bot, 13johnsonky, Lowercase sigmabot, Nate1234567, Carjoyg, BG19bot, Krenair, Roscoejinxx, 9p4gh9gkj, MusikAnimal, Musicasignifica, Dan653, Zauxst, Devin.chaloux, Ninney, Tennisrules55, Soerfm, Snow Blizzard, MrBill3, Ernio48, Glacialfox, Prmcd16, Wer900, Carliitaeliza, Samsawiki, Klawgor, Cyberbot II, Sonphan1, ChrisGualtieri, JYBot, Dexbot, Cwobeel, Lugia2453, Jamesx12345, Zziccardi, Lomicmenes, Cawhee, ElHef, DavidLeighEllis, Maxap28, NeapleBerlina, Jonahbalona, Nyancat69, Jonahbalona13, Ugog Nizdast, Glaisher, XRisional, Fatlizard17, NottNott, Peter12man, Jianhui67, OccultZone, Skulreaper117, JaconaFrere, HeyLookItsACow, Patient Zero, Themanwiththeknowledge, Vieque, Mrbeachguide, BethNaught, Vadaer, Waggie, Ephemeratta, TerryAlex, Sascha Grusche, MRD2014, Mal28, Picklejuice10, Brantiff1, Zppix, FourViolas, YeOldeGentleman, Imthebestyo, Pppppppbbbg, Rv04rmz, Tetra quark, Isambard Kingdom, Wafflesnack69100, GeneralizationsAreBad, Supdiop, Yaboyalwaysright, KasparBot, Camper345, Jwicklatz, 3 of Diamonds, Thetruth97thetruth97, Adam9007, JJMC89, Lance Skelly, BU Rob13, MB, John Lennon ate lot’s of food, CofKOx, Tylergymnast, Themaster322, Helmut von Moltke, Entranced98, Fuortu, Lilboy2002, Marianna251, Fitindia, Colonel Wilhelm Klink, STFD08,


33.10. EXTERNAL LINKS

381

Woodstop45, RunnyAmiga, Griffen Ray, Ghost Writer in the Eye, Yeah zz, Vensco, TOMATECHNOLOGY, Loonfi7, Nanxing2012, Mightyyoung3, Legsmomaster27 and Anonymous: 1429 • De revolutionibus orbium coelestium Source: https://en.wikipedia.org/wiki/De_revolutionibus_orbium_coelestium?oldid=741334775 Contributors: Ahoerstemeier, Djnjwd, Charles Matthews, EmphasisMine, Omegatron, Lumos3, Donarreiskoffer, Giftlite, Alan W, Fastfission, Jacob1207, Michael Devore, Matthead, Toytoy, Antandrus, Piotrus, Pmanderson, MakeRocketGoNow, Discospinster, Stbalbach, Joanjoc~enwiki, Alansohn, Nik42, Ricky81682, JoaoRicardo, Logologist, Kocio, Super-Magician, Sciurinæ, Angr, Mindmatrix, TigerShark, Camw, WadeSimMiser, Eilthireach, Jan van Male, Quiddity, FlaBot, Kvas, JYOuyang, RexNL, Intgr, Krun, TeaDrinker, King of Hearts, Jaraalbe, Volunteer Marek, Gwernol, Bambaiah, Sceptre, Hairy Dude, RussBot, NawlinWiki, Wiki alf, Schlafly, Mlouns, Molobo, Zwobot, Whobot, Appleseed, DVD R W, Finell, SmackBot, Unyoyega, C.Fred, Zaqarbal, HalfShadow, Commander Keane bot, JCSantos, Persian Poet Gal, SchfiftyThree, Neo-Jay, Colonies Chris, Darth Panda, Chlewbot, Leoboudv, Stevenmitchell, Iblardi, Grommel~enwiki, John, Rigadoun, Mathiasrex, Shlomke, Ckatz, Fernando S. Aldado~enwiki, Caiaffa, Iridescent, Yodin, Maestlin, Chris55, CmdrObot, Drinibot, Outriggr (2006-2009), AndrewHowse, Road Wizard, Reywas92, Bellerophon5685, Michael C Price, Gimmetrow, Saintrain, Thijs!bot, N5iln, Oliver202, Hmrox, Luna Santin, AstroLynx, Anatomatic, Nthep, TAnthony, Acroterion, VoABot II, KConWiki, Gun Powder Ma, MartinBot, Wowaconia, David J Wilson, R'n'B, J.delanoy, NewEnglandYankee, Heyitspeter, Juliancolton, Useight, Hugo999, VolkovBot, Black raven2525, Aesopos, Mahal11, JhsBot, Rjm at sleepers, Orestek, Seraphita~enwiki, Thony C., Newbyguesses, Nihil novi, BotMultichill, Gerakibot, Antonio Lopez, Pika ten10, Zharradan.angelfire, Techman224, Escape Orbit, Randy Kryn, ImageRemovalBot, Sfan00 IMG, ClueBot, Snigbrook, Plastikspork, Arakunem, Mild Bill Hiccup, Alexbot, John Nevard, Lartoven, Jawsdesai, NuclearWarfare, Cenarium, Al-Andalusi, Versus22, Qwfp, Johnuniq, SoxBot III, SilvonenBot, Good Olfactory, Addbot, BecauseWhy?, John Chamberlain, Quietmarc, Ppole, Oota~enwiki, Uuda, Mmnaw, Ssaalon, Bootyy, Daatass, Ttassr, Sseedaf, Tide rolls, Bfigura’s puppy, Bbggae, Zorrobot, Noumenon, Wweert, Bbisdo, Mmuusda, Randomness2, Ttasterul, Yobot, Senator Palpatine, Abasass, Houutata, Teammoto, Clubbota, Placcjata, Apptas, Bliduta, Wheenguta, Limttado, Plannatas, Drootopula, Vittsadaf, Givbataska, Toutafada, Portutusd, Wortafad, Givbatad, Heastada, Shogartu, Bludyta, ArthurBot, Drosdaf, Haidata, Namtiota, Lobtutu, Awyhuito, Loodotuyfa, Coutasji, Civjaty, Leabnm, Iamcvb, Bandgjl, Thijhgf, Drojuas, Maiatues, Nexeuitas, Leadusata, Teadegui, Spiretas, Haputdas, Necirsad, Linburats, Pordaguit, Plabogayu, Yeagykiol, Errpudaeqi, Suitawqs, Glafyjk, Voigfdsa, Unigfjkl, Platewq, Maygytr, Briwqio, Inferno, Lord of Penguins, Dayubcpd, Yeafvnl, Binky555, Eidjcb, ^A^.Alders, FrescoBot, Aristofane di bisanzio, Tom.Reding, MastiBot, Mukogodo, EmausBot, John of Reading, WikitanvirBot, GoingBatty, Solomonfromfinland, ZéroBot, John Cline, Unreal7, Xanchester, ClueBot NG, Jack Greenmaven, Kuguar03, MelbourneStar, Benjamin9832, Frietjes, Helpful Pixie Bot, Popcornduff, BG19bot, George Ponderevo, ProfessorBaylock, Mintydan, Ephemeratta, KasparBot, Fuortu, GreenC bot, PittSkib11, Bender the Bot and Anonymous: 99 • Kepler’s laws of planetary motion Source: https://en.wikipedia.org/wiki/Kepler’{}s_laws_of_planetary_motion?oldid=741512415 Contributors: AxelBoldt, WojPob, AstroNomer, Andre Engels, Ben-Zin~enwiki, Heron, Lir, Patrick, Michael Hardy, Alan Peakall, Bcrowell, Lquilter, Eric119, SebastianHelm, Stw, Looxix~enwiki, Pbn~enwiki, AugPi, BenKovitz, Andres, Pizza Puzzle, Seth ze, Charles Matthews, Stan Lioubomoudrov, Jitse Niesen, Timc, Roachmeister, Xaven, JorgeGG, Robbot, Hankwang, Fredrik, Zandperl, Jredmond, Gandalf61, MathMartin, Stewartadcock, Sverdrup, Rtfisher, Hadal, Jleedev, Ancheta Wis, Giftlite, Tnewell, Harp, Tom harrison, MSGJ, Herbee, Karn, Peruvianllama, Wwoods, Zellerin~enwiki, Doshell, Telso, Sreyan, SURIV, LucasVB, Antandrus, Beland, Anythingyouwant, Bosmon, Icairns, Urhixidur, Fg2, Oliver Jennrich, ELApro, D6, Perey, Archer3, Ocon, Bornintheguz, Johan Elisson, Rich Farmbrough, Guanabot, Cfailde, Vsmith, Mat cross, ArnoldReinhold, Aonaran, Sam Derbyshire, Dbachmann, Paul August, SpookyMulder, Bender235, ESkog, Wfisher, Kwamikagami, Hayabusa future, Shanes, Kernco, Bobo192, Harley peters, BillCook, Nhandler, Tms, Jumbuck, Alansohn, Riana, Calton, Emvee~enwiki, Jon Cates, Mikeo, H2g2bob, Gearspring, Dan100, Oleg Alexandrov, Woohookitty, DonPMitchell, StradivariusTV, Kzollman, Cleonis, Drostie, Pdn~enwiki, Frungi, Zzyzx11, Smartech~enwiki, RuM, Graham87, Lasunncty, BorgHunter, Jake Wartenberg, DrTall, Salix alba, Mike Peel, The wub, Drrngrvy, FlaBot, RexNL, David H Braun (1964), Physchim62, Imnotminkus, Chobot, Krishnavedala, DVdm, RashBold, Antiuser, YurikBot, Wavelength, Xihr, Zhatt, NawlinWiki, Bachrach44, Borbrav, ErkDemon, E2mb0t~enwiki, Syrthiss, Kkmurray, Cstaffa, Hirak 99, Modify, CharlesHBennett, Tevildo, GraemeL, Fram, Shyam, QmunkE, Argo Navis, Katieh5584, TLSuda, Sinan Taifour, GrinBot~enwiki, Bo Jacoby, Serendipodous, FyzixFighter, Mejor Los Indios, Sbyrnes321, Finell, Harthacnut, Attilios, SmackBot, Michaelliv, Ashill, Reedy, InverseHypercube, David Shear, Gregory j, Vilerage, W!B:, Munky2, Gilliam, Saros136, JCSantos, B00P, AndrewBuck, Metacomet, SEIBasaurus, Kungming2, Croquant, Jwillbur, Thisisbossi, SundarBot, Aldaron, Waprap, Korako, Wen D House, Radagast83, Decltype, Speedplane, Theodore7, KeithB, Bejnar, Wikiklaas, SashatoBot, Eliyak, Drieux, Kuru, J 1982, Cronholm144, Loodog, Gobonobo, Shlomke, Hemmingsen, Accurizer, Morshem, Chrisch, Mets501, Hu12, MystRivenExile, GDallimore, Octane, Courcelles, Eluchil404, Gunslinger of Gilead, Xod, CmdrObot, RedRollerskate, Imamathwiz, Equendil, Kribbeh, Icek~enwiki, WillowW, JFreeman, UrbenLegend, Richhoncho, Phi*n!x, Epbr123, Jplvnv, Lupogun, TonyTheTiger, Sry85, Martin Hogbin, Headbomb, Marek69, Iviney, Monkeyfett8, Diskid, Mentifisto, AntiVandalBot, Cyrilthemonkey, Orionus, JHFTC, QuiteUnusual, AstroLynx, Leftynm, AlphaAquilae, LaQuilla, Alphachimpbot, Sluzzelin, JAnDbot, MER-C, IanOsgood, Yill577, Acroterion, Magioladitis, VoABot II, Swpb, Fabricebaro, Vssun, BMF203, Youkai no unmei, MartinBot, Ricardogpn, David J Wilson, Schildwaechter, J.delanoy, Fatka, Maurice Carbonaro, Jerry, Katalaveno, Johnbod, McSly, Hut 6.5, Nwbeeson, Srrizvi, Heyitspeter, Superdrew515, Sscruggs, KylieTastic, STBotD, Ricefountian, Idioma-bot, 28bytes, Pleasantville, JohnBlackburne, Danbloch, Thurth, Barneca, IamCanadianEh, Astronomyphile, TXiKiBoT, Oshwah, Vipinhari, Hqb, Qxz, Waleffe, LeaveSleaves, Wassermann~enwiki, Q Science, Millancad, Andy Dingley, SieBot, Ceroklis, Gerakibot, Cwkmail, Flyer22 Reborn, Green6592, Hxhbot, Techman224, Schwabac, Anchor Link Bot, Zeyn1, Vreezkid, ClueBot, Ignacio Javier Igjav, Fyyer, The Thing That Should Not Be, CyrilThePig4, Polyamorph, Niceguyedc, Richerman, Agge1000, Djr32, Excirial, Simonmckenzie, Wumborti, GluonU, Brews ohare, PhySusie, Kentgen1, The Red, C628, Aitias, BunnyFlying, Johnuniq, GabrielVelasquez, XLinkBot, Forbes72, Terry0051, DCCougar, Gonfer, SilvonenBot, Mifter, Keeganmann, Addbot, Some jerk on the Internet, Jojhutton, Dgroseth, FDT, Proxima Centauri, Glane23, Sam lowry2002, Debresser, Favonian, TStein, HAHS 25, Bigzteve, Tide rolls, Charles Leedham-Green, Lightbot, Vasiľ, Luckas-bot, Fraggle81, Nradam, Stamcose, AnomieBOT, Ciphers, Jim1138, IRP, Prasenjit1988, Ulric1313, Materialscientist, Spirit469, RobertEves92, The High Fin Sperm Whale, Citation bot, Kotika98, ArthurBot, LilHelpa, Xqbot, Sionus, Cureden, TechBot, Grim23, NFD9001, Gap9551, NOrbeck, 11kravitzn, Omnipaedista, Frankie0607, Bloodstruck, Nedim Ardoğa, 78.26, Keldino, TASDELEN, Acannas, Dave3457, Max.Casasco, FrescoBot, AllCluesKey, Sławomir Biały, Craig Pemberton, Citation bot 1, Relke, DrilBot, I dream of horses, Tom.Reding, Lithium cyanide, BRUTE, Jaoswald, Mjs1991, ‫کاشف عقیل‬, Etincelles, Lotje, Vrenator, Yong, Duoduoduo, Reaper Eternal, Diannaa, Gegege13, Katovatzschyn, Jfmantis, RjwilmsiBot, WildBot, EmausBot, Schwartz paul, Super48paul, Laurifer, Dewritech, Syncategoremata, Tommy2010, Mmeijeri, Dcirovic, Slawekb, Solomonfromfinland, JSquish, Crua9, StringTheory11, Thisibelieve, Wayne Slam, Samoojas, Donner60, Zfeinst, Fanyavizuri, Teapeat, MFJoergen, Brycehughes, Xanchester, ClueBot NG, Wcherowi, Smeagol25, Delusion23, Braincricket, Widr, AlwaysUnite, Pjbussey, Helpful Pixie Bot, HMSSolent, Gob Lofa, Bibcode Bot, DBigXray, BG19bot, 1994bhaskar, MusikAnimal, Dan653, Mark Arsten, Ninney, Cstalg, HTML2011, BattyBot, The Illusive Man, ChrisGualtieri, Tree2q, Lizard03, Dexbot, Mogism, Lugia2453, Greatuser, 77Mike77, Pforpickaxe, Faizan, CsDix, Eyesnore, JakeWi, Blackroseent98, NeapleBerlina, Hansmuller, Bingston, Bartekltg, Iojknm9090, Crow, Monkbot, Phdaerospace, Pikunsia, Jburdettelinn, Rolbit, Sorryhadtodothis, Hirumeshi, Soulred205, Trackteur, Alaura151695, Coolman468764, 0xF8E8, Zppix,


382

CHAPTER 33. ORBITAL ECCENTRICITY

Llatosz, ImAwesomeSoDealWithIt, Shaelja, VexorAbVikipædia, Crito10, GeneralizationsAreBad, KasparBot, Peaceful mind ap, Niecethe, Srednuas Lenoroc, CAPTAIN RAJU, AnkanDas5, Kcastillo1234, Olivernicguerrero718, White Arabian Filly, Åntøinæ, CheCheDaWaff, Mylesgoins, Griffen Ray, Lasagna gravagne and Anonymous: 649 • Giordano Bruno Source: https://en.wikipedia.org/wiki/Giordano_Bruno?oldid=743340471 Contributors: AxelBoldt, Peter Winnberg, MichaelTinkler, Marj Tiefert, Lee Daniel Crocker, Eloquence, The Anome, Shsilver, XJaM, Gianfranco, Deb, Diatarn iv~enwiki, William Avery, Ben-Zin~enwiki, Panairjdde~enwiki, Graft, Leandrod, Kchishol1970, Michael Hardy, Paul Barlow, Llywrch, Jojo11, Kaczor~enwiki, Nixdorf, Kalki, Lquilter, Sannse, Iluvcapra, Ellywa, Librarian, Ronz, Snoyes, Den fjättrade ankan~enwiki, Kingturtle, Александър, Qed, Cimon Avaro, Med, ²¹², Genie, JASpencer, Charles Matthews, Ww, Anakolouthon, Dandrake, Doradus, WhisperToMe, Zoicon5, Tpbradbury, AnonMoos, Rbellin, Olathe, Wetman, Chl, Robbot, RedWolf, Donreed, Jmabel, Romanm, Babbage, Rursus, Geogre, Modeha, JackofOz, Guy Peters, Alan Liefting, Snobot, Albatross2147, Giftlite, JamesMLane, Matruman, Orangemike, Peruvianllama, Everyking, Curps, Bensaccount, Danohuiginn, Wildt~enwiki, Wmahan, Gadfium, Keith Edkins, Ruy Lopez, Quadell, Antandrus, DragonflySixtyseven, Necrothesp, Zfr, Neutrality, Nulzilla, Klemen Kocjancic, Trilobite, Mennonot, Mike Rosoft, PRiis, D6, Rfl, Wfaulk, DanielCD, Rich Farmbrough, Guanabot, Cnyborg, Carptrash, Stbalbach, Bender235, Mashford, Bobdoe, RJHall, Clement Cherlin, Worldtraveller, Haxwell, Bill Thayer, Billymac00, Dr. Isaac Land, Viriditas, SpeedyGonsales, Rajah, Haham hanuka, Pharos, Jonathunder, Espoo, Jumbuck, Hanuman Das, Alansohn, Jic, LtNOWIS, Ryanmcdaniel, SHIMONSHA, Dabbler, Uucp, Dirac1933, LordAmeth, Richard Arthur Norton (1958- ), Woohookitty, Mindmatrix, Dodiad, Jeff3000, Cbdorsett, Wikiklrsc, Arifhidayat, Ashmoo, Cuchullain, BD2412, Elvey, MarkHudson, Rjwilmsi, Angusmclellan, Nightscream, Koavf, Helvetius, BlueMoonlet, Mike s, Camdic, Olessi, FayssalF, FlaBot, NekoDaemon, M7bot, Chobot, DJProFusion, Jaraalbe, Chakira, Dj Capricorn, Whosasking, Mercury McKinnon, YurikBot, Jimp, Sputnikcccp, Longbow4u, Mathaxiom~enwiki, Pvasiliadis, Varenius, Jessnevins, NawlinWiki, Leutha, Badagnani, Howcheng, PhilipC, Mikeblas, Daizus, Nlu, Dna-webmaster, AdamFunk, Homagetocatalonia, Nikkimaria, PURRAKHS, Nolanus, JoanneB, Che829, Luk, MaeseLeon, Attilios, SmackBot, BAPhilp, Bayardo, DCDuring, Joe1788, Yuyudevil, Eaglizard, Eskimbot, Septegram, Ohnoitsjamie, Hmains, Chris the speller, SMP, MalafayaBot, Greatgavini, Chaoscrowley, Rickythesk8r, Courtenay Young, QuimGil, Egsan Bacon, Leinad-Z, Liontooth, AussieLegend, Vanished User 0001, AndySimpson, Stevenmitchell, King Vegita, Makemi, TedE, Dreadstar, Badgerpatrol, Clean Copy, Aji23, Maelnuneb, Kendrick7, Pkeets, Bejnar, Blahm, SashatoBot, Lambiam, CFLeon, Rklawton, Kipala, Bo99, CoolKoon, Msandi, A. Parrot, Grandpafootsoldier, Meco, Olivierd, Afkbot, Clarityfiend, Maestlin, Joseph Solis in Australia, Catherineyronwode, LadyofShalott, Ewulp, INkubusse, Davidgn, CmdrObot, Fatcat59, Amalas, Dycedarg, Gross1952, Rwflammang, Drinibot, Pseudo-Richard, NickW557, KingPenguin, Gregbard, AndrewHowse, Cydebot, Reywas92, Aristophanes68, Astrochemist, Flowerpotman, Arskoul, Amandajm, Doug Weller, Grant76, NMChico24, Robert.Allen, Mamalujo, Thijs!bot, Biruitorul, Marek69, Itsmejudith, Peter Gulutzan, Catsmoke, Michael A. White, Lajsikonik, Trencacloscas, Escarbot, Kromagg, Seaphoto, Smith2006, Nine9s, Tjmayerinsf, Manushand, JEH, Jordan Rothstein, Arx Fortis, Wahabijaz, Zgrillo2004, JAnDbot, Triviaa, Some thing, Kirrages, Rothorpe, Acroterion, Koren, Magioladitis, Connormah, WolfmanSF, Kikadue~enwiki, Tracker1312, Stolenrays, Disconformist, Tobogganoggin, Catgut, Horse Badorties, TheCormac, Alekjds, Boffob, Edward321, Jomom, Textorus, Patstuart, Mschiffler, R'n'B, Galootius, Marco47jp, Johnpacklambert, Lilac Soul, JStone, Maurice Carbonaro, Yonidebot, Stammer, LittleHow, NewEnglandYankee, 83d40m, Ljgua124, Anthonykelvinlloyd, Inwind, Idioma-bot, Punkerslut, Deor, VolkovBot, Westfalr3, Poldebol, Milenita~enwiki, TXiKiBoT, Moogle343, Tammienorrie, Someguy1221, Andreas Kaganov, Littlealien182, Don4of4, Pleroma, Eric9876, RadiantRay, Billinghurst, Cantiorix, Falcon8765, VanishedUserABC, MCTales, Alcmaeonid, Danielnapierski, HitokiriGaijin, EmxBot, Neminis, SieBot, TJRC, Nihil novi, Swliv, SE7, Typritc, AnthonyJSmith, JSpung, Vospitay, OKBot, Vojvodaen, Tesi1700, Dasmarinas71, Firefly322, Sphilbrick, Felixfelis, Kalidasa 777, Bee Cliff River Slob, ImageRemovalBot, Martarius, ClueBot, SummerWithMorons, IPAddressConflict, Snickeringshadow, Parkjunwung, Farras Octara, Piledhigheranddeeper, DragonBot, Excirial, Jumbolino, Sq178pv, TheRedPenOfDoom, BOTarate, Catalographer, Versus22, Zzadam, Editor2020, DumZiBoT, XLinkBot, RogDel, Valtyr, PK2, Richard-of-Earth, WikHead, Good Olfactory, Inchiquin, Picatrix, Addbot, Roentgenium111, Betterusername, Ashanda, Jim10701, Download, LaaknorBot, Standfest, Glane23, Alandeus, AnnaFrance, LinkFABot, Numbo3-bot, Lightbot, Mdechristi, Luckas-bot, Yobot, Fraggle81, Rachel Bridgeland, Hohenloh, Linket, Jimjilin, Mikhailovich, Againme, AnomieBOT, JackieBot, Materialscientist, Citation bot, QaBobAllah, ArthurBot, LilHelpa, Enok, Xqbot, Perec11, Gensanders, Jsmith1000, Logan6362, Omnipaedista, Auréola, ProfGiles, Green Cardamom, Edgars2007, Nicolas Perrault III, Artimaean, T of Locri, LucienBOT, MathFacts, Sebastiangarth, Machine Elf 1735, Louperibot, Flint1972, Marixist101, Pinethicket, Tom.Reding, Naturalistic, MastiBot, Tannermyoung, Peace and Passion, Davide41, FoxBot, TobeBot, Trappist the monk, Pollinosisss, Silent Billy, Fox Wilson, Bluefist, Tferrere, Daniel the Monk, Gspahr, EmausBot, John of Reading, Mzilikazi1939, WikitanvirBot, Parkywiki, Montgolfière, Faceless Enemy, Sindbad mughal, Brainsteinko, Babiesloverabies, WhisperTooMe, Theirapist, SteveJorbs, Outriggr, Jaysunjp, Dcirovic, Solomonfromfinland, Isumaeru88, Whodatsniper, Bahudhara, Al83tito, AurelianusCaesar, Akasseb, Sbmeirow, 11614soup, Cephascrispus, Jdillonf, Matkatamiba, Pandeist, ClueBot NG, WIERDGREENMAN, Alessandro.de.angelis, MelbourneStar, Quigontimba, Snotbot, Spinoziano, Episcophagus, Helpful Pixie Bot, Titodutta, Wbm1058, Bibcode Bot, Carjoyg, BG19bot, Juro2351, Latenighteditor, George Ponderevo, Ewigekrieg, MusikAnimal, Smcg8374, Frze, Darouet, Zusasa, ERJANIK, Supremeaim, MisterCSharp, MrBill3, HMman, RadicalRedRaccoon, BattyBot, Artieboyaa, Anthrophilos, Vanobamo, Jrodriguez2315, Ninmacer20, Ebdòmero, Dexbot, JPollock412, NaturaNaturans, Eztafette, VIAFbot, Con v66, Matthewrobertolson, Torsade de Pointes, FRCJJY888, Hillbillyholiday, MagistraMundi, Epicgenius, Lekoren, BreakfastJr, Frozenprakash, Julian Felsenburgh, Jodosma, Kranich22, Bobthepoop, Twilightstorm, Vasya.photographer, Rolf h nelson, Ouroborosian, Hansmuller, Alfredbabich, Kind Tennis Fan, Jed1103, OccultZone, Livioandronico2013, Robevans123, Hillbillyholiday81, Glovacki, Jim Carter, Silas Haslam, P.g.duffy, 400 Lux, Stacie Croquet, MitLaw, RileyFreckMoka, Knowledgebattle, Co9man, Tetra quark, Uhs anonymous, UlanbekMambetakunov, Roonyjwelch, KasparBot, Torowhynot, Postcocious, CAPTAIN RAJU, Dilidor, LVHynes, Kanjuzi, Stribes, Teecoot, S.R. Summerfield, Holdoffhunger, Stribe22, Jujutsuan and Anonymous: 342 • Copernican heliocentrism Source: https://en.wikipedia.org/wiki/Copernican_heliocentrism?oldid=743805166 Contributors: Jrauser, William M. Connolley, EmphasisMine, Postdlf, Academic Challenger, Humus sapiens, Jason Quinn, Matthead, Andycjp, Antandrus, OverlordQ, JimWae, Vsmith, ArnoldReinhold, Bender235, Bobo192, Alansohn, Btyner, Cuchullain, Jake Wartenberg, ChongDae, TeaDrinker, Volunteer Marek, Wavelength, Gaius Cornelius, Schlafly, Wiqi55, Snaxe920, James Hannam, Finell, SmackBot, Selfworm, C.Fred, Jagged 85, Gilliam, Hmains, JCSantos, SchfiftyThree, Colonies Chris, Novangelis, Clarityfiend, Courcelles, Myasuda, Xanthoptica, DumbBOT, Headbomb, Marek69, Seaphoto, AstroLynx, Dan D. Ric, Professor marginalia, Boffob, David J Wilson, J.delanoy, Uncle Dick, Oshwah, LeaveSleaves, Rjm at sleepers, Pleroma, Hrafn, ClueBot, The Thing That Should Not Be, SchreiberBike, Versus22, Johnuniq, HumphreyW, EENola, Sjappé, Crazysane, Tide rolls, Lightbot, Worm That Turned, AnomieBOT, Vittsadaf, Givbataska, Jim1138, Materialscientist, Heastada, Drosdaf, LilHelpa, Gsmgm, Coutasji, Capricorn42, FrescoBot, StephenWade, Tlhslobus, DocYako, Zbayz, Suffusion of Yellow, RjwilmsiBot, Bibletruthistruth, Super48paul, Syncategoremata, Rarevogel, K6ka, Solomonfromfinland, Knight1993, Thine Antique Pen, Wiggles007, Samoojas, Xanchester, ClueBot NG, Jack Greenmaven, Widr, Helpful Pixie Bot, KLBot2, Try1572, JZCL, Advlokanath, Rkaup, Acetotyce, EvergreenFir, JackBrad419, Millokill, Piledhighandeep, Isambard Kingdom, BradWinward15, Huritisho, Malmasi, Bender the Bot and Anonymous: 124 • Aristarchus of Samos Source: https://en.wikipedia.org/wiki/Aristarchus_of_Samos?oldid=740691714 Contributors: Eloquence, Mal-


33.10. EXTERNAL LINKS

383

colm Farmer, Ed Poor, Andre Engels, XJaM, Lir, Michael Hardy, Ellywa, Ugen64, Qed, Pizza Puzzle, Jm34harvey, Omegatron, Phoebe, Dimadick, Robbot, Adamahill, Goethean, Stewartadcock, Flauto Dolce, Hadal, Wikibot, Alan Liefting, Giftlite, Awolf002, Peruvianllama, Everyking, Curps, Jason Quinn, Jackol, DefLog~enwiki, Andycjp, Alexf, The Singing Badger, Pmanderson, TonyW, Robin klein, Adashiel, ELApro, Mike Rosoft, Discospinster, Rich Farmbrough, Guanabot, YUL89YYZ, Francis Davey, Bender235, Quietly, Brian0918, RJHall, Noren, Russ3Z, Toh, HasharBot~enwiki, Jumbuck, Alansohn, Marie Rowley, Kanodin, Deacon of Pndapetzim, Sciurinæ, Tobyc75, DavidK93, FeanorStar7, LOL, Merlinme, Daniel Case, Kzollman, Cbustapeck, Scm83x, Macaddct1984, SDC, BD2412, Keithpickering, Sjö, Rjwilmsi, Mike s, Maurog, MWAK, FlaBot, Gurch, TeaDrinker, Piniricc65, Idaltu, Jaraalbe, EamonnPKeane, YurikBot, StuffOfInterest, RussBot, Dantheox, ENeville, Aldux, Whobot, Curpsbot-unicodify, Ilmari Karonen, Airconswitch, Sardanaphalus, SmackBot, FocalPoint, Selfworm, Hftf, Radiz8, Jagged 85, Gilliam, Ian13, Miquonranger03, Can't sleep, clown will eat me, Sumahoy, Dart evader, Jgoulden, Selatos, Stevenmitchell, Khoikhoi, Aldaron, KRBN, Jan.Kamenicek, Captainbeefart, SashatoBot, Atkinson 291, F15 sanitizing eagle, The Man in Question, Tyrrell McAllister, Mr Stephen, Asyndeton, Hu12, Iridescent, JMK, Sjb72, DFurlani, Richard75, Kurtan~enwiki, Megannnn, Karenjc, Cydebot, Jgtl2, Jasperdoomen, Robert.Allen, Thijs!bot, Headbomb, SusanLesch, AntiVandalBot, Mal4mac, Nine9s, Dr. Submillimeter, JAnDbot, Kaobear, Raisin212k, Hoplites, Naughtyca, VoABot II, Tito-, Waacstats, David Eppstein, DerHexer, Gun Powder Ma, Geboy, Robheart, Questionc, Rettetast, David J Wilson, CommonsDelinker, J.delanoy, Skeptic2, Salih, Brooklyntj, E. James Brennan, Student7, DorganBot, Doctoroxenbriery, Useight, Idioma-bot, PeaceNT, VolkovBot, Macedonian, Tzetzes, Philip Trueman, TXiKiBoT, Rei-bot, Someguy1221, Sintaku, Therob91, Broadbot, Pleroma, Robert1947, Enviroboy, Ajrocke, PGWG, SieBot, Hertz1888, Fabullus, Gerakibot, Cwkmail, Yintan, Phil Bridger, Harry-, Alatari, Muhends, Athenean, ClueBot, Victor Chmara, Avenged Eightfold, Jgeortsis, Pomona17, Tasos Serbis, Harland1, Singinglemon~enwiki, DragonBot, Excirial, Alexbot, Erebus Morgaine, Estirabot, Thingg, Crowsnest, Little Mountain 5, WikiDao, Ridgididgi, Kbdankbot, Addbot, Roentgenium111, Some jerk on the Internet, CanadianLinuxUser, Proxima Centauri, LaaknorBot, CarsracBot, Ehrenkater, Tide rolls, Taketa, Davidmedlar, Ccaarft, Legobot, Luckasbot, Yobot, II MusLiM HyBRiD II, AnomieBOT, 1exec1, Piano non troppo, Surya31415, ArthurBot, Xqbot, Gap9551, Faramir333, GrouchoBot, Riotrocket8676, Omnipaedista, RibotBOT, GhalyBot, Erik9, FrescoBot, Pergamino, HJ Mitchell, Machine Elf 1735, DefaultsortBot, Tom.Reding, Calmer Waters, Tlhslobus, Oracleofottawa, Weedwhacker128, Reach Out to the Truth, RjwilmsiBot, TjBot, NerdyScienceDude, WikitanvirBot, Gfoley4, Syncategoremata, RA0808, RenamedUser01302013, Tommy2010, Dcirovic, Loinoflamb, AvicBot, Shuipzv3, Badger980, Wayne Slam, Arahana~enwiki, Peace is contagious, Samoojas, Chewings72, Albert Nestar, DASHBotAV, ClueBot NG, Widr, Md.altaf.rahman, Zakhalesh, Helpful Pixie Bot, Sceptic1954, HMSSolent, Carjoyg, BG19bot, Manzanomiddleschool, ElphiBot, Davidiad, Glevum, The Almightey Drill, WP Editor 2011, MrBill3, BattyBot, Khazar2, Welshwatch, Dexbot, Makecat-bot, VIAFbot, Jaidan2022, Telfordbuck, Me, Myself, and I are Here, Hillbillyholiday, Uwe Lück, JaconaFrere, Asdfghjkl124, Gaurd.vanforlife, PackFANN, Integralsignlesscause, Fofo101, KasparBot, Nihon, CAPTAIN RAJU, Chenhalls, Brachney, Kirk Leonard and Anonymous: 311 • Ellipse Source: https://en.wikipedia.org/wiki/Ellipse?oldid=742302151 Contributors: AxelBoldt, Brion VIBBER, Mav, Bryan Derksen, Zundark, Tarquin, Ap, Andre Engels, Matusz, FvdP, Lir, Patrick, Michael Hardy, Norm, Eric119, CliffTaylor, Angela, Ojs, Mihai~enwiki, AugPi, BenKovitz, Raven in Orbit, Pizza Puzzle, RodC, Charles Matthews, Timwi, Dino, Doradus, Hyacinth, Saltine, Sabbut, Indefatigable, Frazzydee, Sdedeo, Romanm, Wikibot, Guy Peters, Wile E. Heresiarch, Dina, Sushi~enwiki, Snobot, Tosha, Giftlite, Jyril, Gene Ward Smith, Harp, Herbee, Wwoods, Joconnor, Wikibob, Joe Kress, Leonard G., Guanaco, Yekrats, Jorge Stolfi, Ptk~enwiki, AlistairMcMillan, Pne, Geomon, CryptoDerk, LucasVB, Phe, Anythingyouwant, Maximaximax, Gauss, Pmanderson, NoPetrol, Neutrality, Urhixidur, Sonett72, Karl Dickman, ELApro, Oskar Sigvardsson, Perey, Rfl, Guanabot, Pie4all88, Ivan Bajlo, Jamadagni, Paul August, Bender235, Maaf, Zaslav, S.K., CanisRufus, El C, Gershwinrb, Rslippert, Army1987, La goutte de pluie, Kjkolb, Tgr, Haham hanuka, Pearle, Mdd, Tsirel, Jumbuck, Oxyclean333, Etxrge, Keenan Pepper, Sligocki, EvenT, Suruena, Egg, Oleg Alexandrov, Woohookitty, Linas, DonPMitchell, Hello5959us, StradivariusTV, Kristaga, Damicatz, Silverleaftree, Waldir, Graham87, BD2412, Qwertyus, Abstracte, Coneslayer, Rjwilmsi, Kinu, Viktor~enwiki, NeonMerlin, R.e.b., Mikm, MikeJ9919, EchoAlpha, Mathbot, Nivix, AJR, Revned, Fresheneesz, Gurubrahma, Imnotminkus, Md7t, Chobot, Krishnavedala, DVdm, Ahpook, YurikBot, Wavelength, TexasAndroid, Kafziel, NawlinWiki, Rick Norwood, DragonHawk, Astral, Nur Hamur~enwiki, Dhollm, Ospalh, Cheeser1, Bota47, Tachyon01, Arthur Rubin, Adilch, Reyk, MathsIsFun, Anclation~enwiki, Ethan Mitchell, Bo Jacoby, Cmglee, Veinor, Jsnx, SmackBot, RDBury, PaulWay, Incnis Mrsi, Unyoyega, Jagged 85, Kaimbridge, Elronxenu, Aksi great, KYN, Gilliam, Skizzik, Kurykh, RDBrown, Telempe, AndrewBuck, SchfiftyThree, Piper2000ca, Colonies Chris, Gwenstacy, Sct72, Scwlong, Tamfang, RProgrammer, RyanCu, Chcknwnm, SundarBot, Cybercobra, Dreadstar, Minipie8, Clean Copy, Wybot, Proinsias, Qmwne235, SashatoBot, Zchenyu, UberCryxic, JorisvS, Mgiganteus1, Jim.belk, Phancy Physicist, PseudoSudo, BillFlis, Hvn0413, Special-T, Jmgonzalez, Dicklyon, Markjdb, KJS77, Pjrm, Quaeler, Hetar, Iridescent, Newone, CapitalR, Torrazzo, Kenkleinman, Mjohnrussell, Dave Runger, Daniel5127, George100, Vaughan Pratt, Jackzhp, Crescentnebula, LotR, MarsRover, Myasuda, Badseed, Doctormatt, Captainm, Goldencako, Dr.enh, SteveMcCluskey, Cinderblock63, MishaThal, Mikuszefski, Cwtyler, Siawase, Nick Number, Escarbot, EdJogg, AntiVandalBot, Ben pcc, John.d.page, Thecarrotdude, Pichote, Spencer, Huttarl, JAnDbot, 0smartbomb, Olaf, MSBOT, Magioladitis, Ferritecore, Hullaballoo Wolfowitz, SineWave, Catgut, Bcherkas, David Eppstein, Docduke, JaGa, Philg88, BaubiPacific, RaitisMath, MartinBot, Agricolae, Anaxial, Gcranston, R'n'B, HEL, J.delanoy, RJBotting, SharkD, Salih, Katalaveno, Krishnachandranvn, Nwbeeson, Potatoswatter, Juliancolton, Eugeneus, Warlordwolf, Bcnof, Ross Fraser, Michael Angelkovich, VolkovBot, Onedognight, JohnBlackburne, Nousernamesleft, TXiKiBoT, Dajwilkinson, Abc135246, Pdx scooter, Rei-bot, Fangxujing, HarryAlffa, Young.malcolm, Don4of4, CanOfWorms, Postie77, Inductiveload, Deipnosopher, Kmhkmh, Auyloxuk, Synthebot, Enviroboy, AlleborgoBot, Logan, Jwhosken, Dvidby0, SieBot, Ceroklis, Jauerback, Revent, Oda Mari, Cffk, Texnic, Oxymoron83, Anchor Link Bot, Dhexus~enwiki, Sign Creator, AllHailZeppelin, RWSchwartz, Nic bor, Lindum, Athenean, DEMcAdams, MenoBot, ClueBot, Zeptomoon, Rfrancis1954, Mild Bill Hiccup, Polyamorph, Boing! said Zebedee, Niceguyedc, Thegeneralguy, Piledhigheranddeeper, FalkonG4, Dhoerl, Morana, Worth my salt, Lartoven, RussPorter, Stepheng3, J lemmuh, Onomou, Johnuniq, SoxBot III, Sandrobt, XLinkBot, DaL33T, WikHead, Addbot, Narayansg, Willking1979, Some jerk on the Internet, Tcncv, Fgnievinski, TutterMouse, Paul Yeratz, MrOllie, Download, Vega2, Ggmukul, AndersBot, TStein, Jasper Deng, Prim Ethics, Ehrenkater, Tide rolls, Lightbot, Wwannsda, Legobot, T-Rithy, Luckas-bot, Yobot, Timeroot, Roydude1, Godden46, Stamcose, AnomieBOT, Götz, 08glasgow08, Jim1138, Abshirdheere, Dubsed, Materialscientist, Pcantin, LilHelpa, V35b, Xqbot, DSisyphBot, Gilo1969, Tad Lincoln, Magnesium, The Evil IP address, Br77rino, Gap9551, NOrbeck, Nigelgspencer, Colfulus, Srinivas.zinka, Klknoles, TASDELEN, Dave3457, FrescoBot, Fortdj33, Ace of Spades, JL 09, Gouranga Gupta, Jc3s5h, X7q, Gueomme, Majopius, Weetoddid, Peterhil, Tetraedycal, Kwiki, Cannolis, MastiBot, Jomanted, Turian, Tjlafave, BlueEventHorizon, Reallyskeptic, Etincelles, Akshit Goyal, KarthikeyanKC, Aowdey, Extra999, Duoduoduo, Cherrry77up, RjwilmsiBot, Mikeyoumans, Elsieharpist, Wikilupos, Mactechy28, Immunize, Sadalsuud, Fly by Night, Syncategoremata, Slightsmile, Tommy2010, Dcirovic, ZéroBot, Josve05a, Ashishkhare663, Philtodd, Donner60, Tim Zukas, Ddrakulic, , Matthewrbowker, Kérek kerék kerek, Anita5192, Mikhail Ryazanov, ClueBot NG, Salequieter, Wcherowi, Matthiaspaul, Invitrovanitas, Acrazydiamond, FeelUs, Frietjes, Helpful Pixie Bot, PeterMinin, Khrodos, HMSSolent, BG19bot, Mezzon, Carlos olalla, CitationCleanerBot, Glevum, Msruzicka, Nfk953, Mathetudes, Brad7777, ‫יהודה שמחה ולדמן‬, Snapdragontulip, Pjh009, BattyBot, Thoughtful living, Esszet, PopePompus, AlexLowson, Dexbot, JeffAEdmonds, BScMScMD, Marvinthefish, Numbertruth, Cobalt174, Boazkaka, Ag2gaeh,


384

CHAPTER 33. ORBITAL ECCENTRICITY

Tentinator, LaurentianShield, Wamiq, Tigraan, Ginsuloft, George8211, Balljust, Elizabeth sunny, Anrnusna, Abitslow, Elephantsofearth, Trucksmonk24, Mr.khassi, LucaMoro, ASCarretero, JMP EAX, Loraof, JOE SUPPLE BRUNS, Millie erf, Jeevanpriyanka, Boobahhh12, De la Marck, Jrheller1, Gameplayer10, Npyee, PseudoScientist, Giochanturia and Anonymous: 548 • Elliptic orbit Source: https://en.wikipedia.org/wiki/Elliptic_orbit?oldid=740693437 Contributors: Bryan Derksen, Patrick, Cherkash, Robbot, Jyril, Wolfkeeper, Alison, Karol Langner, Tomruen, Rich Farmbrough, RJHall, 0.39, Aquillion, Hooperbloob, Simone, Zntrip, Woohookitty, LOL, MONGO, Viswaprabha, Rjwilmsi, Latka, Gaius Cornelius, Zhatt, Gbm, KnightRider~enwiki, SmackBot, Jagged 85, Autarch, Neo-Jay, Trekphiler, Tamfang, Salamurai, Harryboyles, J 1982, JForget, CmdrObot, CWY2190, Ecophreek, Alaibot, NHammen, RaNdOm26, Luna Santin, Swpb, Rustyfence, ExplicitImplicity, Stardust8297, Useight, Nattgew, HatFury, Aalox, PlanetStar, Athenean, ClueBot, Easphi, Jusdafax, Simon Villeneuve, Feyrauth, SilvonenBot, Addbot, Luckas-bot, Stamcose, Materialscientist, Citation bot, Xqbot, Invent2HelpAll, GrouchoBot, GliderMaven, Trewal, Duoduoduo, RjwilmsiBot, EmausBot, Syncategoremata, Ciripo, Mmeijeri, Hhhippo, ZéroBot, Bollyjeff, R. J. Mathar, Teapeat, ClueBot NG, Helpful Pixie Bot, Bibcode Bot, WikiHannibal, Ginsuloft, Stamptrader, Wickedwing, Foxfuries and Anonymous: 71 • Astronomia nova Source: https://en.wikipedia.org/wiki/Astronomia_nova?oldid=738007768 Contributors: Andres, MakeRocketGoNow, ELApro, Bender235, Stesmo, Sandius, Mu301, GregorB, Mike s, Chobot, Jaraalbe, Bambaiah, Conscious, Salsb, Ragesoss, Caerwine, Pegship, SmackBot, Chris the speller, Egsan Bacon, Ohconfucius, Will Beback, Korovioff, Maestlin, Alaibot, SteveMcCluskey, Headbomb, VoABot II, Gaussbach, FisherQueen, (jarbarf), STBotD, Hugo999, TXiKiBoT, Edybevk, Wassermann~enwiki, Rjm at sleepers, Cwkmail, Marvin Diode, Hxhbot, Le Pied-bot~enwiki, Westwind2, Dolphin51, Binksternet, John Nevard, Polly Hedra, SilvonenBot, Good Olfactory, Addbot, Luckas-bot, Yobot, AnomieBOT, Götz, ArthurBot, Xqbot, Ywaz, Druiffic, GrouchoBot, Omnipaedista, FrescoBot, Tom.Reding, Trappist the monk, EmausBot, Josve05a, H3llBot, Xanchester, Bribett618, Euty, Helpful Pixie Bot, Dantrom, Cyberbot II, Monkbot, KasparBot, GreenC bot and Anonymous: 29 • Aristotelian physics Source: https://en.wikipedia.org/wiki/Aristotelian_physics?oldid=734347771 Contributors: Ed Poor, Ewen, Edward, Fred Bauder, SebastianHelm, William M. Connolley, Timwi, EmphasisMine, Alan Liefting, Beland, Doops, DragonflySixtyseven, Discospinster, Bender235, Rgdboer, Art LaPella, Wareh, Giraffedata, Jeltz, Ahruman, Stemonitis, Woohookitty, BD2412, Rjwilmsi, Koavf, Bgwhite, Dialectric, Moe Epsilon, Syrthiss, Maunus, Sardanaphalus, SmackBot, TestPilot, J-beda, C.Fred, Neptunius, Jagged 85, EVula, Zvis~enwiki, Rigadoun, Fatworm, JHunterJ, Rinnenadtrosc, Iridescent, RekishiEJ, Chris55, ‫הסרפד‬, Headbomb, Colin MacLaurin, Yureieggtart, Giggy, JaGa, R'n'B, J.delanoy, Belovedfreak, DadaNeem, Layzner, Treisijs, Deor, Anonymous Dissident, Jungegift, The Mad Genius, SieBot, Likebox, Dabomb87, Mr. Granger, Ideal gas equation, J8079s, SuperHamster, Auntof6, MelonBot, Johnuniq, DumZiBoT, Jack Bauer00, JKeck, Addbot, LightSpectra, Juan During, Lightbot, Ccaarft, Rubinbot, Almabot, GrouchoBot, Patrizio18, Ibinthinkin, Machine Elf 1735, Tetraedycal, Citation bot 1, Haida19, Jean-François Clet, Angstorm, Thinking of England, DARTH SIDIOUS 2, Magmalex, RjwilmsiBot, Thomas Peardew, DASHBot, Syncategoremata, Thywob, Wayne Slam, Jacobisq, Donner60, JFB80, Doctorambient, ClueBot NG, Helpful Pixie Bot, Bibcode Bot, ‫أبو حمزة‬, BG19bot, WithSelet, BattyBot, David.moreno72, Gebars, ChrisGualtieri, Khazar2, Mmxiicybernaut, IndigoDeberry, Bieber74, 22merlin, Ioannes Piscator, Redzemp and Anonymous: 78 • Gravity Source: https://en.wikipedia.org/wiki/Gravity?oldid=743779597 Contributors: Bryan Derksen, Danny, Rmhermen, Caltrop, Heron, Montrealais, Stevertigo, Patrick, D, Michael Hardy, Ixfd64, TakuyaMurata, GTBacchus, Wintran, Snarfies, Ahoerstemeier, Mac, Dgaubin, William M. Connolley, Jeff Relf, TonyClarke, Smack, Ec5618, Tpbradbury, Phoebe, Fairandbalanced, BenRG, Pollinator, Lumos3, Jni, Northgrove, Donarreiskoffer, Robbot, Sander123, Jakohn, TimothyPilgrim, Academic Challenger, Caknuck, Bkell, Nerval, Aetheling, Ruakh, Dina, Alan Liefting, Cedars, Ancheta Wis, Giftlite, Mikez, Haeleth, Wolfkeeper, Inkling, Fropuff, Everyking, Frencheigh, Aechols, Bobblewik, Utcursch, Keith Edkins, Antandrus, Phe, Quarl, Elembis, Kiteinthewind, Jossi, Karol Langner, Lindberg G Williams Jr, Demiurge, Trevor MacInnis, Grstain, Mike Rosoft, &Delta, DanielCD, Shipmaster, JimJast, Discospinster, Zaheen, Supercoop, Vsmith, Smyth, Notinasnaid, Dbachmann, Bender235, Rubicon, Loren36, El C, Huntster, Kwamikagami, Aude, Diomidis Spinellis, RoyBoy, Nrbelex, Gershwinrb, Bobo192, Smalljim, Elipongo, WoKrKmFK3lwz8BKvaB94, Larryv, MPerel, Danski14, Alansohn, JYolkowski, Anthony Appleyard, Davetcoleman, Atlant, Maya Levy, Paleorthid, Andrew Gray, Cjthellama, Riana, Goldom, Mac Davis, Wdfarmer, Hdeasy, Snowolf, Mononoke~enwiki, BRW, Yuckfoo, RainbowOfLight, Jesvane, Bookandcoffee, Kazvorpal, Falcorian, Stephen, Feezo, Richard Arthur Norton (1958- ), OwenX, Linas, Camw, LOL, Benhocking, JFG, MONGO, Mpatel, Tabletop, GregorB, Eaolson, Isnow, Scm83x, SDC, Philbarker, TheAlphaWolf, Brownsteve, Radiant!, Dysepsion, Sin-man, Ashmoo, Chrispasquale, Chun-hian, Drbogdan, Rjwilmsi, Tangotango, Nichiran, Fel64, Kazrak, Ligulem, Ems57fcva, LjL, Boccobrock, Bhadani, MarnetteD, Matt Deres, Sango123, Syced, Yamamoto Ichiro, Fish and karate, JanSuchy, Magmafox, Titoxd, RobertG, Old Moonraker, Nihiltres, Nivix, RexNL, Gurch, Fresheneesz, Alphachimp, Tardis, Srleffler, King of Hearts, DVdm, Guliolopez, Hall Monitor, Bomb319, Gwernol, EamonnPKeane, Raelx, The Rambling Man, Wavelength, Drdisque, Sceptre, Hairy Dude, Jimp, Hillman, Brandmeister (old), Ohwilleke, Red Slash, Musicpvm, Anonymous editor, Loom91, Bhny, Pigman, Epolk, Philip Hazelden, DanMS, Scott5834, CambridgeBayWeather, Wimt, Ccmccm, NawlinWiki, Nowa, Wiki alf, Ytcracker, SigPig, SCZenz, Apokryltaros, Nick, Brandon, Katrina Graziano, Semperf, Aaron Schulz, Roy Brumback, Addps4cat, Jessemerriman, Rayc, Mgnbar, Dna-webmaster, Eurosong, Heeroyuy135, Enormousdude, 2over0, SFGiants, Chase me ladies, I'm the Cavalry, Lappado, Endomion, E Wing, Fmyhr, Smurrayinchester, Kevin, Geoffrey.landis, Anclation~enwiki, Emc2, Willtron, Kungfuadam, RG2, JDspeeder1, Bo Jacoby, Draicone, FyzixFighter, Mejor Los Indios, Sbyrnes321, DVD R W, Hide&Reason, That Guy, From That Show!, Shenhemu, Luk, TravisTX, Sardanaphalus, SmackBot, Ulterior19802005, Incnis Mrsi, Reedy, KnowledgeOfSelf, Hydrogen Iodide, NaiPiak, David Shear, Kilo-Lima, Jagged 85, Thunderboltz, Delldot, Hardyplants, Cessator, Syckls, BiT, Timotheus Canens, GraemeMcRae, HalfShadow, Typhoonchaser, Yamaguchi , Gilliam, Algont, Hmains, Ppntori, ERcheck, Andy M. Wang, Kmarinas86, Marc Kupper, The monkeyhate, Saros136, Bluebot, Cush, Keegan, Raymond arritt, Fplay, Silly rabbit, Lehkost, Complexica, Bbq332, Jeff5102, Sbharris, Hallenrm, CharonM72, Scwlong, Can't sleep, clown will eat me, Scott3, UNHchabo, MJCdetroit, Apostolos Margaritis, Lesnail, Cryocide, Rsm99833, Amazins490, Jmlk17, Cybercobra, Nakon, Steve Pucci, TedE, Red1~enwiki, Jiddisch~enwiki, Dreadstar, Dave-ros, Weregerbil, Cockneyite, Crd721, Bryanmcdonald, Jklin, DMacks, Wizardman, Where, LeoNomis, Risker, Sadi Carnot, Carlosp420, TTE, Yevgeny Kats, Will Beback, Jonpalmer, Lambiam, Nathanael Bar-Aur L., Bcasterline, Geoffrey Wickham, Rklawton, Djeneba, Sophia, Dsantesteban, Kuru, Thefro552, Titus III, Richard L. Peterson, John, Scientizzle, Stephane Yelle, DocRocks1, Jaganath, Thegathering, Skoobieschnax, JorisvS, LestatdeLioncourt, Coredesat, Accurizer, Minna Sora no Shita, Mgiganteus1, A5y, Nonsuch, Ridersbydelta, Mr. Lefty, AtD, Jess Mars, Ben Moore, JHunterJ, MarkSutton, Slakr, Special-T, Momolee, LuYiSi, Mr Stephen, Samaster1991, Spiel496, Buttle, Novangelis, PSUMark2006, Inquisitus, Dl2000, ShakingSpirit, Hgrobe, Ginkgo100, Vanished user, JMK, Craigboy, Lakers, Newone, MOBle, J Di, Sjb72, Matt Bernius, Igoldste, Taucetiman, Tofoo, Tawkerbot2, Lsskys, Chetvorno, George100, Kurtan~enwiki, Lahiru k, CalebNoble, SkyWalker, JForget, CmdrObot, Tanthalas39, Gholson, Porterjoh, Ale jrb, Scohoust, Aherunar, Galo1969X, Picaroon, Shakespeare87, User92361, Zureks, Basawala, Ruslik0, GHe, Dgw, OMGsplosion, ShelfSkewed, WHATaintNOcountryIeverHEARDofDOtheySPEAKenglishINwhat, MarsRover, Hi There, Groosh, Myasuda, Anthony Bradbury, Gregbard, Logicus, Cydebot, Steel, Travelbird, Red Director, Jon Stockton, A Softer Answer, Adolphus79, Nicesai, Rracecarr, Codingmasters, Ch0rx, Tawkerbot4, Alexnye, Christian75, M a s, DumbBOT, DarkLink, Interwiki gl, FastLizard4, Optimist on the run, Jimip, Waxigloo, SteveMcCluskey, Omicronpersei8,


33.10. EXTERNAL LINKS

385

Stoked, Gimmetrow, Sevenaces, Raoul NK, FrancoGG, Thijs!bot, Epbr123, DarlingFriend, Opabinia regalis, Pajz, Ishdarian, Jamesluster, Andyjsmith, 24fan24, Gamer007, ClosedEyesSeeing, Headbomb, John254, Bobblehead, Neil916, Pogogunner, Grayshi, EdJohnston, HistoryMaster 1, Zachary, The Hybrid, Nick Number, Lithpiperpilot, CarbonX, MichaelMaggs, Sam42, J.S.B.Anderson, Escarbot, Eleuther, Mentifisto, Hmrox, AntiVandalBot, Yonatan, Luna Santin, CodeWeasel, Themaxeditor, Prolog, Yay unto the Chicken, Dylan Lake, Gdo01, Myanw, Ioeth, JAnDbot, Leuko, Husond, Vorpal blade, Kaobear, ThomasO1989, Roman à clef, MER-C, Nevadacall, Andonic, Hut 8.5, 100110100, Acroterion, N shaji, Pablothegreat85, Magioladitis, Foobird107, Murgh, Bennybp, Bongwarrior, VoABot II, AuburnPilot, Xn4, Wikidudeman, Hendrixjoseph, Careless hx, Aerographer1981, Crazytonyi, 9holdss, ThomasThePolishMan, Bubba hotep, Mi6agent00g off, BatteryIncluded, Beetfarm Louie, Adrian J. Hunter, Alexei Kojenov, Kane1047, LorenzoB, Mollwollfumble, Scot.parker, Andykass, Talon Artaine, Chris G, DerHexer, MeEricYay, WLU, Seph Vellius, TheRanger, Patstuart, Seba5618, Oroso, NatureA16, FisherQueen, Hdt83, E.vondarkmoor, MartinBot, Sinfear, Shimwell, Flamingpanda, The Ubik, UnfriendlyFire, APT, Rettetast, Juansidious, Anaxial, Sm8900, David J Wilson, Mschel, R'n'B, GarrisonGreen, AlexiusHoratius, Pekaje, LittleOldMe old, PrestonH, J.delanoy, Filll, Trusilver, Tonmoy Chowdhury, Bloomingiris, 72Dino, MoogleEXE, Lhynard, Ginsengbomb, WarthogDemon, Willow123~enwiki, SubwayEater, Yeti Hunter, Hisagi, James Mead, M C Y 1008, Wandering Ghost, Redmotherfive, Rod57, Vertigo900, Mr Rookles, Samtheboy, Gurchzilla, Supuhstar, Pyrospirit, AntiSpamBot, GhostPirate, Belovedfreak, Raichu Trainer, Ohms law, Mitchell is hollywood, SJP, Policron, Touch Of Light, Pwnasaurusrex38, MKoltnow, Mufka, FJPB, Blckavnger, Cmichael, Mohrflies, Stoned Proffesor, Kenneth M Burke, Cosmictinker, RB972, Tiggerjay, U.S.A.U.S.A.U.S.A., Treisijs, Mike V, Redrocket, Gtg204y, MtyQuinn, Darkfrog24, Jxzj, Annax3, Smartman10, Ronbo76, Micmic28, Yecril, Missphysics, GoldenGolem, Xiahou, Lorax835, Steel1943, Washboard6, Sheliak, Funandtrvl, Gravityc, Tecsup, Black Kite, Chinneeb, Deor, VolkovBot, TreasuryTag, TJ Elliot Scott, Meaningful Username, Danwills, DSRH, Mtesm, Indubitably, Gseletko, Cullaloe, Veddan, Boaex, Dominics Fire, Heerojyuy, Philip Trueman, Childhoodsend, TXiKiBoT, Oshwah, GVIlleneuve27, Davecas0, Adamwang, BuickCenturyDriver, 99DBSIMLR, MeStevo, Lolerballer~enwiki, Brocq 18, Andrius.v, Z.E.R.O., Anonymous Dissident, Jonnymagic, Ask123, Trentc, MattCarterSurrealist, IPSOS, Sarthella, Seraphim, Fizzackerly, Wvogeler, The One Cause, Tallcreek, Markp93, Drappel, PDFbot, Freak104, Manticore55, Cremepuff222, Blackdragon 1002, Wiae, Vrsixfire, Liberal Classic, Witchzilla, Noel rebeira, Inductiveload, Gladiator2155, Sydweighz, Spiral5800, Larklight, RobertFritzius, Dirkbb, SQL, SallyBoseman, Frag1983, Synthebot, ChillDeity, Speria, Heroesrule17, Enviroboy, Hollop09, Sylent, Kaseman519, Ballsucker22, Sesshomaru, Brianga, Skins88, Chickyfuzz14, AlleborgoBot, GavinTing, Shaidar cuebiyar, Happyhacker101, FlyingLeopard2014, Steven Weston, D. Recorder, Kastrel, Al.Glitch, Xarr, The Random Editor, Mr. dick 008, SieBot, Tosun, Crunchedfor6, High2lowo, K. Annoyomous, Thong123456789, Work permit, Scarian, Invmog, Gerakibot, Mazza uk04, Mickeyd24, LealandA, Caltas, BreakfastTom, Beethoven314, Pieman123456789, RJaguar3, Triwbe, Rangutan, Chs³, Tubular bells83, The way, the truth, and the light, Garrett gagne, Keilana, Elliott Fontain, CaptainIraq, RadicalOne, Flyer22 Reborn, Tiptoety, CombatCraig, Bhahn0125, Oda Mari, Sunayanaa, Cffk, Cnormansen, Thin joe, M keshe, Jirachipokemon, Kcin213, Chives4life, Luskj, Oxymoron83, Faradayplank, Smilesfozwood, AngelOfSadness, Nuttycoconut, Edwardwittenstein, Zharradan.angelfire, John fromer, Lightmouse, AMCKen, Iain99, Techman224, Skateboards fly, Mr mimises, Blobbucket, BenoniBot~enwiki, Dillard421, Panicum, Fedosin, C'est moi, Hamiltondaniel, ShexRox, Dolphin51, M2Ys4U, Into The Fray, Canglesea, C0nanPayne, Albin&dani, Quinling, Muhends, Moony1000, Atif.t2, Tomasz Prochownik, ClueBot, Thejman123456789, Artichoker, PipepBot, The Thing That Should Not Be, JavaJesus, Mr.Pinklesworth, Meekywiki, Artist7337, Drmies, Firth m, Mild Bill Hiccup, Boing! said Zebedee, CounterVandalismBot, Kitty9992, VandalCruncher, Harland1, Otolemur crassicaudatus, Jackey0105, Andwor9, AikBkj, Another Matt, RogerEllman, Puchiko, Shocky95, Gakusha, DragonBot, Joshisamazing, Chris earl 89, Alexbot, Mccann tom, Icreaser, Robbie098, Sct5333, Shinkolobwe, Fsunka, Itel94, Ola Hansen, Ice Cold Beer, Aurora2698, Jotterbot, PhySusie, Glacialvortex, Razorflame, Handcannonbeast, Applejacks47, Chaosdruid, Thingg, Venera 7, Wnt, Myagooshki666, Deproduction, MasterOfHisOwnDomain, Jaykay0424, Ioannes93, TimothyRias, Misterbeal, InternetMeme, Mhamhamha, XLinkBot, Royboturso, Gwandoya, Crustillicus, BodhisattvaBot, Rror, Ance.cdas, Baconlover13, Ost316, Srossman07, Noctibus, JinJian, Truthnlove, Ttimespan, Airplaneman, Infonation101, EEng, Freestyle-69, Kbdankbot, Xerbaycom, Addbot, Nyw195, Willking1979, NateDres23, Bobocheese, Betterusername, Non-dropframe, Olli Niemitalo, Cre84u, TutterMouse, Presentabsent, Eedlee, Veraptor, WFPM, Ashanda, MrOllie, Lost on Belmont, FerrousTigrus, Ld100, Delaszk, Glass Sword, Maddox1, Jasper Deng, Harvardstudent, Kicka, Tide rolls, EugeneKantarovich, Cesiumfrog, Krano, WikiDreamer Bot, Hartz, Narutolovehinata5, Legobot, Drpickem, Luckas-bot, Yobot, Dov Henis, Senator Palpatine, II MusLiM HyBRiD II, JustWong, Becky Sayles, THEN WHO WAS PHONE?, AnakngAraw, Solo Zone, Azcolvin429, Atqueamemus, MacTire02, AnomieBOT, Cantanchorus, Jdiyef, Ahmediq152, Jt16733, Gatoradeparade, Kanwaraj, Piano non troppo, Chaosmaker39, Gsd65, LlywelynII, Rhlowe, Unicornlad, VCleemput, Kanat Abildinov, Typesships, Are you ready for IPv6?, Dje 8, Citation bot, Oddball.bfi, Nyrox395, Maxis ftw, Persistent76, Chase4813, ArthurBot, SnorlaxMonster, Gravityforce, ChococatR, Xqbot, TinucherianBot II, Wikidushyant, TechBot, Millahnna, Gap9551, Markell West, GrouchoBot, Celebration1981, Gsard, Amaury, Charvest, Doulos Christos, A. di M., Acannas, CES1596, Ninjainventor, LucienBOT, Paine Ellsworth, Tobby72, TedlyW, Lookang, Lipsquid, , Sławomir Biały, ArkianNWM, Allen Jesus, Parvons, Cannolis, Orion 8, Citation bot 1, Pinethicket, Tom.Reding, RedBot, IceBlade710, SpaceFlight89, Rohitphy, Jauhienij, RockSolidCosmo, FoxBot, TobeBot, Yunshui, Gafferuk, Comet Tuttle, Le Docteur, Schwede66, MitchLay, Oms22, Earthandmoon, Tbhotch, RobertMfromLI, Brambleclawx, Mean as custard, RjwilmsiBot, Androstachys, DASHBot, EmausBot, John of Reading, Mnkyman, Atwarwiththem, Qurq, Gfoley4, Kueller1, Dewritech, Baguettes, Syncategoremata, Jmencisom, Dcirovic, Sheeana, The Blade of the Northern Lights, Solomonfromfinland, JSquish, Ryan.vilbig, ZéroBot, Crua9, GoldRenet, Dffgd, Everard Proudfoot, Quondum, Wikfr, Confession0791, JosJuice, Ocaasi, Wtsbeynon, BrokenAnchorBot, Brandmeister, L Kensington, Zayzya, Donner60, Ally1604, Checkmark56, Fluctuating metric, RockMagnetist, Teapeat, Laned130, Rememberway, ClueBot NG, Nebulosus, CocuBot, PoqVaUSA, Jj1236, Ntrikha, Lilptrsn, Megalobingosaurus, MerlIwBot, Helpful Pixie Bot, BG19bot, Negativecharge, Furkhaocean, GKFX, Bryanpiczon, Ninney, Cadiomals, Mr.viktor.stepanov, RGloucester, BattyBot, Tutelary, David.moreno72, GravityForce, Padenton, Khazar2, JYBot, Davidlwinkler, LightandDark2000, Mogism, Rudrene, Reatlas, CsDix, Everymorning, Vanderoops, Yuan Jullian Morales, Gacman67, DavidLeighEllis, Prokaryotes, Jwratner1, My name is not dave, Mfb, Konveyor Belt, Mproncace, Mahusha, Monkbot, Opencooper, Filedelinkerbot, Gronk Oz, 3primetime3, WaryLouka, Oiyarbepsy, Stefania.deluca, Loraof, Danmcz, Ps20231131, Gladamas, Pishcal, Freedom2003, Tetra quark, James 123234, Inorout, Supdiop, KasparBot, MusikBot, The oracle 2015, Sweepy, Jeffryan123, ImperatorRomanorvm, Addycrisp, Sir Cumference, The golden colten, CAPTAIN RAJU, J.A.Witt (Tony), Hiimemilylol, Dan6233, Sunshine2night, H.dryad, Dr Peter Donald Rodgers, L3erdnik, Worldandhistory, Rekzy FFA, New Speech Killer, BIGMANFI17, Crazyguys123, Ahmadhammo2, Wikipedia-Translator, Bear-rings, Dat nuke tho, ApokryItaroes, Prashanthds, John David Best, FabulousFerd, Arbor Fici, Ozi67864, Todd Troll, Namaneinstein, Josh Everitt, Kayallwestfall, Coolkid63, Sonicsword, Turkeybutt JC, Iudshkjhc.ad, Blelealale, Geo2145379 and Anonymous: 1302 • Planet Source: https://en.wikipedia.org/wiki/Planet?oldid=744009911 Contributors: Brion VIBBER, Mav, Bryan Derksen, Zundark, The Anome, Tarquin, Stephen Gilbert, Jeronimo, -- April, Andre Engels, XJaM, Christian List, Enchanter, William Avery, Roadrunner, Mjb, Heron, Hephaestos, Rickyrab, Ram-Man, Lir, Nealmcb, Patrick, D, Michael Hardy, Alan Peakall, Chris-martin, DopefishJustin, Dominus, Liftarn, Ixfd64, Fruge~enwiki, Cyde, Sannse, Gbleem, Alfio, Looxix~enwiki, Ellywa, Ahoerstemeier, Kingturtle, Glenn, Marteau, JasCollins, Cimon Avaro, Jeandré du Toit, Evercat, Jonik, Denny, Hike395, Waffles~enwiki, Jengod, The Tom, Crusadeonilliteracy, Charles Matthews, Timwi, Nohat, Wikiborg, Doradus, Markhurd, Tpbradbury, Marshman, Dragons flight, Jeffrey Smith, Morwen, RayKiddy,


386

CHAPTER 33. ORBITAL ECCENTRICITY

Traroth, Nickshanks, Chrisjj, Jusjih, Jamesday, Northgrove, Phil Boswell, Donarreiskoffer, AlexPlank, Robbot, Juro, Fredrik, Zandperl, RedWolf, Jmabel, Altenmann, Lowellian, Cyvh, StefanPernar, Lsy098~enwiki, Sverdrup, Rursus, Hemanshu, Texture, Ktotam, Meelar, Joelwest, Caknuck, Bkell, Wereon, Borislav, Jimduck, Mushroom, Anthony, Jor, Invalid username 35117~enwiki, Xanzzibar, Cyrius, Filemon, Solver, Enochlau, StefanosKozanis~enwiki, Stirling Newberry, Matthew Stannard, Nephelin~enwiki, Centrx, Giftlite, Metapsyche, Mike mian, Gtrmp, DavidCary, Jyril, Isam, Elf, Wolfkeeper, Nunh-huh, Meursault2004, Mark Richards, Leflyman, Monedula, COMPATT, Curps, Michael Devore, Wikibob, Mperrin, Cantus, Mboverload, Horatio, Falcon Kirtaran, SWAdair, Pne, Bobblewik, John Abbe, Joseph Dwayne, Wmahan, Electrawn, Changep, Utcursch, Geni, Yath, Ran, Antandrus, The Singing Badger, Beland, Onco p53, Joeblakesley, FelineAvenger, Kaldari, Armaced, Richardsur, 1297, Kesac, Latitude0116, Tomruen, Satori, Icairns, DenisMoskowitz, KarlHenner, Histrion, Iantresman, Urhixidur, IcycleMort, Ojw, Robin klein, Nike, Trevor MacInnis, Bluemask, Mike Rosoft, Jwolfe, T2X, Citizensunshine, N328KF, Spiffy sperry, Stepp-Wulf, Ultratomio, RossPatterson, Discospinster, Rich Farmbrough, KneeLess, Inkypaws, Vsmith, Florian Blaschke, Ponder, Roodog2k, Dbachmann, MuDavid, Paul August, SpookyMulder, Bender235, Patton1138, Crevaner, NeilTarrant, Swid, Jnestorius, JoeSmack, Evice, Tompw, XelaG, RJHall, Ben Webber, El C, Ganesha, Bluap, Kwamikagami, QuartierLatin1968, Downhighest, Shanes, Remember, Art LaPella, Triona, Bookofjude, Spoon!, Pablo X, Causa sui, Bobo192, Smalljim, Viriditas, R. S. Shaw, Angie Y., Geoff.green, Julleras~enwiki, Chirag, Man vyi, Deryck Chan, Thewayforward, Haham hanuka, Pharos, Caeruleancentaur, Hagerman, Pearle, Supersexyspacemonkey, Edital, Jez, HasharBot~enwiki, Methegreat, Honeycake, Alansohn, Gary, Anthony Appleyard, LtNOWIS, Halsteadk, Hydriotaphia, The RedBurn, Plumbago, Andrew Gray, Person112, Riana, Titanium Dragon, Bootstoots, Wtmitchell, Mike Beidler, Suruena, Garzo, Evil Monkey, ElderKorean, Harej, Amorymeltzer, RainbowOfLight, Sciurinæ, IngeLyubov, Kaushik twin, Computerjoe, Itsmine, ReelExterminator, Feezo, Siafu, Noz92, WilliamKF, Zanaq, Angr, Firsfron, Jeffrey O. Gustafson, DavidK93, Bellhalla, Georgia guy, Mu301, Justinlebar, Awostrack, Thorpe, Uncle G, Benhocking, Kokoriko, Koolman2, Duncan.france, MONGO, Mpatel, Eleassar777, Tabletop, Kmg90, Albertindian2001, Huhsunqu, Aristotle Pagaltzis, Sengkang, Pgilman, JamesH, Frankie1969, Btyner, Alec Connors, Smartech~enwiki, Pfalstad, Mattd4u2nv, 0pera, Ashmoo, Graham87, Marskell, Chupon, Magister Mathematicae, Zeromaru, Chun-hian, Dwaipayanc, Pmj, Protargol, Josh Parris, Sjö, Drbogdan, Sjakkalle, Rjwilmsi, Mayumashu, Koavf, GamblinMonkey, Vary, Marasama, Josiah Rowe, Bruce1ee, Salix alba, Mike s, Oblivious, Ligulem, The wub, Bhadani, Remurmur, AySz88, Mordecai, Cassowary, Yamamoto Ichiro, Titoxd, FlaBot, Cbvt, RobertG, John Baez, Ilovetolearn, Nivix, Anurag Garg, Jeff02, RexNL, Gurch, Jay-W, Enon, Darlene4, TeaDrinker, Alphachimp, Diza, Consumed Crustacean, Argyrios Saccopoulos, Srleffler, Butros, King of Hearts, Jeffr, Chobot, DVdm, Antiuser, Bgwhite, Cactus.man, Digitalme, Bomb319, The Rambling Man, YurikBot, Wavelength, TexasAndroid, Bennity, Spacepotato, RobotE, Neitherday, Sceptre, Hairy Dude, Deeptrivia, Jimp, Apollosfire, RussBot, Pleonic, Conscious, SpuriousQ, TinusVL, Stephenb, Archelon, Gaius Cornelius, Yyy, Kimchi.sg, Wimt, Kasajian, Ugur Basak, Joelloughead, Jehoshaphat, Terra Green, NormalAsylum, NawlinWiki, Wiki alf, Mipadi, Pagrashtak, Grafen, NickBush24, Terfili, Lexicon, Nick, Robdurbar, Haoie, RL0919, Misza13, Dbfirs, Zirland, BOT-Superzerocool, MrBark, Sesshy, Bota47, T-rex, Caerwine, Martinwilke1980, Wknight94, Igiffin, Crisco 1492, Yisraelasper, FF2010, PrincessJO, Poppy, Serendipitous, Zzuuzz, PTSE, Nebuchadnezzar o'neill, Chesnok, Roderick Mallia, Ageekgal, Thnidu, Jeffw57, Fang Aili, E Wing, Reyk, CWenger, Armor Nick, QmunkE, Kevin, Geoffrey.landis, JLaTondre, Wbrameld, Nixer, Ybbor, Katieh5584, Kungfuadam, Junglecat, RG2, Iago Dali, Serendipodous, Cmglee, One, The Yeti, AndrewWTaylor, Phil 1970, Hal peridol, Deuar, Sardanaphalus, Veinor, Sintonak.X, 6SJ7, SmackBot, Nfitz, Debuskjt, Ashill, Byberg, David Kernow, Zazaban, Reedy, KnowledgeOfSelf, Pgk, Praetor alpha, Vald, Blue520, Jagged 85, AndreasJS, CMD Beaker, Jrockley, Salmonstrut, Canthusus, Flamarande, Edgar181, Alsandro, Srnec, Yamaguchi , Cuddlyopedia, Anarkisto, PeterSymonds, Gilliam, Ohnoitsjamie, Folajimi, Hmains, Jushi, Skizzik, Kinhull, Saros136, Equiprimordial, Thegn, I know about this, Ian13, Cchenoweth, Rick7425, Thumperward, MalafayaBot, SchfiftyThree, Stephen.frede, Deli nk, T.scrace, Farry, DHN-bot~enwiki, Raistuumum, Xeriandros, Emurphy42, Diyako, Mooncow, Dethme0w, Can't sleep, clown will eat me, JoeOnSunset, John Hyams, Scott3, Nick Levine, Tamfang, Writtenright, Chlewbot, Jennica, AlexHajnal, Avb, Surfermoon, EvelinaB, Rrburke, MDCollins, Computerman45, Whpq, GrahameS, SundarBot, Thefroman, COMPFUNK2, Aldaron, Wen D House, Hopquick, Bowlhover, Nakon, RJN, Dreadstar, Ermalai, Lpgeffen, LoveEncounterFlow, BullRangifer, Jan.Kamenicek, Kleuske, Das Baz, Cdlw93, Ck lostsword, Kukini, Martianlostinspace, SashatoBot, Nareek, JzG, SS2005, Kuru, John, Coricus, General Ization, Vgy7ujm, J 1982, Heimstern, Gobonobo, Trotterjt, Firewall, Shlomke, Enfolder, JorisvS, Robert Stevens, Jess Mars, Ckatz, Chrisch, RandomCritic, Reid1867, Loadmaster, Wikipete, Smith609, 81120906713, Booksworm, Beetstra, Noah Salzman, Eurocommuter, PRRfan, Don Alessandro, SandyGeorgia, Geologyguy, Ryulong, Languagegeek Chris, Risingpower, TPIRFanSteve, Citicat, Hogyn Lleol, Novangelis, Zapvet, Jose77, Mego'brien, TJ Spyke, Levineps, Vanished user, Seqsea, Alessandro57, Mikehelms, Joseph Solis in Australia, Rhillman, Scooter20, Shoeofdeath, Newone, NativeForeigner, Richard75, Aeons, Civil Engineer III, Courcelles, JustSayin, Eluchil404, Tawkerbot2, Daniel5127, Spiderboy12, Ghaly, Orangutan, SkyWalker, JForget, WCar1930, CRGreathouse, Postmodern Beatnik, CmdrObot, Irwangatot, Wafulz, Zarex, Bryan27, Tuvas, Picaroon, Ruslik0, GHe, Benwildeboer, MarsRover, Shandris, Bobnorwal, RagingR2, Elreymc, Fox6453, AndrewHowse, Grenno, Cydebot, The Matrix Prime, Derek Balsam, Terri G, Jammy simpson, SyntaxError55, Gogo Dodo, Travelbird, Odie5533, Martin Jensen, Tawkerbot4, Christian75, DumbBOT, Chrislk02, Paddles, Minamina, Arbitrary username, Brad101, SteveMcCluskey, FrancoGG, CieloEstrellado, Thijs!bot, Epbr123, Yesiammanu, Sowff, Mercury~enwiki, Aktornado, Qwyrxian, Holopoj, Thunder, Aster2, Bear475, HappyInGeneral, MoEgna, N5iln, Headbomb, Sobreira, Marek69, Bobblehead, Tellyaddict, Landon Curt Noll, Lars Lindberg Christensen, Joymmart, Davidhorman, Dfrg.msc, CharlotteWebb, BlytheG, Post Falls Man, X96lee15, Dawnseeker2000, RoboServien, AlefZet, Escarbot, Sidasta, AntiVandalBot, RobotG, Majorly, Luna Santin, Akradecki, Finktank3000, Odikuas, Opelio, QuiteUnusual, Gnixon, Jj137, Farosdaughter, Gdo01, Altamel, Myanw, CPitt76, The Dan, DOSGuy, Leuko, Husond, MER-C, Dsp13, Something14, Stephen Roth, Fetchcomms, QuantumEngineer, Conk 9, Awien, Hut 8.5, Greensburger, Rothorpe, Acroterion, Wildhartlivie, Magioladitis, WolfmanSF, Rooyintan, Murgh, Bongwarrior, VoABot II, AuburnPilot, Fusionmix, Mileage, Yandman, Xkcd, Poggymoose, The Enlightened, Hristodulo, Twsx, EvilFred, Squallypukkerdum, Indon, Atb129, Animum, PlanetCeres, Homo cosmosicus, Constcon, Baselbonsai, Dday76, BilCat, Allstarecho, Odros, Meadow Soprano Wheels!, Chivista~enwiki, Cpl Syx, Spellmaster, T'Seral, Danielbaumann~enwiki, Barrylius, Chris G, DerHexer, WhoMe?, Esanchez7587, Seansinc, Khalid Mahmood, Applrpn, Bloduck, TheRanger, Figures&Puck, Madonna Can, Kheider, Ozherb, Riccardobot, Hdt83, MartinBot, FlieGerFaUstMe262, PAK Man, Arjun01, Poeloq, ARCG, GrzegorzWu, Rettetast, Azalea pomp, CalendarWatcher, R'n'B, CommonsDelinker, AlexiusHoratius, Hairchrm, DBlomgren, Lilac Soul, Wiki Raja, LedgendGamer, Mausy5043, Tgeairn, J.delanoy, Pharaoh of the Wizards, Child of Albion, DrKay, Trusilver, Nickr95, Psycho Kirby, Uncle Dick, VAcharon, NerdyNSK, TomS TDotO, Ian.thomson, L337 kybldmstr, Tdadamemd, IdLoveOne, Ohfosho, Ncmvocalist, McSly, Planetfreak101, Cin.H, Elitehaxor7, Pyrospirit, Plasticup, Rwessel, Zerokitsune, Nikkitacroix, Poopluver666, Cue the Strings, Cometstyles, WJBscribe, Tocoolforschool107, Asteroidz R not planetz, Gtg204y, Useight, TheNewPhobia, Mehulxtreme, Idioma-bot, Redtigerxyz, Xnuala, Black Kite, Ironrooster, Deor, MWurtz, VolkovBot, Uyvsdi, Ndsg, Jeff G., Nessiehibs, Eggman1115, VasilievVV, Rsaxvc, Sumayyah94, DancingMan, Quentonamos, Philip Trueman, PGSONIC, TXiKiBoT, Oshwah, Nate111, GimmeBot, The absolute real deal, Orgads, Maximillion Pegasus, Vipinhari, Planetary Chaos, GDonato, Miranda, Nxavar, Mefityes, Qxz, Cosmium, Retiono Virginian, Anna Lincoln, MasterSci, Kay7110, Henrykus, Leafyplant, KarynN1, DoktorDec, Moonvapor, Cremepuff222, Cheetahgir22, ARUNKUMAR P.R, 1981willy, SQL, Falcon8765, Sai2020, Kruzer8421, WatermelonPotion, Why Not A Duck, Brianga, Gatorluver41792, Dinkiethebearkittie, Alle-


33.10. EXTERNAL LINKS

387

borgoBot, Wingman90, SoopahMan, Tvinh, Vsst, FlyingLeopard2014, HowardMorland, Demmy100, SieBot, Findingemodude77, Robo Toaster, Tosun, Zmanq, PlanetStar, Spartan, Suklaa, Articunobird55, Scarian, Tim101565, Jauerback, T Arndt 40, Dawn Bard, Ravensfire, Carapar999, Aristolaos, Keilana, Flyer22 Reborn, Tiptoety, Radon210, Mercuriophilus, The juggresurection, Ferret, Doestube, Teles.ME, Aruton, Oxymoron83, Thehotelambush, Dragn42, Jdaloner, Steven Crossin, Lightmouse, Flexijane, RSStockdale, Kaboooz, Ctxppc, MadmanBot, LonelyMarble, The Stickler, StaticGull, Cosmo0, Anchor Link Bot, Jacob.jose, Randomblue, Nergaal, Denisarona, Escape Orbit, Freewayguy, ImageRemovalBot, Steve, Athenean, Atif.t2, Martarius, Tanvir Ahmmed, ClueBot, PipepBot, Snigbrook, The Thing That Should Not Be, Kleptosquirrel, Wwheaton, Drmies, Firth m, Mild Bill Hiccup, CounterVandalismBot, Blanchardb, Harland1, Orthoepy, Neverquick, Thomas Kist, Fulmer7, Razorazar69, DragonBot, Copyeditor42, Stepshep, Drewm123, Excirial, Alexbot, Jusdafax, Birdym1, Namelessned, Tomeasy, Kanguole, PixelBot, Dichdiger, Enouhin, 5W’s&1H, Abrech, Atomic7732, Ally&marli, Technobadger, Patricius Augustus, Newslyman, LarryMorseDCOhio, Nvvchar, Pawco9, Foogus, Kakofonous, La Pianista, Matthew Desjardins, Another Believer, Jamesmorrey, Cold Phoenix, Thingg, Aitias, Burner0718, Toodle boop, HumphreyW, Wnt, Wkboonec, XLinkBot, Jimmythatdawg, Gwandoya, Darkaidreth, Lotoskaaay, RAWR BRI, Avoided, Chefzapp, Facts707, WikHead, PL290, Badgernet, Aurilios, ElMeBot, Dioxinfreak, Dark Gaia, Planetdood, Limsont, Nicolascabraljr, Addbot, Scubeesnax, Mr0t1633, Roentgenium111, Supstarr, Heartzmm, Tighe, Some jerk on the Internet, Caprenicus11, Manisero399, DOI bot, Mansuk95, Dancer2girl, Irock1126, Fieldday-sunday, GD 6041, Fluffernutter, Polemarchus, Cst17, Delaszk, Debresser, Favonian, ChenzwBot, LinkFA-Bot, 5 albert square, Numbo3-bot, Tide rolls, સતિષચંદ્ર, Zorrobot, Alpalfour, CountryBot, LuK3, Hartz, Swarm, Rrmsjp, Alfie66, Luckas-bot, Yobot, Adi, Azcolvin429, ‫محبوب عالم‬, MacTire02, AnomieBOT, Paulthomas2, Archon 2488, Jim1138, Applejoin2, Icalanise, AdjustShift, Emperornutz, Kingpin13, Darolew, ShannonRawks, Killers007, Flewis, Materialscientist, DoomsYourDay, The High Fin Sperm Whale, ArdWar, Citation bot, Soccerkid9627, ArthurBot, Quebec99, Redwodka, Xqbot, Timir2, Cureden, JimVC3, Mononomic, Gilo1969, Mlpearc, Gap9551, AbigailAbernathy, Almabot, Nasa-verve, Abce2, Bhostjuck, Ute in DC, ProtectionTaggingBot, Omnipaedista, RibotBOT, GreekAlexander, Basharh, N419BH, Adavis444, Shadowjams, PM800, S. 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Crapola, Grideon, TylerE09, Lilylover9, TyPup24, Gulumeemee, Samfinlay, Mohammed Adnan 321, Don atari, Cowcow25171, Qazxzaqazxzaq, Chickadee46 (alt), Kayleigh marshall, LeoWal1 and Anonymous: 1464 • Ecliptic Source: https://en.wikipedia.org/wiki/Ecliptic?oldid=732241868 Contributors: Magnus Manske, Zundark, The Anome, XJaM, Bignose, Lir, Pit~enwiki, Arpingstone, Looxix~enwiki, Raven in Orbit, Pizza Puzzle, The Tom, Lumos3, Robbot, Hankwang, Sverdrup, Wikibot, Ambarish, Enochlau, Giftlite, Javier Carro, Karol Langner, OwenBlacker, Icairns, B.d.mills, Mike Rosoft, Guanabot, Vsmith, Warpflyght, Byrial, DcoetzeeBot~enwiki, Bender235, RJHall, Sharkford, Summer Song, Haxwell, Art LaPella, 0.39, Dungodung, Timl, HasharBot~enwiki, Jumbuck, Apoc2400, Velella, RainbowOfLight, Woodstone, Martian, HenryLi, ReelExterminator, WilliamKF, Bacteria, Joriki, Dagg, Pi@k~enwiki, Pdn~enwiki, Alec Connors, Palica, Mekong Bluesman, Mana Excalibur, Mike s, FlaBot, Chobot, YurikBot, Deeptrivia, Conscious, Gillean666, Jworker, Dna-webmaster, BBFlatt, Nathan24601, GrinBot~enwiki, Cmglee, Fjeinca, SmackBot, Psiphiorg, Saros136, DHN-bot~enwiki, Danielcohn, OrphanBot, Clean Copy, Drphilharmonic, Adavidw, J 1982, Fev, JorisvS, Misteror, Osel, 16@r, A. Pichler, Tauʻolunga, Bill Michaelson, Drinibot, Ruslik0, Michaelbarreto, ShelfSkewed, Icek~enwiki, Cydebot, Wikipedia crusader, Thijs!bot, Mungomba, Cplot, Escarbot, Orionus, AstroLynx, Typochimp, Magioladitis, Edward321, Kheider, MartinBot, IdLoveOne, Mikael Häggström, Nwbeeson, STBotD, TXiKiBoT, Piperh, Dendodge, Leafyplant, Wassermann~enwiki, DAK4Blizzard, Insanity Incarnate, Alcmaeonid, SieBot, Silver Spoon, KING SHALMANESER II, Jdaloner, OKBot, Astrologist, Mesosphere, Beofluff, Twinsday, ClueBot, Pomona17, Arakunem, HenrikErlandsson, Polyamorph, Doyleb23, Lee merrill, AikBkj, Njardarlogar, JasonAQuest, Ankurtg, TimothyRias, Terry0051, Addbot, Mortense, Fgnievinski, Download, AndersBot, Summer3434, ScAvenger, QuadrivialMind, Legobot, Luckas-bot, Yobot, V35b, Xqbot, Br77rino, Banjaloupe, David.jaco, Trafford09, Pwrsc, MeDrewNotYou, FrescoBot, Coroboy, Jc3s5h, Craig Pemberton, Tom.Reding, RedBot, ‫عباد مجاهد ديرانية‬, TobeBot, DARTH SIDIOUS 2, Mean as custard, RjwilmsiBot, TjBot, EmausBot, WikitanvirBot, Teerickson, ZéroBot, S.fonsi, Tim Zukas, ClueBot NG, RegularJoe4, Episcophagus, Helpful Pixie Bot, Curb Chain, Bibcode Bot, Guy vandegrift, Vagobot, Ninney, Meatsgains, Filiosus’s Saga, GRighta, Tfr000, ChrisGualtieri, EnzaiBot, Paolopomponi, Dexbot, KWiki, 3142, Razibot, Sndeep81, Rfassbind, WPGA2345, Monkbot, Mario Castelán Castro, Huwnhxiewqbhuewx, Loraof,


388

CHAPTER 33. ORBITAL ECCENTRICITY

Yeezus3rd, Gallit69 and Anonymous: 103 • Orbital eccentricity Source: https://en.wikipedia.org/wiki/Orbital_eccentricity?oldid=739481988 Contributors: Atlan, Patrick, JakeVortex, Robbot, Smb1001, Jyril, Pgan002, ELApro, GregBenson, Syp, RJHall, El C, 0.39, Harley peters, Shenme, SpeedyGonsales, Neitram, Keenan Pepper, Ricky81682, Simone, Alec Connors, Smartech~enwiki, Palica, RuM, Rjwilmsi, Erkcan, Nihiltres, ScottAlanHill, Wormholio, RobotE, Hairy Dude, RussBot, Pigman, Rsrikanth05, Test-tools~enwiki, RazorICE, Beanyk, Caerwine, Bartsas~enwiki, Geoffrey.landis, Erik J, MaeseLeon, SmackBot, Tennekis, Kmarinas86, OrphanBot, A5b, Lambiam, J 1982, JorisvS, Ckatz, Douglas Spencer, Novangelis, W0lfie, Lvzon, King Hildebrand, Gogo Dodo, Sergei Schmalz, Thijs!bot, Konradek, AntiVandalBot, After Shock~enwiki, Tweesdad, JAnDbot, CosineKitty, WolfmanSF, Swpb, Ling.Nut, EstebanF, DerHexer, Kheider, ChrisfromHouston, Gurchzilla, Philip tao, Mustafa 03011, NatePhysics, Larryisgood, Technopat, Madhero88, Telecineguy, Spinningspark, SieBot, Portalian, I Like Cheeseburgers, Callipides~enwiki, Pfvlloyd, Dawn Bard, Driftwood87, Pinkadelica, Vinay Jha, ClueBot, Renacat, Mkjo, Excirial, BobKawanaka, Warren oO, DumZiBoT, Hyunrosa91, Addbot, Wælgæst wæfre, HerculeBot, Yobot, Amirobot, Stamcose, AnomieBOT, PianoDan, ArthurBot, MeDrewNotYou, Dougofborg, Dave3457, Almuhammedi, Tom.Reding, Just a guy from the KP, ‫عباد مجاهد ديرانية‬, FoxBot, Double sharp, Duoduoduo, Jfmantis, EmausBot, Padurar2009, Octaazacubane, JasonKnade, MrGachapon, ZéroBot, ChuispastonBot, Teapeat, Ebehn, Fjörgynn, ClueBot NG, CocuBot, Moneya, Helpful Pixie Bot, 26 Ramadan, HMSSolent, Snaevar-bot, Nimesh Mistry, Mogism, Jayy357, Lugia2453, Rfassbind, A guy saved by Jesus, 0xF8E8, Deepanshu1707, Cminkoff98 and Anonymous: 109 | • File:(253)_mathilde_crop.jpg Source: https://upload.wikimedia.org/wikipedia/commons/a/aa/%28253%29_mathilde_crop.jpg License: Public domain Contributors: http://nssdc.gsfc.nasa.gov/imgcat/html/object_page/nea_19970627_mos.html Original artist: NASA • File:046CupolaSPietro.jpg Source: https://upload.wikimedia.org/wikipedia/commons/5/5a/046CupolaSPietro.jpg License: CC BY-SA 3.0 Contributors: Own work Original artist: [//commons.wikimedia.org/w/index.php?title=User:MarkusMark&action=edit&redlink=1 MarkusMark] • File:14-236-LunarGrailMission-OceanusProcellarum-Rifts-Overall-20141001.jpg Source: https://upload.wikimedia.org/ wikipedia/commons/8/89/14-236-LunarGrailMission-OceanusProcellarum-Rifts-Overall-20141001.jpg License: Public domain Contributors: http://www.nasa.gov/sites/default/files/14-236_0.jpg Original artist: NASA/GSFC/JPL/Colorado School of Mines/MIT • File:14284-Moon-Maskelyne-LRO-20141012.jpg Source: https://upload.wikimedia.org/wikipedia/commons/c/c4/ 14284-Moon-Maskelyne-LRO-20141012.jpg License: Public domain Contributors: http://www.nasa.gov/sites/default/files/14-284_0.jpg Original artist: NASA/GSFC/Arizona State University • File:15-044a-SuperNovaRemnant-PlanetFormation-SOFIA-20150319.jpg Source: https://upload.wikimedia.org/wikipedia/ commons/1/19/15-044a-SuperNovaRemnant-PlanetFormation-SOFIA-20150319.jpg License: Public domain Contributors: http://www.nasa.gov/sites/default/files/thumbnails/image/15-044a.jpg Original artist: NASA/CXO/Herschel/VLA/Lau et al • File:15-044b-SuperNovaRemnant-PlanetFormation-SOFIA-20150319.jpg Source: https://upload.wikimedia.org/wikipedia/ commons/0/01/15-044b-SuperNovaRemnant-PlanetFormation-SOFIA-20150319.jpg License: Public domain Contributors: http://www.nasa.gov/sites/default/files/thumbnails/image/15-044b.jpg Original artist: NASA/CXO/Lau et al • File:1550_SACROBOSCO_Tractatus_de_Sphaera_-_(16)_Ex_Libris_rare_-_Mario_Taddei_.JPG Source: https: //upload.wikimedia.org/wikipedia/commons/9/9e/1550_SACROBOSCO_Tractatus_de_Sphaera_-_%2816%29_Ex_Libris_rare_ -_Mario_Taddei.JPG License: Public domain Contributors: Photo of 1550 SACROBOSCO “Tractatus de Sphaera” book, from Mario Taddei ancient books collection Original artist: Mauro Fiorentino, Theosebo, Phonasco, & Philopanareto. • File:171879main_LimbFlareJan12_lg.jpg Source: https://upload.wikimedia.org/wikipedia/commons/d/da/171879main_ LimbFlareJan12_lg.jpg License: Public domain Contributors: http://www.nasa.gov/mission_pages/solar-b/solar_017.html Original artist: Hinode JAXA/NASA • File:172197main_NASA_Flare_Gband_lg-withouttext.jpg Source: https://upload.wikimedia.org/wikipedia/commons/4/44/ 172197main_NASA_Flare_Gband_lg-withouttext.jpg License: Public domain Contributors: http://www.nasa.gov/mission_pages/solar-b/ solar_022.html Original artist: NASA / JAXA • File:2007_jpl_open_house.jpg Source: https://upload.wikimedia.org/wikipedia/commons/e/e1/2007_jpl_open_house.jpg License: Public domain Contributors: A FranksValli Photo Original artist: FranksValli • File:2009_Austria_25_Euro_Year_of_Astronomy_Front.jpg Source: https://upload.wikimedia.org/wikipedia/en/f/fe/2009_Austria_ 25_Euro_Year_of_Astronomy_Front.jpg License: Fair use Contributors: http://austrian-mint.at Original artist: ? • File:236084main_MilkyWay-full-annotated.jpg Source: https://upload.wikimedia.org/wikipedia/commons/8/89/ Public domain Contributors: http://www.spitzer.caltech.edu/images/ 236084main_MilkyWay-full-annotated.jpg License: 1925-ssc2008-10b-A-Roadmap-to-the-Milky-Way-Annotated- Original artist: NASA/JPL-Caltech/R. Hurt • File:243_Ida_large.jpg Source: https://upload.wikimedia.org/wikipedia/commons/9/9d/243_Ida_large.jpg License: Public domain Contributors: http://photojournal.jpl.nasa.gov/catalog/PIA00135 (subsequently cropped) Original artist: NASA/JPL • File:6_Warszawa_153.jpg Source: https://upload.wikimedia.org/wikipedia/commons/c/cf/6_Warszawa_153.jpg License: CC BY-SA 3.0 Contributors: http://www.poczta-polska.pl/mw Original artist: Marek & Ewa Wojciechowscy • File:AS12-52-7745.jpg Source: https://upload.wikimedia.org/wikipedia/commons/c/c3/AS12-52-7745.jpg License: Public domain Contributors: ? Original artist: ? • File:A_1960s_advert_for_working_at_NASA’{}s_Jet_Propulsion_Laboratories_(JPL).jpeg Source: https://upload.wikimedia.org/ wikipedia/commons/6/6c/A_1960s_advert_for_working_at_NASA%27s_Jet_Propulsion_Laboratories_%28JPL%29.jpeg License: CC BY 2.0 Contributors: http://www.flickr.com/photos/fdecomite/7906694440/in/photostream/ Original artist: fdecomite • File:A_Swarm_of_Ancient_Stars_-_GPN-2000-000930.jpg Source: https://upload.wikimedia.org/wikipedia/commons/6/6a/A_ Swarm_of_Ancient_Stars_-_GPN-2000-000930.jpg License: Public domain Contributors: Great Images in NASA Description Original artist: NASA, The Hubble Heritage Team, STScI, AURA • File:Actual_Sunrise.jpeg Source: https://upload.wikimedia.org/wikipedia/commons/e/e5/Actual_Sunrise.jpeg License: CC BY-SA 3.0 Contributors: Own work Original artist: Jessie Eastland


33.10. EXTERNAL LINKS

389

• File:Africa_and_Europe_from_a_Million_Miles_Away.png Source: https://upload.wikimedia.org/wikipedia/commons/0/0d/Africa_ and_Europe_from_a_Million_Miles_Away.png License: Public domain Contributors: NASA Original artist: NASA • File:Africa_and_Europe_from_a_Million_Miles_Away_(cropped).png Source: https://upload.wikimedia.org/wikipedia/commons/ 2/25/Africa_and_Europe_from_a_Million_Miles_Away_%28cropped%29.png License: Public domain Contributors: NASA Original artist: NASA • File:Ambox_important.svg Source: https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg License: Public domain Contributors: Own work, based off of Image:Ambox scales.svg Original artist: Dsmurat (talk · contribs) • File:Anatomy_of_a_Sunset-2.jpg Source: https://upload.wikimedia.org/wikipedia/commons/a/a4/Anatomy_of_a_Sunset-2.jpg License: CC BY-SA 3.0 Contributors: Own work Original artist: Jessie Eastland • File:Angular_Parameters_of_Elliptical_Orbit.png Source: https://upload.wikimedia.org/wikipedia/commons/1/1d/Angular_ Parameters_of_Elliptical_Orbit.png License: CC-BY-SA-3.0 Contributors: No machine-readable source provided. Own work assumed (based on copyright claims). Original artist: No machine-readable author provided. Peo~commonswiki assumed (based on copyright claims). • File:Apollo_15_feather_and_hammer_drop.ogg Source: https://upload.wikimedia.org/wikipedia/commons/3/3c/Apollo_15_feather_ and_hammer_drop.ogg License: Public domain Contributors: Taken from Spacecraftfilms.com DVD “Apollo 15: The Great Explorations Begin” Original artist: NASA • File:Apollo_17_twilight_ray_sketch.jpg Source: https://upload.wikimedia.org/wikipedia/commons/7/72/Apollo_17_twilight_ray_ sketch.jpg License: Public domain Contributors: http://science.nasa.gov/headlines/y2005/30mar_moonfountains.htm Original artist: Apollo 17 astronauts • File:Apparent_retrograde_motion.gif Source: https://upload.wikimedia.org/wikipedia/commons/e/ea/Apparent_retrograde_motion. gif License: CC BY-SA 2.5 Contributors: http://en.wikipedia.org/wiki/File:Apparent_retrograde_motion.gif Original artist: user:cleonis in the english wikipedia • File:Archimedes_Trammel.gif Source: https://upload.wikimedia.org/wikipedia/commons/e/ee/Archimedes_Trammel.gif License: CC BY-SA 3.0 Contributors: Own work Original artist: Alastair Rae • File:Aristarchus_working.jpg Source: https://upload.wikimedia.org/wikipedia/commons/2/2b/Aristarchus_working.jpg License: Public domain Contributors: ? Original artist: ? • File:Aristoteles_Louvre.jpg Source: https://upload.wikimedia.org/wikipedia/commons/a/a4/Aristoteles_Louvre.jpg License: CC BYSA 2.5 Contributors: Eric Gaba (User:Sting), July 2005. 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Bacon (STScI) • File:As11-40-5886,_uncropped.jpg Source: https://upload.wikimedia.org/wikipedia/commons/f/fb/As11-40-5886%2C_uncropped. jpg License: Public domain Contributors: ? Original artist: ? • File:Astronomia_Nova.jpg Source: https://upload.wikimedia.org/wikipedia/commons/6/62/Astronomia_Nova.jpg License: Public domain Contributors: http://www.library.usyd.edu.au/libraries/rare/modernity/kepler4.html Original artist: Johannes Kepler • File:Autograph-MikolajKopernik.svg Source: https://upload.wikimedia.org/wikipedia/commons/f/f1/Nicolaus_Copernicus_ Public domain Contributors: SVG conversion of signature_%28podpis_Miko%C5%82aja_Kopernika%29.svg License: File:Autograph-MikolajKopernik.png Original artist: Nicolaus Copernicus • File:AxialTiltObliquity.png Source: https://upload.wikimedia.org/wikipedia/commons/6/61/AxialTiltObliquity.png License: CC BY 3.0 Contributors: self-made by Dna-webmaster; earth-image from NASA Original artist: Dna-webmaster • File:Barbara_Müller_and_Johannes_Kepler.jpg Source: https://upload.wikimedia.org/wikipedia/commons/2/2a/Barbara_M%C3% BCller_and_Johannes_Kepler.jpg License: Public domain Contributors: ? Original artist: ? • File:Bartolomeu_Velho_1568.jpg Source: https://upload.wikimedia.org/wikipedia/commons/7/7b/Bartolomeu_Velho_1568.jpg License: Public domain Contributors: Own work Original artist: Bartolomeu Velho • File:Bertini_fresco_of_Galileo_Galilei_and_Doge_of_Venice.jpg Source: https://upload.wikimedia.org/wikipedia/commons/e/e7/ Bertini_fresco_of_Galileo_Galilei_and_Doge_of_Venice.jpg License: Public domain Contributors: Embedding web page: http://www.gabrielevanin.it/S.%20Marco%201609.htm Original artist: Giuseppe Bertini • File:Brahe_kepler.jpg Source: https://upload.wikimedia.org/wikipedia/commons/6/6c/Brahe_kepler.jpg License: Public domain Contributors: ? Original artist: ? • File:Brunostatue.jpg Source: https://upload.wikimedia.org/wikipedia/commons/c/cd/Brunostatue.jpg License: CC-BY-SA-3.0 Contributors: ? Original artist: ? • File:Buzz_salutes_the_U.S._Flag.jpg Source: https://upload.wikimedia.org/wikipedia/commons/d/dd/Buzz_salutes_the_U.S._Flag.jpg License: Public domain Contributors: Apollo 11 Image Library (image link) Original artist: NASA / Neil A. Armstrong • File:COTS2_Dragon_is_berthed.jpg Source: https://upload.wikimedia.org/wikipedia/commons/c/cf/COTS2_Dragon_is_berthed.jpg License: Public domain Contributors: http://spaceflight.nasa.gov/gallery/images/station/crew-31/html/iss031e070804.html Original artist: NASA • File:Cake_hubble.JPG Source: https://upload.wikimedia.org/wikipedia/commons/a/a6/Cake_hubble.JPG License: CC BY-SA 3.0 Contributors: Own work (Original text: I (RadioFan (talk)) created this work entirely by myself.) Original artist: RadioFan (talk)


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• File:Callisto.jpg Source: https://upload.wikimedia.org/wikipedia/commons/e/e9/Callisto.jpg License: Public domain Contributors: http: //photojournal.jpl.nasa.gov/catalog/PIA03456 Original artist: NASA/JPL/DLR(German Aerospace Center) • File:Callisto_(cropped)$-$1.jpg Source: https://upload.wikimedia.org/wikipedia/commons/1/11/Callisto_%28cropped%29-1.jpg License: Public domain Contributors: http://photojournal.jpl.nasa.gov/catalog/PIA03456 Original artist: NASA/JPL/DLR(German Aerospace Center) • File:Ceres_symbol.svg Source: https://upload.wikimedia.org/wikipedia/commons/c/ca/Ceres_symbol.svg License: Public domain Contributors: No machine-readable source provided. Own work assumed (based on copyright claims). Original artist: No machine-readable author provided. Lexicon assumed (based on copyright claims). • File:Charon_in_Color_(HQ).jpg Source: https://upload.wikimedia.org/wikipedia/commons/2/2b/Charon_in_Color_%28HQ%29.jpg License: Public domain Contributors: Image modified using Adobe Photoshop CS5 Original artist: NASA-JHUAPL-SWRI (colored using Adobe Photoshop CS5) • File:Claudius_Ptolemy-_The_World.jpg Source: https://upload.wikimedia.org/wikipedia/commons/f/f0/Claudius_Ptolemy-_The_ World.jpg License: Public domain Contributors: Decorative Maps by Roderick Barron - ISBN 1851702989 Original artist: Lord Nicolas the German (Donnus Nicholas Germanus), cartographer • File:Clear.png Source: https://upload.wikimedia.org/wikipedia/commons/6/62/Clear.png License: Public domain Contributors: Own work Original artist: Xession • File:Collegium_Maius_07.JPG Source: https://upload.wikimedia.org/wikipedia/commons/9/9b/Collegium_Maius_07.JPG License: CC-BY-SA-3.0 Contributors: Own work Original artist: Cancre • File:Color_Image_of_Ariel_as_seen_from_Voyager_2.jpg Source: https://upload.wikimedia.org/wikipedia/commons/0/0d/Color_ Image_of_Ariel_as_seen_from_Voyager_2.jpg License: Public domain Contributors: http://solarviews.com/raw/uranus/ariel.jpg Original artist: NASA/JPL (Digital with colortable: Calvin J. Hamilton) • File:Comet-Hale-Bopp-29-03-1997_hires_adj.jpg Source: https://upload.wikimedia.org/wikipedia/commons/d/df/ Comet-Hale-Bopp-29-03-1997_hires_adj.jpg License: CC BY-SA 2.0 at Contributors: http://salzgeber.at/astro/pics/9703293.html Original artist: Philipp Salzgeber • File:Commons-logo.svg Source: https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg License: CC-BY-SA-3.0 Contributors: ? Original artist: ? • File:Conicas1.PNG Source: https://upload.wikimedia.org/wikipedia/commons/1/12/Conicas1.PNG License: CC-BY-SA-3.0 Contributors: pt.wikipedia Original artist: Marcelo Reis • File:Copernic_Montreal_01.jpg Source: https://upload.wikimedia.org/wikipedia/commons/2/20/Copernic_Montreal_01.jpg License: CC BY-SA 3.0 Contributors: Own work Original artist: Jeangagnon • File:Copernican_heliocentrism_diagram-2.jpg Source: https://upload.wikimedia.org/wikipedia/commons/2/28/Copernican_ heliocentrism_diagram-2.jpg License: Public domain Contributors: • Copernican_heliocentrism_diagram.jpg Original artist: Copernican_heliocentrism_diagram.jpg: Own work from Copernicus 1543 • File:Copernican_heliocentrism_theory_diagram.svg Source: https://upload.wikimedia.org/wikipedia/commons/9/95/Copernican_ heliocentrism_theory_diagram.svg License: Public domain Contributors: [1] Original artist: Nicolai Copernici Created in vector format by Scewing

• File:Copernico_commemorative_plate.jpg Source: https://upload.wikimedia.org/wikipedia/en/3/36/Copernico_commemorative_ plate.jpg License: CC-BY-SA-3.0 Contributors: I (Daniele.tampieri (talk)) created this work entirely by myself. Original artist: Daniele.tampieri (talk) • File:Copernicus’{}s_heliocentric_model.jpg Source: https://upload.wikimedia.org/wikipedia/commons/6/68/Copernicus%27s_ heliocentric_model.jpg License: CC0 Contributors: available online Original artist: All images courtesy History of Science Collections, University of Oklahoma Libraries. • File:Copernicus-Boissard.gif Source: https://upload.wikimedia.org/wikipedia/commons/9/97/Copernicus-Boissard.gif License: Public domain Contributors: Uni Mannheim Mateo (Mannheimer Texte Online); Source [1]; Image:[2] Original artist: Theodor de Bry • File:Copernicus-an-Herzog-Albrecht.png Source: https://upload.wikimedia.org/wikipedia/commons/b/b2/ Copernicus-an-Herzog-Albrecht.png License: Public domain Contributors: http://www.archive.org/details/nicolauscoppern02prowgoog Original artist: Nicolaus Copernicus • File:Copernicus.jpg Source: https://upload.wikimedia.org/wikipedia/commons/2/28/Copernicus.jpg License: Public domain Contributors: Unknown Original artist: Unknown<a href='//www.wikidata.org/wiki/Q4233718' title='wikidata:Q4233718'><img alt='wikidata: Q4233718' src='https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/20px-Wikidata-logo.svg.png' width='20' height='11' srcset='https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/30px-Wikidata-logo. svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/40px-Wikidata-logo.svg.png 2x' data-file-width='1050' data-file-height='590' /></a> • File:CopernicusHouse.jpg Source: https://upload.wikimedia.org/wikipedia/commons/f/fb/CopernicusHouse.jpg License: CC BY-SA 2.5 Contributors: Own work Original artist: Stephen McCluskey • File:CopernicusStamp.jpg Source: https://upload.wikimedia.org/wikipedia/commons/f/fe/CopernicusStamp.jpg License: Public domain Contributors: Transferred from en.wikipedia to Commons by User:Stefan4 using CommonsHelper. Original artist: ? • File:Copernicus_Tower_in_Frombork.jpg Source: https://upload.wikimedia.org/wikipedia/commons/f/fa/Copernicus_Tower_in_ Frombork.jpg License: CC BY-SA 2.0 de Contributors: Transferred from de.wikipedia to Commons. Original artist: Hans Weingartz - http://www.hans-weingartz.de ; • File:Copernicus_Walhalla.jpg Source: https://upload.wikimedia.org/wikipedia/commons/6/6e/Copernicus_Walhalla.jpg License: CC BY-SA 3.0 Contributors: Own work Original artist: Matthead


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• File:Copernicus_central_peaks.png Source: https://upload.wikimedia.org/wikipedia/commons/7/70/Copernicus_central_peaks.png License: Public domain Contributors: http://lroc.sese.asu.edu/posts/629 Original artist: NASA (image by Lunar Reconnaissance Orbiter) • File:Crab_Nebula.jpg Source: https://upload.wikimedia.org/wikipedia/commons/0/00/Crab_Nebula.jpg License: Public domain Contributors: HubbleSite: gallery, release. Original artist: NASA, ESA, J. Hester and A. Loll (Arizona State University) • File:Cygnus_Orb-D1.8.jpg Source: https://upload.wikimedia.org/wikipedia/commons/5/5b/Cygnus_Orb-D1.8.jpg License: Public domain Contributors: http://www.flickr.com/photos/nasa2explore/10331195786/ Original artist: NASA • File:De_Revolutionibus_manuscript_p9b.jpg Source: https://upload.wikimedia.org/wikipedia/commons/e/e8/De_Revolutionibus_ manuscript_p9b.jpg License: Public domain Contributors: www.bj.uj.edu.pl Original artist: Nicolas Copernicus • File:De_revolutionibus_1617_Astronomia_instaurata.png Source: https://upload.wikimedia.org/wikipedia/commons/f/f4/ De_revolutionibus_1617_Astronomia_instaurata.png License: Public domain Contributors: http://books.google.com/books?id= GxEOAAAAQAAJ&printsec=frontcover#PPA13,M1 Original artist: Nicolaus Copernicus • File:De_revolutionibus_orbium_coeleftium.jpg Source: https://upload.wikimedia.org/wikipedia/en/1/10/De_revolutionibus_orbium_ coeleftium.jpg License: PD Contributors: ? 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Original artist: Daniele.tampieri (talk) • File:Doppelsonne_Halo_Echzell_Hessen_12-08-2012.jpg Source: https://upload.wikimedia.org/wikipedia/commons/f/f7/ Doppelsonne_Halo_Echzell_Hessen_12-08-2012.jpg License: CC BY-SA 3.0 Contributors: Own work Original artist: Neptuul • File:Drawing_an_ellipse_via_two_tacks_a_loop_and_a_pen.jpg Source: https://upload.wikimedia.org/wikipedia/commons/2/22/ Drawing_an_ellipse_via_two_tacks_a_loop_and_a_pen.jpg License: CC BY-SA 3.0 Contributors: Own work (Original text: I created this work entirely by myself.) Original artist: Dino at English Wikipedia • File:Dscovrepicmoontransitfull.gif Source: https://upload.wikimedia.org/wikipedia/commons/5/50/ Dscovrepicmoontransitfull.gif License: Public domain Contributors: http://www.nasa.gov/feature/goddard/ from-a-million-miles-away-nasa-camera-shows-moon-crossing-face-of-earth (image link) Original artist: NASA/EPIC • File:E_pur_si_muove.jpg Source: https://upload.wikimedia.org/wikipedia/commons/0/06/E_pur_si_muove.jpg License: Public domain Contributors: Scan by uploader of plate XVI in Memorials of Galileo (1564–1642), the Courier Press (London), 1929, by J.J. 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Colvin • File:Earth-Moon.PNG Source: https://upload.wikimedia.org/wikipedia/commons/4/43/Earth-Moon.PNG License: Public domain Contributors: NASA http://visibleearth.nasa.gov/ Original artist: Earth-image from NASA; arrangement by brews_ohare • File:Earth-moon.jpg Source: https://upload.wikimedia.org/wikipedia/commons/5/5c/Earth-moon.jpg License: Public domain Contributors: NASA [1] Original artist: Apollo 8 crewmember Bill Anders • File:Earth_symbol.svg Source: https://upload.wikimedia.org/wikipedia/commons/e/e7/Earth_symbol.svg License: Public domain Contributors: Unicode (U+2295:⊕ U+2641:♁ U+2A01:⨁ U+2D32: ) Original artist: OsgoodeLawyer • File:Earths_orbit_and_ecliptic.PNG Source: https://upload.wikimedia.org/wikipedia/commons/b/bd/Earths_orbit_and_ecliptic.PNG License: CC BY-SA 3.0 Contributors: Own work Original artist: Tfr000 (<a href='//commons.wikimedia.org/wiki/User_talk:Tfr000' title='User talk:Tfr000'>talk</a>) 01:59, 15 March 2012 (UTC) • File:Eccentricity_rocky_planets.jpg Source: https://upload.wikimedia.org/wikipedia/commons/9/98/Eccentricity_rocky_planets.jpg License: GPL Contributors: Data generated with Gravity Simulator written by Tony Dunn. Source JPG on server Original artist: frankuitaalst from the Gravity Simulator message board. • File:Ecliptic_inclination_dziobek.PNG Source: https://upload.wikimedia.org/wikipedia/commons/a/af/Ecliptic_inclination_dziobek. PNG License: CC BY-SA 3.0 Contributors: Own work Original artist: Tfr000 (<a href='//commons.wikimedia.org/wiki/User_talk:Tfr000' title='User talk:Tfr000'>talk</a>) 14:41, 22 March 2012 (UTC) • File:Ecliptic_plane_3d_view.gif Source: https://upload.wikimedia.org/wikipedia/commons/0/0d/Ecliptic_plane_3d_view.gif License: CC BY-SA 3.0 Contributors: Own work Original artist: Lookang many thanks to author of original simulation = Todd K. Timberlake author of Easy Java Simulation = Francisco Esquembre • File:Ecliptic_plane_side_view.gif Source: https://upload.wikimedia.org/wikipedia/commons/c/c1/Ecliptic_plane_side_view.gif License: CC BY-SA 3.0 Contributors: Own work Original artist: Lookang many thanks to author of original simulation = Todd K. Timberlake author of Easy Java Simulation = Francisco Esquembre • File:Ecliptic_plane_top_view.gif Source: https://upload.wikimedia.org/wikipedia/commons/4/44/Ecliptic_plane_top_view.gif License: CC BY-SA 3.0 Contributors: Own work Original artist: Lookang many thanks to author of original simulation = Todd K. Timberlake author of Easy Java Simulation = Francisco Esquembre • File:Ecliptic_vs_equator_small.gif Source: https://upload.wikimedia.org/wikipedia/commons/a/a3/Ecliptic_vs_equator_small.gif License: CC BY-SA 3.0 Contributors: Own work Original artist: Tfr000 (<a href='//commons.wikimedia.org/wiki/User_talk:Tfr000' title='User talk:Tfr000'>talk</a>) 15:06, 13 April 2012 (UTC)


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• File:Ecliptic_with_earth_and_sun_animation.gif Source: https://upload.wikimedia.org/wikipedia/commons/8/8c/Ecliptic_ with_earth_and_sun_animation.gif License: CC BY-SA 3.0 Contributors: Own work Original artist: Tfr000 (<a href='//commons.wikimedia.org/wiki/User_talk:Tfr000' title='User talk:Tfr000'>talk</a>) 16:54, 15 March 2012 (UTC) • File:Ed_White_performs_first_U.S._spacewalk_-_GPN-2006-000025.jpg Source: https://upload.wikimedia.org/wikipedia/ commons/f/fb/Ed_White_performs_first_U.S._spacewalk_-_GPN-2006-000025.jpg License: Public domain Contributors: Great Images in NASA Description Original artist: NASA • File:Edit-clear.svg Source: https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg License: Public domain Contributors: The Tango! Desktop Project. Original artist: The people from the Tango! project. And according to the meta-data in the file, specifically: “Andreas Nilsson, and Jakub Steiner (although minimally).” • File:EffectiveTemperature_300dpi_e.png Source: https://upload.wikimedia.org/wikipedia/commons/0/0d/EffectiveTemperature_ 300dpi_e.png License: CC-BY-SA-3.0 Contributors: Drawn by myself. The solar spectrum is the WRC spectrum provided by M. Iqbal: An Introduction to Solar Radiation, Academic Press 1983, Table C1. The black body spectral irradiance has been computed from a black-body spectrum for T equal 5777 K and assuming a solid angle of 6.8e-5 steradian for the source (the solar disk). Original artist: Sch • File:EightTNOs.png Source: https://upload.wikimedia.org/wikipedia/commons/9/91/EightTNOs.png License: CC-BY-SA-3.0 Contributors: Based on the public domain Nasa images: Image:2006-16-d-print.jpg, Image:Orcus art.png. Original artist: Lexicon • File:Ellipse_Animation_Small.gif Source: https://upload.wikimedia.org/wikipedia/commons/2/2e/Ellipse_Animation_Small.gif License: CC-BY-SA-3.0 Contributors: ? Original artist: ? • File:Ellipse_Polar.svg Source: https://upload.wikimedia.org/wikipedia/commons/e/ef/Ellipse_Polar.svg License: Public domain Contributors: Own work Original artist: Inductiveload • File:Ellipse_Polar_center.svg Source: https://upload.wikimedia.org/wikipedia/commons/8/82/Ellipse_Polar_center.svg License: Public domain Contributors: This file was derived from: Ellipse Polar.svg Original artist: User:Srinivas.zinka • File:Ellipse_Properties_of_Directrix.svg Source: Directrix.svg License: Public domain Contributors:

https://upload.wikimedia.org/wikipedia/commons/6/62/Ellipse_Properties_of_

• Ellipse_Properties.svg Original artist: Ellipse_Properties.svg: Inductiveload • File:Ellipse_Properties_of_Directrix_and_String_Construction.svg Source: https://upload.wikimedia.org/wikipedia/commons/6/ 65/Ellipse_Properties_of_Directrix_and_String_Construction.svg License: Public Domain Contributors: • Ellipse_Properties.svg Original artist: Ellipse_Properties.svg: Inductiveload • File:Ellipse_Reflection.ogg Source: https://upload.wikimedia.org/wikipedia/commons/d/de/Ellipse_Reflection.ogg License: CC BY-SA 4.0 Contributors: Own work Original artist: George Chanturia • File:Ellipse_as_hypotrochoid.gif Source: https://upload.wikimedia.org/wikipedia/commons/5/5c/Ellipse_as_hypotrochoid.gif License: CC-BY-SA-3.0 Contributors: Wikipedia Ingles Original artist: Dino • File:Ellipse_construction_-_parallelogram_method.gif Source: https://upload.wikimedia.org/wikipedia/commons/6/6a/Ellipse_ construction_-_parallelogram_method.gif License: CC BY-SA 3.0 Contributors: Own work Original artist: Cmapm • File:Ellipse_latus_rectum.svg Source: https://upload.wikimedia.org/wikipedia/commons/4/47/Ellipse_latus_rectum.svg License: Public domain Contributors: Own work Original artist: Krishnavedala • File:Elliptic_orbit.gif Source: https://upload.wikimedia.org/wikipedia/commons/9/94/Elliptic_orbit.gif License: CC-BY-SA-3.0 Contributors: Own work. Rendered with PovRay-3.0, animated with gifsicle. Original artist: Brandir • File:Elps-slr.svg Source: https://upload.wikimedia.org/wikipedia/commons/3/35/Elps-slr.svg License: Public domain Contributors: Transferred from en.wikipedia to Commons. Original artist: Mikm at English Wikipedia • File:En-NASA.ogg Source: https://upload.wikimedia.org/wikipedia/commons/e/e0/En-NASA.ogg License: CC-BY-SA-3.0 Contributors: • Derivative of NASA Original artist: Speaker: [[User:En:User:Coolcat|En:User:Coolcat]] Authors of the article • File:Euler_diagram_of_solar_system_bodies.svg Source: https://upload.wikimedia.org/wikipedia/commons/f/fc/Euler_diagram_of_ solar_system_bodies.svg License: CC BY-SA 3.0 Contributors: Derivative work of File:Diagramme d'Euler des corps du Système solaire.svg, translated from French to English Original artist: SounderBruce (translated version), Ariel Provost (French version), Tahc (original version) • File:Europa-moon.jpg Source: https://upload.wikimedia.org/wikipedia/commons/5/54/Europa-moon.jpg License: Public domain Contributors: http://photojournal.jpl.nasa.gov/catalog/PIA00502 (TIFF image link) Original artist: NASA/JPL/DLR • File:Evolution_of_a_Sun-like_star.svg Source: https://upload.wikimedia.org/wikipedia/commons/f/f8/Evolution_of_a_Sun-like_star. svg License: CC BY-SA 4.0 Contributors: Own work Original artist: Szczureq • File:Evolution_of_the_Moon.ogv Source: https://upload.wikimedia.org/wikipedia/commons/d/df/Evolution_of_the_Moon.ogv License: Public domain Contributors: Goddard Multimedia Original artist: NASA/Goddard Space Flight Center • File:Exoplanet_Discovery_Methods_Bar.png Source: https://upload.wikimedia.org/wikipedia/commons/c/c5/Exoplanet_Discovery_ Methods_Bar.png License: Public domain Contributors: Own work Original artist: Aldaron, a.k.a. Aldaron • File:Falling_ball.jpg Source: https://upload.wikimedia.org/wikipedia/commons/0/02/Falling_ball.jpg License: CC BY-SA 3.0 Contributors: Own work Original artist: MichaelMaggs • File:Flag_of_Algeria.svg Source: https://upload.wikimedia.org/wikipedia/commons/7/77/Flag_of_Algeria.svg License: Public domain Contributors: SVG implementation of the 63-145 Algerian law "on Characteristics of the Algerian national emblem" ("Caractéristiques du Drapeau Algérien", in English). Original artist: This graphic was originaly drawn by User:SKopp.


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• File:Flag_of_Argentina.svg Source: https://upload.wikimedia.org/wikipedia/commons/1/1a/Flag_of_Argentina.svg License: Public domain Contributors: Here, based on: http://manuelbelgrano.gov.ar/bandera/creacion-de-la-bandera-nacional/ Original artist: Government of Argentina • File:Flag_of_Australia.svg Source: https://upload.wikimedia.org/wikipedia/en/b/b9/Flag_of_Australia.svg License: Public domain Contributors: ? 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Original artist: ? • File:Flag_of_Brazil.svg Source: https://upload.wikimedia.org/wikipedia/en/0/05/Flag_of_Brazil.svg License: PD Contributors: ? Original artist: ? • File:Flag_of_Bulgaria.svg Source: https://upload.wikimedia.org/wikipedia/commons/9/9a/Flag_of_Bulgaria.svg License: Public domain Contributors: The flag of Bulgaria. The colors are specified at http://www.government.bg/cgi-bin/e-cms/vis/vis.pl?s=001&p=0034& n=000005&g= as: Original artist: SKopp • File:Flag_of_Canada.svg Source: https://upload.wikimedia.org/wikipedia/en/c/cf/Flag_of_Canada.svg License: PD Contributors: ? 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• File:Flag_of_Luxembourg.svg Source: https://upload.wikimedia.org/wikipedia/commons/d/da/Flag_of_Luxembourg.svg License: Public domain Contributors: Own work http://www.legilux.public.lu/leg/a/archives/1972/0051/a051.pdf#page=2, colors from http://www. legilux.public.lu/leg/a/archives/1993/0731609/0731609.pdf Original artist: Drawn by User:SKopp • File:Flag_of_Malaysia.svg Source: https://upload.wikimedia.org/wikipedia/commons/6/66/Flag_of_Malaysia.svg License: domain Contributors: Create based on the Malaysian Government Website (archive version) Original artist: SKopp, Zscout370 and Ranking Update

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<a data-x-rel='nofollow' class='external text' href='http://81.192.52.100/BO/AR/1915/BO_135_ar.PDF'>Moroccan royal decree (17 November 1915), BO-135-ar page 6</a> Original artist: Denelson83, Zscout370 • File:Flag_of_Nigeria.svg Source: https://upload.wikimedia.org/wikipedia/commons/7/79/Flag_of_Nigeria.svg License: Public domain Contributors: ? Original artist: ? • File:Flag_of_North_Korea.svg Source: https://upload.wikimedia.org/wikipedia/commons/5/51/Flag_of_North_Korea.svg License: Public domain Contributors: Own work Original artist: Zscout370 • File:Flag_of_Norway.svg Source: https://upload.wikimedia.org/wikipedia/commons/d/d9/Flag_of_Norway.svg License: Public domain Contributors: Own work Original artist: Dbenbenn • File:Flag_of_Pakistan.svg Source: https://upload.wikimedia.org/wikipedia/commons/3/32/Flag_of_Pakistan.svg License: Public domain Contributors: The drawing and the colors were based from flagspot.net. Original artist: User:Zscout370 • File:Flag_of_Poland.svg Source: https://upload.wikimedia.org/wikipedia/en/1/12/Flag_of_Poland.svg License: Public domain Contributors: ? Original artist: ? • File:Flag_of_Romania.svg Source: https://upload.wikimedia.org/wikipedia/commons/7/73/Flag_of_Romania.svg License: Public domain Contributors: Own work Original artist: AdiJapan • File:Flag_of_Russia.svg Source: https://upload.wikimedia.org/wikipedia/en/f/f3/Flag_of_Russia.svg License: PD Contributors: ? Original artist: ? • File:Flag_of_Singapore.svg Source: https://upload.wikimedia.org/wikipedia/commons/4/48/Flag_of_Singapore.svg License: Public domain Contributors: The drawing was based from http://app.www.sg/who/42/National-Flag.aspx. Colors from the book: (2001). The National Symbols Kit. Singapore: Ministry of Information, Communications and the Arts. pp. 5. ISBN 8880968010 Pantone 032 shade from http://www.pantone.com/pages/pantone/colorfinder.aspx?c_id=13050 Original artist: Various • File:Flag_of_South_Africa.svg Source: https://upload.wikimedia.org/wikipedia/commons/a/af/Flag_of_South_Africa.svg License: Public domain Contributors: Per specifications in the Constitution of South Africa, Schedule 1 - National flag Original artist: Flag design by Frederick Brownell, image by Wikimedia Commons users • File:Flag_of_South_Korea.svg Source: https://upload.wikimedia.org/wikipedia/commons/0/09/Flag_of_South_Korea.svg License: Public domain Contributors: Ordinance Act of the Law concerning the National Flag of the Republic of Korea, Construction and color guidelines (Russian/English) Original artist: Various • File:Flag_of_Spain.svg Source: https://upload.wikimedia.org/wikipedia/en/9/9a/Flag_of_Spain.svg License: PD Contributors: ? Original artist: ? • File:Flag_of_Sweden.svg Source: https://upload.wikimedia.org/wikipedia/en/4/4c/Flag_of_Sweden.svg License: PD Contributors: ? Original artist: ? • File:Flag_of_Switzerland.svg Source: https://upload.wikimedia.org/wikipedia/commons/f/f3/Flag_of_Switzerland.svg License: Public domain Contributors: PDF Colors Construction sheet Original artist: User:Marc Mongenet Credits: • File:Flag_of_Syria.svg Source: https://upload.wikimedia.org/wikipedia/commons/5/53/Flag_of_Syria.svg License: Public domain Contributors: see below Original artist: see below • File:Flag_of_Thailand.svg Source: https://upload.wikimedia.org/wikipedia/commons/a/a9/Flag_of_Thailand.svg License: Public domain Contributors: Own work Original artist: Zscout370 • File:Flag_of_Tunisia.svg Source: https://upload.wikimedia.org/wikipedia/commons/c/ce/Flag_of_Tunisia.svg License: Public domain Contributors: http://www.w3.org/ Original artist: entraîneur: BEN KHALIFA WISSAM • File:Flag_of_Turkey.svg Source: https://upload.wikimedia.org/wikipedia/commons/b/b4/Flag_of_Turkey.svg License: Public domain Contributors: Turkish Flag Law (Türk Bayrağı Kanunu), Law nr. 2893 of 22 September 1983. Text (in Turkish) at the website of the Turkish Historical Society (Türk Tarih Kurumu) Original artist: David Benbennick (original author) • File:Flag_of_Turkmenistan.svg Source: https://upload.wikimedia.org/wikipedia/commons/1/1b/Flag_of_Turkmenistan.svg License: Public domain Contributors: ? Original artist: ? • File:Flag_of_Ukraine.svg Source: https://upload.wikimedia.org/wikipedia/commons/4/49/Flag_of_Ukraine.svg License: Public domain Contributors: ДСТУ 4512:2006 — Державний прапор України. Загальні технічні умови Original artist: Government of Ukraine


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• File:Flag_of_Venezuela.svg Source: https://upload.wikimedia.org/wikipedia/commons/0/06/Flag_of_Venezuela.svg License: Public domain Contributors: official websites Original artist: Zscout370 • File:Flag_of_the_Czech_Republic.svg Source: https://upload.wikimedia.org/wikipedia/commons/c/cb/Flag_of_the_Czech_Republic. svg License: Public domain Contributors: • -xfi-'s file • -xfi-'s code • Zirland’s codes of colors Original artist: (of code): SVG version by cs:-xfi-. • File:Flag_of_the_National_Aeronautics_and_Space_Administration.svg Source: https://upload.wikimedia.org/wikipedia/ commons/d/da/Flag_of_the_United_States_National_Aeronautics_and_Space_Administration.svg License: Public domain Contributors: This vector image includes elements that have been taken or adapted from this: <a href='//commons.wikimedia.org/wiki/File: NASA_seal.svg' class='image'><img alt='NASA seal.svg' src='https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/NASA_ seal.svg/20px-NASA_seal.svg.png' width='20' height='20' srcset='https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/NASA_ seal.svg/30px-NASA_seal.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/NASA_seal.svg/40px-NASA_ seal.svg.png 2x' data-file-width='272' data-file-height='272' /></a> NASA seal.svg. 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• File:FullMoon2010.jpg Source: https://upload.wikimedia.org/wikipedia/commons/e/e1/FullMoon2010.jpg License: CC BY-SA 3.0 Contributors: Own work Original artist: Gregory H. Revera • File:FullMoon2010_(cropped)$-$1.jpg Source: https://upload.wikimedia.org/wikipedia/commons/d/db/FullMoon2010_ %28cropped%29-1.jpg License: CC BY-SA 3.0 Contributors: Own work Original artist: Gregory H. 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Original artist: RadioFan (talk) • File:Grabmal_Nikolaus_Kopernikus_Frauenburger_Dom_2010.jpg Source: https://upload.wikimedia.org/wikipedia/commons/8/ 87/Grabmal_Nikolaus_Kopernikus_Frauenburger_Dom_2010.jpg License: CC BY-SA 3.0 de Contributors: Own work Original artist: Holger Weinandt • File:Gravity_Wells_Potential_Plus_Kinetic_Energy_-_Circle-Ellipse-Parabola-Hyperbola.png Source: https://upload.wikimedia. org/wikipedia/commons/9/94/Gravity_Wells_Potential_Plus_Kinetic_Energy_-_Circle-Ellipse-Parabola-Hyperbola.png License: CC0 Contributors: http://preview.tinyurl\protect\char"007B\relaxdot\protect\char"007D\relaxcom/Thesis-EnergyPotentialAnalysis - Figure 3.2 on pdf pg34of64. 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Original artist: U.S. Government • File:Greater_coat_of_arms_of_the_United_States.svg Source: https://upload.wikimedia.org/wikipedia/commons/5/5b/Greater_ coat_of_arms_of_the_United_States.svg License: CC BY-SA 3.0 Contributors: Own work + File:Seal of the House of Representatives.svg Original artist: Ssolbergj • File:Gsfc-campus.png Source: https://upload.wikimedia.org/wikipedia/commons/4/44/Gsfc-campus.png License: Public domain Contributors: From NASA Goddard Space Flight Center main page (www.nasa.gov/centers/goddard) Original artist: Unknown<a href='//www.wikidata.org/wiki/Q4233718' title='wikidata:Q4233718'><img alt='wikidata:Q4233718' src='https://upload. wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/20px-Wikidata-logo.svg.png' width='20' height='11' srcset='https:// upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/30px-Wikidata-logo.svg.png 1.5x, https://upload.wikimedia. org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/40px-Wikidata-logo.svg.png 2x' data-file-width='1050' data-file-height='590' /></a> • File:He1523a.jpg Source: https://upload.wikimedia.org/wikipedia/commons/5/5f/He1523a.jpg License: CC BY 4.0 Contributors: http: //www.solstation.com/x-objects/he1523.htm Original artist: ESO, European Southern Observatory • File:Heliocentric.jpg Source: https://upload.wikimedia.org/wikipedia/commons/5/57/Heliocentric.jpg License: Public domain Contributors: first upload to de:wikipedia 22:42, 5. Apr 2004 by de:UserRivi . . 570 x 480 (63.606 Byte) (Heliozentrisches Weltbild) Original artist: Andreas Cellarius • File:Heliospheric-current-sheet.gif Source: https://upload.wikimedia.org/wikipedia/commons/b/b6/Heliospheric-current-sheet.gif License: Public domain Contributors: [1] from http://lepmfi.gsfc.nasa.gov/mfi/hcs/hcs_shape.html . Original artist: Werner Heil (see “other version” below). • File:Hipparcos_Catalogue_equirectangular_plot.svg Source: https://upload.wikimedia.org/wikipedia/commons/d/d8/Hipparcos_ Catalogue_equirectangular_plot.svg License: Public domain Contributors: Own work, http://svs.gsfc.nasa.gov/vis/a000000/a003500/ a003572 Original artist: Cmglee, Timwi, NASA • File:House_of_Johannes_Kepler.JPG Source: https://upload.wikimedia.org/wikipedia/commons/8/8b/House_of_Johannes_Kepler. JPG License: CC BY-SA 3.0 Contributors: Own work Original artist: Mrbeachguide • File:Hyperion_in_natural_colours.jpg Source: https://upload.wikimedia.org/wikipedia/commons/e/e0/Hyperion_in_natural_colours. jpg License: Public domain Contributors: ? Original artist: ? • File:ISS_March_2009.jpg Source: https://upload.wikimedia.org/wikipedia/commons/8/80/ISS_March_2009.jpg License: Public domain Contributors: http://www.nasa.gov/images/content/322546main_s119e008357_full.jpg Original artist: NASA • File:Iapetus_as_seen_by_the_Cassini_probe_-_20071008_(cropped).jpg Source: https://upload.wikimedia.org/wikipedia/commons/ 1/19/Iapetus_as_seen_by_the_Cassini_probe_-_20071008_%28cropped%29.jpg License: Public domain Contributors: PIA08384: The Other Side of Iapetus Original artist: NASA/JPL/Space Science Institute • File:Ilc_9yr_moll4096.png Source: https://upload.wikimedia.org/wikipedia/commons/3/3c/Ilc_9yr_moll4096.png License: Public domain Contributors: http://map.gsfc.nasa.gov/media/121238/ilc_9yr_moll4096.png Original artist: NASA / WMAP Science Team • File:Ina_(LRO).jpg Source: https://upload.wikimedia.org/wikipedia/commons/f/f0/Ina_%28LRO%29.jpg License: Public domain Contributors: Lunar Reconnaissance Orbiter images M113921307LE and M113921307RE. Aligned and merged manually. Resolution is decreased by factor of 2 to reduce file size. Projected by rotating 2.15° clockwise (the angle is obtained from JMARS) and decreasing of horizontal size by 17.8% (taken from NASA ortophoto), so, north is up and proportions are real. Brightness is increased. Original artist: NASA


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• File:Increase2.svg Source: https://upload.wikimedia.org/wikipedia/commons/b/b0/Increase2.svg License: Public domain Contributors: Own work Original artist: Sarang • File:InnerSolarSystem-en.png Source: https://upload.wikimedia.org/wikipedia/commons/f/f3/InnerSolarSystem-en.png License: Public domain Contributors: Transferred from en.wikipedia to Commons. Original artist: Mdf at English Wikipedia • File:Innovative_Interstellar_Explorer_interstellar_space_probe_.jpg Source: https://upload.wikimedia.org/wikipedia/commons/3/ 3d/Innovative_Interstellar_Explorer_interstellar_space_probe_.jpg License: Public domain Contributors: from http://interstellarexplorer. jhuapl.edu/gallery/artist_concepts.html Original artist: NASA/JPL • File:Io,_moon_of_Jupiter,_NASA.jpg Source: https://upload.wikimedia.org/wikipedia/commons/1/14/Io%2C_moon_of_Jupiter% 2C_NASA.jpg License: Public domain Contributors: ? Original artist: ? • File:Io_highest_resolution_true_color.jpg Source: https://upload.wikimedia.org/wikipedia/commons/7/7b/Io_highest_resolution_ true_color.jpg License: Public domain Contributors: http://photojournal.jpl.nasa.gov/catalog/PIA02308 Original artist: NASA / JPL / University of Arizona • File:JPL1.jpg Source: https://upload.wikimedia.org/wikipedia/commons/3/33/JPL1.jpg License: CC BY 2.0 Contributors: JPL Original artist: Kevin Stanchfield from Pasadena, CA., America • File:JPLControlRoom.jpg Source: https://upload.wikimedia.org/wikipedia/commons/d/db/JPLControlRoom.jpg License: CC-BY-SA3.0 Contributors: w:Image:JPLControlRoom.jpg Original artist: Alan Mak • File:Jet_Propulsion_Laboratory_logo.svg Source: https://upload.wikimedia.org/wikipedia/commons/c/c6/Jet_Propulsion_ Laboratory_logo.svg License: Public domain Contributors: Transferred from en.wikipedia Original artist: Original uploader was King of Hearts at en.wikipedia • File:Jewel_of_the_Solar_System.jpg Source: https://upload.wikimedia.org/wikipedia/commons/f/f7/Jewel_of_the_Solar_System.jpg License: Public domain Contributors: • JPEG File: http://www.nasa.gov/mission_pages/cassini/multimedia/pia17474.html#.Um1oeeig5w0 Original artist: Caltech/SSI/Cornell

NASA/JPL-

• File:Jsc2004e18852.jpg Source: https://upload.wikimedia.org/wikipedia/commons/a/a9/Jsc2004e18852.jpg License: Public domain Contributors: from http://spaceflight.nasa.gov/gallery/images/vision/mars/html/jsc2004e18852.html Original artist: ? • File:Juno_symbol.svg Source: https://upload.wikimedia.org/wikipedia/commons/3/3f/Juno_symbol.svg License: Public domain Contributors: ? Original artist: ? • File:Jupiter_New_Horizons.jpg Source: https://upload.wikimedia.org/wikipedia/commons/c/c1/Jupiter_New_Horizons.jpg License: Public domain Contributors: National Aeronautics and Space Administration Original artist: NASA/Johns Hopkins University Applied Physics Laboratory/Southwest Research Institute • File:Jupiter_and_its_shrunken_Great_Red_Spot_(cropped).jpg Source: https://upload.wikimedia.org/wikipedia/commons/0/0d/ Jupiter_and_its_shrunken_Great_Red_Spot_%28cropped%29.jpg License: Public domain Contributors: http://www.spacetelescope.org/ images/heic1410a/ or http://hubblesite.org/newscenter/archive/releases/2014/24/image/b/ Original artist: NASA, ESA, and A. Simon (Goddard Space Flight Center) • File:Jupiter_interior.png Source: https://upload.wikimedia.org/wikipedia/commons/f/f7/Jupiter_interior.png License: Public domain Contributors: The background image is from NASA PIA02873. The overlaid cut-away illustration is by the contributor. Original artist: NASA/R.J. Hall • File:Jupiter_symbol.svg Source: https://upload.wikimedia.org/wikipedia/commons/2/26/Jupiter_symbol.svg License: Public domain Contributors: Own work Original artist: Lexicon • File:KOS_sarkofag_ze_szczątkami_Kopernika.jpg Source: https://upload.wikimedia.org/wikipedia/commons/1/10/KOS_sarkofag_ ze_szcz%C4%85tkami_Kopernika.jpg License: GFDL Contributors: Own work Original artist: Mazaki • File:Karlova_str_No4,_Prague_Old_Town.jpg Source: https://upload.wikimedia.org/wikipedia/commons/0/05/Karlova_str_No4% 2C_Prague_Old_Town.jpg License: CC BY-SA 3.0 Contributors: Own work Original artist: Czech Wikipedia user Packa • File:Kennedy_Receives_Mariner_2_Model.jpg Source: https://upload.wikimedia.org/wikipedia/commons/1/13/Kennedy_Receives_ Mariner_2_Model.jpg License: Public domain Contributors: Great Images in NASA Original artist: NASA • File:Kepler-1619-pl-3.jpg Source: https://upload.wikimedia.org/wikipedia/commons/9/9b/Kepler-1619-pl-3.jpg License: Public domain Contributors: ? Original artist: ? • File:Kepler-Bruno.jpg Source: https://upload.wikimedia.org/wikipedia/commons/6/61/Kepler-Bruno.jpg License: Public domain Contributors: Iohannes Kepler, Epitome astronomiae Copernicanae, 1618 (http://www.sacred-texts.com/astro/cwiu/cwiu06.htm) Original artist: Iohannes Kepler • File:Kepler-Geburtshaus.jpg Source: https://upload.wikimedia.org/wikipedia/commons/9/95/Kepler-Geburtshaus.jpg License: CCBY-SA-3.0 Contributors: Transferred from de.wikipedia to Commons. Original artist: MarkusHagenlocher at German Wikipedia • File:Kepler-Wallenstein-Horoskop.jpg Source: https://upload.wikimedia.org/wikipedia/commons/5/51/ Kepler-Wallenstein-Horoskop.jpg License: Public domain Contributors: http://www.welten.net/Horoskop/keplerum.jpg; Originally from de.wikipedia; description page is/was here. Original artist: The original uploader was Dvoigt at German Wikipedia • File:Kepler-first-law.svg Source: https://upload.wikimedia.org/wikipedia/commons/1/1a/Kepler-first-law.svg License: CCBY-SA-3.0 Contributors: The original PNG version: <a href='//commons.wikimedia.org/wiki/File:Kepler-first-law.png' class='image'><img alt='Kepler-first-law.png' src='https://upload.wikimedia.org/wikipedia/commons/thumb/8/87/Kepler-first-law. png/32px-Kepler-first-law.png' width='32' height='24' srcset='https://upload.wikimedia.org/wikipedia/commons/thumb/8/87/ Kepler-first-law.png/48px-Kepler-first-law.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/8/87/Kepler-first-law. png/64px-Kepler-first-law.png 2x' data-file-width='250' data-file-height='186' /></a> Kepler-first-law.png Original artist: Original by Arpad Horvath


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• File:Kepler-second-law.gif Source: https://upload.wikimedia.org/wikipedia/commons/6/69/Kepler-second-law.gif License: CC BY-SA 3.0 Contributors: Gonfer Original artist: Gonfer (talk) • File:Kepler-solar-system-1.png Source: https://upload.wikimedia.org/wikipedia/commons/1/19/Kepler-solar-system-1.png License: Public domain Contributors: ? Original artist: ? • File:Kepler-solar-system-2.gif Source: https://upload.wikimedia.org/wikipedia/commons/1/1d/Kepler-solar-system-2.gif License: Public domain Contributors: ? Original artist: ? • File:Kepler-solar-system-2.png Source: https://upload.wikimedia.org/wikipedia/commons/2/25/Kepler-solar-system-2.png License: Public domain Contributors: ? Original artist: ? • File:Kepler_Celestial_Spheres.jpg Source: https://upload.wikimedia.org/wikipedia/commons/0/04/Kepler_Celestial_Spheres.jpg License: Public domain Contributors: Johannes Kepler, Mysterium Cosmographicum, (Frankfurt, 1621) http://www.library.illinois.edu/rbx/ exhibitions/Plato/Archival%20Images/Large%20jpg/Q.%20521.3%20K44p%201621,%20tab.IV%20L.jpg Original artist: Johannes Kepler • File:Kepler_Drawing_of_SN_1604.png Source: https://upload.wikimedia.org/wikipedia/commons/3/3d/Kepler_Drawing_of_SN_ 1604.png License: Public domain Contributors: ? Original artist: ? • File:Kepler_Mars_retrograde.jpg Source: https://upload.wikimedia.org/wikipedia/commons/e/e9/Kepler_Mars_retrograde.jpg License: Public domain Contributors: ? Original artist: ? • File:Kepler_Optica.jpg Source: https://upload.wikimedia.org/wikipedia/commons/5/5c/Kepler_Optica.jpg License: Public domain Contributors: ? Original artist: ? • File:Kepler_Statue_Linz.jpg Source: https://upload.wikimedia.org/wikipedia/commons/d/d3/Kepler_Statue_Linz.jpg License: CC BY 3.0 Contributors: Own work Original artist: Aldaron, a.k.a. Aldaron • File:Kepler_astronomia_nova.jpg Source: https://upload.wikimedia.org/wikipedia/commons/e/eb/Kepler_astronomia_nova.jpg License: Public domain Contributors: http://www.library.usyd.edu.au/libraries/rare/modernity/kepler4.html Original artist: Johannes Kepler • File:Kepler_conjecture_2.jpg Source: https://upload.wikimedia.org/wikipedia/commons/f/fe/Kepler_conjecture_2.jpg License: Public domain Contributors: http://www.math.sunysb.edu/~{}tony/whatsnew/column/pennies-1200/cass1.html Original artist: Johannes Kepler • File:Kepler_laws_diagram.svg Source: https://upload.wikimedia.org/wikipedia/commons/9/98/Kepler_laws_diagram.svg License: CC BY 2.5 Contributors: Own work Original artist: Hankwang • File:Kepler_orbits.svg Source: https://upload.wikimedia.org/wikipedia/commons/b/b7/Kepler_orbits.svg License: GFDL Contributors: Own work Original artist: Stamcose • File:Keplers_supernova.jpg Source: https://upload.wikimedia.org/wikipedia/commons/d/d4/Keplers_supernova.jpg License: Public domain Contributors: http://www.nasa.gov/multimedia/imagegallery/image_feature_219.html Larger version uploaded from http://chandra. harvard.edu/photo/printgallery/2004/ a NASA-sponsored site. Per Bridgeman Art Library v. Corel Corp., no new copyright should apply anyway. Original artist: NASA/ESA/JHU/R.Sankrit & W.Blair • File:Kraków_-_Pomnik_Mikołaja_Kopernika_02.JPG Source: https://upload.wikimedia.org/wikipedia/commons/a/a9/Krak%C3% B3w_-_Pomnik_Miko%C5%82aja_Kopernika_02.JPG License: CC-BY-SA-3.0 Contributors: Own work Original artist: Lestat (Jan Mehlich) • File:Kuiper_belt_plot_objects_of_outer_solar_system.png Source: https://upload.wikimedia.org/wikipedia/commons/5/5b/Kuiper_ belt_plot_objects_of_outer_solar_system.png License: CC BY-SA 3.0 Contributors: • the Minor Planet Centre: minorplanetcenter.org Original artist: WilyD at English Wikipedia • File:Kuiper_oort-en.svg Source: https://upload.wikimedia.org/wikipedia/commons/5/56/Kuiper_belt_-_Oort_cloud-en.svg License: Public domain Contributors: http://herschel.jpl.nasa.gov/solarSystem.shtml Original artist: • This SVG image was created by Medium69. • File:LRO_WAC_Nearside_Mosaic.jpg Source: https://upload.wikimedia.org/wikipedia/commons/c/cc/LRO_WAC_ Nearside_Mosaic.jpg License: Public domain Contributors: http://wms.lroc.asu.edu/lroc_browse/view/WAC_GL000 (see also http://lroc.sese.asu.edu/news/index.php?/archives/345-Farside!-And-all-the-way-around.html) Original artist: NASA/GSFC/Arizona State University • File:LRO_WAC_North_Pole_Mosaic_(PIA14024).jpg Source: https://upload.wikimedia.org/wikipedia/commons/8/86/LRO_WAC_ North_Pole_Mosaic_%28PIA14024%29.jpg License: Public domain Contributors: http://wms.lroc.asu.edu/lroc_browse/view/npole (see also http://photojournal.jpl.nasa.gov/catalog/PIA14024) Original artist: NASA/GSFC/Arizona State University • File:LRO_WAC_South_Pole_Mosaic.jpg Source: https://upload.wikimedia.org/wikipedia/commons/4/40/LRO_WAC_South_Pole_ Mosaic.jpg License: Public domain Contributors: http://wms.lroc.asu.edu/lroc_browse/view/SP_Mosaic (see also http://photojournal.jpl. nasa.gov/catalog/PIA13523) Original artist: NASA/GSFC/Arizona State University • File:La_Cosmographie_de_Claude_Ptolemée.djvu Source: https://upload.wikimedia.org/wikipedia/commons/6/65/La_ Cosmographie_de_Claude_Ptolem%C3%A9e.djvu License: Public domain Contributors: http://bmn-renaissance.nancy.fr/items/ show/1236 Original artist: Ptolemy, Latin translation by Jacobus Angelus, maps by Claudius Clavus, scanned by the Library of Nancy, DJVU file made by Yann • File:Launch_of_Friendship_7_-_GPN-2000-000686.jpg Source: https://upload.wikimedia.org/wikipedia/commons/3/36/Launch_ of_Friendship_7_-_GPN-2000-000686.jpg License: Public domain Contributors: Great Images in NASA Description Original artist: NASA/photographer unknown • File:Leading_hemisphere_of_Helene_-_20110618.jpg Source: https://upload.wikimedia.org/wikipedia/commons/d/d6/Leading_ hemisphere_of_Helene_-_20110618.jpg License: Public domain Contributors: http://www.ciclops.org/view/6796/Helene_Rev_149_ Raw_Preview_1. Original artist: NASA / Jet Propulsion Laboratory / Space Science Institute. • File:Local_Interstellar_Clouds_with_motion_arrows.jpg Source: https://upload.wikimedia.org/wikipedia/commons/7/74/Local_ Interstellar_Clouds_with_motion_arrows.jpg License: Public domain Contributors: http://www.nasa.gov/mission_pages/sunearth/news/ gallery/solar-journey.html Original artist: NASA/Goddard/Adler/U. Chicago/Wesleyan


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• File:Luna_2_Soviet_moon_probe.jpg Source: https://upload.wikimedia.org/wikipedia/commons/2/20/Luna_2_Soviet_moon_probe. jpg License: Public domain Contributors: http://nssdc.gsfc.nasa.gov/database/MasterCatalog?sc=1959-014A Original artist: NASA • File:Lunar_basalt_70017.jpg Source: https://upload.wikimedia.org/wikipedia/commons/2/2c/Lunar_basalt_70017.jpg License: Public domain Contributors: http://curator.jsc.nasa.gov/lunar/lsc/70017.pdf Original artist: NASA • File:Lunar_eclipse_October_8_2014_California_Alfredo_Garcia_Jr_mideclipse.JPG Source: https://upload.wikimedia.org/ wikipedia/commons/1/13/Lunar_eclipse_October_8_2014_California_Alfredo_Garcia_Jr_mideclipse.JPG License: CC BY-SA 2.0 Contributors: Flickr [1] Original artist: Alfredo Garcia, Jr, [2] • File:Lunar_eclipse_al-Biruni.jpg Source: https://upload.wikimedia.org/wikipedia/commons/6/62/Lunar_eclipse_al-Biruni.jpg License: Public domain Contributors: Scanned from: Seyyed Hossein Nasr (1976) Islamic Science: An Illustrated Study, World of Islam Festival Publishing Company ISBN 090503502X Original artist: Abū Rayḥān al-Bīrūnī • File:Lunar_libration_with_phase_Oct_2007_450px.gif Source: https://upload.wikimedia.org/wikipedia/commons/b/ba/Lunar_ libration_with_phase_Oct_2007_450px.gif License: Public domain Contributors: • Lunar_libration_with_phase_Oct_2007.gif Original artist: Tomruen • File:MAVENnMars.jpg Source: https://upload.wikimedia.org/wikipedia/en/7/7c/MAVENnMars.jpg License: PD Contributors: http://photojournal.jpl.nasa.gov/jpeg/PIA14761.jpg Parent: http://www.jpl.nasa.gov/spaceimages/details.php?id=PIA14761 Original artist: NASA • File:MHW-RTGs.gif Source: https://upload.wikimedia.org/wikipedia/commons/7/72/MHW-RTGs.gif License: Public domain Contributors: http://voyager.jpl.nasa.gov/gallery/assembly.html Original artist: ? • File:Map_of_the_full_sun.jpg Source: https://upload.wikimedia.org/wikipedia/commons/9/99/Map_of_the_full_sun.jpg License: Public domain Contributors: STEREO Reaches New Milestone At Its Sixth Anniversary Original artist: NASA/STEREO/SDO/GSFC • File:Mappa_Mundi_2_from_Bede,_De_natura_rerum.jpg Source: https://upload.wikimedia.org/wikipedia/commons/5/5f/Mappa_ Mundi_2_from_Bede%2C_De_natura_rerum.jpg License: CC BY 4.0 Contributors: The Bodleian Libraries, Oxford Original artist: Bede • File:Marius_Crater.jpg Source: https://upload.wikimedia.org/wikipedia/commons/7/74/Marius_Crater.jpg License: Public domain Contributors: National Aeronautics and Space Administration Original artist: National Aeronautics and Space Administration • File:Mars_23_aug_2003_hubble.jpg Source: https://upload.wikimedia.org/wikipedia/commons/5/58/Mars_23_aug_2003_hubble.jpg License: Public domain Contributors: http://hubblesite.org/newscenter/archive/releases/2005/34/image/j/ (image link) Original artist: NASA, ESA, and The Hubble Heritage Team (STScI/AURA) • File:Mars_23_aug_2003_hubble_(cropped).jpg Source: https://upload.wikimedia.org/wikipedia/commons/6/66/Mars_23_aug_2003_ hubble_%28cropped%29.jpg License: Public domain Contributors: http://hubblesite.org/newscenter/archive/releases/2005/34/image/j/ (image link) Original artist: NASA, ESA, and The Hubble Heritage Team (STScI/AURA) • File:Mars_Science_Laboratory_mockup_comparison.jpg Source: https://upload.wikimedia.org/wikipedia/commons/0/0d/ Mars_Science_Laboratory_mockup_comparison.jpg License: Public domain Contributors: http://appel.nasa.gov/2009/03/01/ mars-science-laboratory-integrating-science-and-engineering-teams/ (image link) Original artist: NASA/JPL/Thomas “Dutch” Slager • File:Mars_symbol.svg Source: https://upload.wikimedia.org/wikipedia/commons/b/b7/Mars_symbol.svg License: Public domain Contributors: Own work Original artist: This vector image was created with Inkscape by Lexicon, and then manually replaced by sarang. • File:Martian_gravel_beneath_one_of_the_wheels_of_the_Curiosity_rover.jpg Source: https://upload.wikimedia.org/wikipedia/ commons/6/61/Martian_gravel_beneath_one_of_the_wheels_of_the_Curiosity_rover.jpg License: Public domain Contributors: http:// mars.jpl.nasa.gov/msl/multimedia/raw/?rawid=0003ML0000125000I1_DXXX&s=3 Original artist: NASA/JPL-Caltech/Malin Pakistani based Space Science Systems (PTV sources) • File:Mean_Anomaly.svg Source: https://upload.wikimedia.org/wikipedia/commons/b/bc/Mean_Anomaly.svg License: CC BYSA 4.0 Contributors: This file was derived from Anomalies.PNG: <a href='//commons.wikimedia.org/wiki/File:Anomalies. PNG' class='image'><img alt='Anomalies.PNG' src='https://upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Anomalies.PNG/ 50px-Anomalies.PNG' width='50' height='44' srcset='https://upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Anomalies.PNG/ 75px-Anomalies.PNG 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Anomalies.PNG/100px-Anomalies.PNG 2x' data-file-width='718' data-file-height='627' /></a> Original artist: CheCheDaWaff • File:Mercury_in_color_-_Prockter07-edit1.jpg Source: https://upload.wikimedia.org/wikipedia/commons/d/d9/Mercury_in_color_ -_Prockter07-edit1.jpg License: Public domain Contributors: NASA/JPL. Original artist: NASA/Johns Hopkins University Applied Physics Laboratory/Carnegie Institution of Washington • File:Mercury_in_color_-_Prockter07_centered.jpg Source: https://upload.wikimedia.org/wikipedia/commons/3/30/Mercury_in_ color_-_Prockter07_centered.jpg License: Public domain Contributors: NASA/JPL Original artist: NASA/Johns Hopkins University Applied Physics Laboratory/Carnegie Institution of Washington. Edited version of Image:Mercury in color - Prockter07.jpg by Papa Lima Whiskey. • File:Mercury_symbol.svg Source: https://upload.wikimedia.org/wikipedia/commons/2/2e/Mercury_symbol.svg License: Public domain Contributors: Own work Original artist: Lexicon • File:Micrographia_Schem_38.jpg Source: https://upload.wikimedia.org/wikipedia/commons/4/43/Micrographia_Schem_38.jpg License: Public domain Contributors: This image is available from the National Library of Wales Original artist: Robert Hooke (1635-1703) • File:Mikolaj_Kopernik.jpg Source: https://upload.wikimedia.org/wikipedia/commons/e/e7/Mikolaj_Kopernik.jpg License: Public domain Contributors: ? Original artist: ? • File:Milky_Way_Arms_ssc2008-10.svg Source: ssc2008-10.svg License: Public domain Contributors:

https://upload.wikimedia.org/wikipedia/commons/a/a7/Milky_Way_Arms_


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• Milky_Way_2005.jpg Original artist: Milky_Way_2005.jpg: R. Hurt • File:Milky_Way_Emerges_as_Sun_Sets_over_Paranal.jpg Source: https://upload.wikimedia.org/wikipedia/commons/9/90/Milky_ Way_Emerges_as_Sun_Sets_over_Paranal.jpg License: CC BY 4.0 Contributors: http://www.eso.org/public/images/potw1517a/ Original artist: ESO/J. Colosimo • File:Mimas_PIA12568.jpg Source: https://upload.wikimedia.org/wikipedia/commons/b/be/Mimas_PIA12568.jpg License: Public domain Contributors: http://www.ciclops.org/view.php?id=6220 Original artist: NASA / Jet Propulsion Lab / Space Science Institute • File:Miranda.jpg Source: https://upload.wikimedia.org/wikipedia/commons/d/d0/Miranda.jpg License: Public domain Contributors: Keele Astrophysics Group; Photojournal Original artist: NASA/JPL-Caltech • File:Montagem_Sistema_Solar.jpg Source: https://upload.wikimedia.org/wikipedia/commons/8/86/Montagem_Sistema_Solar.jpg License: Public domain Contributors: http://solarsystem.nasa.gov/multimedia/display.cfm?Category=Planets&IM_ID=10164 Original artist: NASA • File:Moon-Mdf-2005.jpg Source: https://upload.wikimedia.org/wikipedia/commons/4/4d/Moon-Mdf-2005.jpg License: CC-BY-SA3.0 Contributors: No machine-readable source provided. Own work assumed (based on copyright claims). Original artist: No machinereadable author provided. 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Wieczorek • File:Moon_Crescent_-_False_Color_Mosaic.jpg Source: https://upload.wikimedia.org/wikipedia/commons/2/21/Moon_Crescent_-_ False_Color_Mosaic.jpg License: Public domain Contributors: http://photojournal.jpl.nasa.gov/catalog/PIA00131 (image link) Original artist: NASA/JPL • File:Moon_Farside_LRO.jpg Source: https://upload.wikimedia.org/wikipedia/commons/0/04/Moon_Farside_LRO.jpg License: Public domain Contributors: http://wms.lroc.asu.edu/lroc_browse/view/WAC_GL180 (see also http://photojournal.jpl.nasa.gov/catalog/ PIA14021) Original artist: NASA/GSFC/Arizona State University • File:Moon_by_Johannes_hevelius_1645.PNG Source: https://upload.wikimedia.org/wikipedia/commons/0/03/Moon_by_Johannes_ hevelius_1645.PNG License: Public domain Contributors: http://dziedzictwo.polska.pl/katalogskarb,Selenographia_Jana_Heweliusza_ (Selenographia_sive_lunae_descriptio)_,gid,262839,cid,1688.htm?body=desc (monochrome version of the image in 1647 year edition of Selenographia) Original artist: Johannes Hevelius (1611–1687) • File:Moon_diagram.svg Source: https://upload.wikimedia.org/wikipedia/commons/e/eb/Moon_diagram.svg License: CC BY 3.0 Contributors: Own work Original artist: Kelvinsong • File:Moon_names.svg Source: https://upload.wikimedia.org/wikipedia/commons/6/61/Moon_names.svg License: CC BY-SA 3.0 Contributors: • Remake of File:FullMoon2010.jpg Original artist: • Peter Freiman • File:Moon_phases_en.jpg Source: https://upload.wikimedia.org/wikipedia/commons/4/46/Moon_phases_en.jpg License: CC BY-SA 3.0 Contributors: Own work Original artist: Orion 8 • File:Moon_symbol_decrescent.svg Source: https://upload.wikimedia.org/wikipedia/commons/c/c6/Moon_symbol_decrescent.svg License: Public domain Contributors: Own work Original artist: Lexicon • File:Moon_transit_of_sun_large.ogg Source: https://upload.wikimedia.org/wikipedia/commons/0/0c/Moon_transit_of_sun_large.ogg License: Public domain Contributors: http://science.nasa.gov/headlines/y2007/12mar_stereoeclipse.htm?list39638 Original artist: NASA • File:Mountain_Moonset.jpg Source: https://upload.wikimedia.org/wikipedia/commons/b/b6/Mountain_Moonset.jpg License: CC BYSA 3.0 Contributors: Own work Original artist: Jessie Eastland • File:NASA-Apollo8-Dec24-Earthrise.jpg Source: https://upload.wikimedia.org/wikipedia/commons/a/a8/ NASA-Apollo8-Dec24-Earthrise.jpg License: Public domain Contributors: http://www.hq.nasa.gov/office/pao/History/alsj/a410/ AS8-14-2383HR.jpg Original artist: NASA / Bill Anders • File:NASA-Budget-Federal.svg Source: https://upload.wikimedia.org/wikipedia/commons/0/09/NASA-Budget-Federal.svg License: CC0 Contributors: Own work Original artist: 0x0077BE • File:NASA_Apollo_17_Lunar_Roving_Vehicle.jpg Source: https://upload.wikimedia.org/wikipedia/commons/4/4d/NASA_Apollo_ 17_Lunar_Roving_Vehicle.jpg License: Public domain Contributors: http://grin.hq.nasa.gov/ABSTRACTS/GPN-2000-001139.html Original artist: NASA • File:NASA_Goddard’{}s_Innovation.ogv Source: https://upload.wikimedia.org/wikipedia/commons/7/78/NASA_Goddard%27s_ Innovation.ogv License: Public domain Contributors: Goddard Multimedia Original artist: NASA/Goddard Space Flight Center • File:NASA_Goddard_Space_Flight_Center_Aerial_view_2010_facing_south.jpg Source: https://upload.wikimedia.org/wikipedia/ commons/1/1c/NASA_Goddard_Space_Flight_Center_Aerial_view_2010_facing_south.jpg License: Public domain Contributors: https: //www.flickr.com/photos/gsfc/22183953822/in/album-72157659863041612/ Original artist: NASA Goddard/Bill Hrybyk • File:NASA_Science_Update_-_The_Voyager_Spacecraft_-_Humanity’{}s_Farthest_Journey.jpg Source: https://upload. wikimedia.org/wikipedia/commons/7/76/NASA_Science_Update_-_The_Voyager_Spacecraft_-_Humanity%27s_Farthest_Journey.jpg License: Public domain Contributors: Voyager: Humanity’s Farthest Journey Original artist: NASA; edited by Jaybear


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• File:Voyager_-_Filters_-_Orange.png Source: https://upload.wikimedia.org/wikipedia/commons/4/41/Voyager_-_Filters_-_Orange. png License: CC BY 3.0 Contributors: Own work Original artist: Xession • File:Voyager_-_Filters_-_UV.png Source: https://upload.wikimedia.org/wikipedia/commons/5/5e/Voyager_-_Filters_-_UV.png License: CC BY 3.0 Contributors: Own work Original artist: Xession • File:Voyager_-_Filters_-_Violet.png Source: https://upload.wikimedia.org/wikipedia/commons/e/e6/Voyager_-_Filters_-_Violet.png License: CC BY 3.0 Contributors: Own work Original artist: Xession • File:Voyager_2_-_Saturn_Rings_-_3085_7800_2.png Source: https://upload.wikimedia.org/wikipedia/commons/4/47/Voyager_2_-_ Saturn_Rings_-_3085_7800_2.png License: Public domain Contributors: • http://www.ciclops.org/view/3085/Saturns_rings_-_High_resolution Original artist: NASA/JPL • File:Voyager_2_picture_of_Oberon.jpg Source: https://upload.wikimedia.org/wikipedia/commons/0/09/Voyager_2_picture_of_ Oberon.jpg License: Public domain Contributors: http://photojournal.jpl.nasa.gov/catalog/PIA00034 http://ciclops.org/view/3653/Oberon_at_Voyager_Closest_Approach Original artist: NASA • File:Voyager_Golden_Record_fx.png Source: https://upload.wikimedia.org/wikipedia/commons/b/bd/Voyager_Golden_Record_fx. png License: Public domain Contributors: • Voyager_Golden_Record.jpg Original artist: Voyager_Golden_Record.jpg: created by NASA • File:Voyager_Path.svg Source: https://upload.wikimedia.org/wikipedia/commons/5/53/Voyager_Path.svg License: Public domain Contributors: • Original from http://solarsystem.nasa.gov/multimedia/display.cfm?IM_ID=2143 Original artist: Voyager_Path.jpg: created by NASA • File:Voyager_probes_with_the_outer_worlds.jpg Source: https://upload.wikimedia.org/wikipedia/commons/d/d9/Voyager_probes_ with_the_outer_worlds.jpg License: Public domain Contributors: Donald Davis’ official site. Original artist: Don Davis • File:Voyager_spacecraft_structure_vector.svg Source: https://upload.wikimedia.org/wikipedia/commons/c/ce/Voyager_spacecraft_ structure_vector.svg License: Public domain Contributors: • Voyager_spacecraft_structure.jpg Original artist: Voyager_spacecraft_structure.jpg: NASA • File:Wiki_letter_w_cropped.svg Source: https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg License: CC-BY-SA-3.0 Contributors: This file was derived from Wiki letter w.svg: <a href='//commons.wikimedia.org/wiki/File: Wiki_letter_w.svg' class='image'><img alt='Wiki letter w.svg' src='https://upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_ letter_w.svg/50px-Wiki_letter_w.svg.png' width='50' height='50' srcset='https://upload.wikimedia.org/wikipedia/commons/thumb/6/6c/ Wiki_letter_w.svg/75px-Wiki_letter_w.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/ 100px-Wiki_letter_w.svg.png 2x' data-file-width='44' data-file-height='44' /></a> Original artist: Derivative work by Thumperward • File:Wikibooks-logo.svg Source: https://upload.wikimedia.org/wikipedia/commons/f/fa/Wikibooks-logo.svg License: CC BY-SA 3.0 Contributors: Own work Original artist: User:Bastique, User:Ramac et al. • File:Wikinews-logo.svg Source: https://upload.wikimedia.org/wikipedia/commons/2/24/Wikinews-logo.svg License: CC BY-SA 3.0 Contributors: This is a cropped version of Image:Wikinews-logo-en.png. Original artist: Vectorized by Simon 01:05, 2 August 2006 (UTC) Updated by Time3000 17 April 2007 to use official Wikinews colours and appear correctly on dark backgrounds. Originally uploaded by Simon. • File:Wikiquote-logo.svg Source: https://upload.wikimedia.org/wikipedia/commons/f/fa/Wikiquote-logo.svg License: Public domain Contributors: Own work Original artist: Rei-artur • File:Wikisource-logo.svg Source: https://upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg License: CC BY-SA 3.0 Contributors: Rei-artur Original artist: Nicholas Moreau • File:Wikiversity-logo-Snorky.svg Source: https://upload.wikimedia.org/wikipedia/commons/1/1b/Wikiversity-logo-en.svg License: CC BY-SA 3.0 Contributors: Own work Original artist: Snorky • File:Wikiversity-logo.svg Source: https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg License: CC BY-SA 3.0 Contributors: Snorky (optimized and cleaned up by verdy_p) Original artist: Snorky (optimized and cleaned up by verdy_p) • File:Wikivoyage-Logo-v3-icon.svg Source: https://upload.wikimedia.org/wikipedia/commons/d/dd/Wikivoyage-Logo-v3-icon.svg License: CC BY-SA 3.0 Contributors: Own work Original artist: AleXXw • File:Wiktionary-logo-v2.svg Source: https://upload.wikimedia.org/wikipedia/commons/0/06/Wiktionary-logo-v2.svg License: CC BYSA 4.0 Contributors: Own work Original artist: Dan Polansky based on work currently attributed to Wikimedia Foundation but originally created by Smurrayinchester • File:World_map_green.png Source: https://upload.wikimedia.org/wikipedia/commons/9/95/World_map_green.png License: CC-BYSA-3.0 Contributors: http://upload.wikimedia.org/wikipedia/commons/archive/c/cf/20051110080552!A_large_blank_world_map_with_ oceans_marked_in_blue.PNG Original artist: Derivative work: Gaaarg • File:Yellow_Arrow_Down.png Source: https://upload.wikimedia.org/wikipedia/commons/0/0c/Yellow_Arrow_Down.png License: Public domain Contributors: Own work Original artist: User:Primate • File:Łukasz_Watzenrode.jpeg Source: https://upload.wikimedia.org/wikipedia/commons/0/01/%C5%81ukasz_Watzenrode.jpeg License: Public domain Contributors: www-groups.dcs.st-and.ac.uk Original artist: Unknown<a href='//www.wikidata.org/wiki/Q4233718' title='wikidata:Q4233718'><img alt='wikidata:Q4233718' src='https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/ Wikidata-logo.svg/20px-Wikidata-logo.svg.png' width='20' height='11' srcset='https://upload.wikimedia.org/wikipedia/commons/ thumb/f/ff/Wikidata-logo.svg/30px-Wikidata-logo.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/ Wikidata-logo.svg/40px-Wikidata-logo.svg.png 2x' data-file-width='1050' data-file-height='590' /></a> | • Creative Commons Attribution-Share Alike 3.0 }}


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