21st century astronomy the solar system fifth edition test bank chapter 13 by asmacandy

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Chapter 13: Taking the Measure of Stars LEARNING OBJECTIVES Define the bold-faced vocabulary terms within the chapter. 13.1 Astronomers Can Measure the Distance, Brightness, and Luminosity of Stars Illustrate how parallax is used to measure the distance to nearby stars. Multiple Choice: 1, 2, 3, 4, 6, 7, 8, 9, 10 Short Answer: 1, 2, 5

Relate luminosity, brightness, and distance. Multiple Choice: 11, 12, 13, 14, 15 Short Answer: 3 13.2 Astronomers Can Determine the Temperature, Size, and Composition of Stars Explain how the spectrum or color of a star is used to determine its temperature. Multiple Choice: 18, 23, 24, 25 Short Answer: 8, 9, 10 List the spectral types of stars in order of decreasing temperature. Multiple Choice: 26 Explain why stars of different temperatures have different spectral lines. Multiple Choice: 20, 22, 31 Short Answer: 11 Relate the spectral type of a star to its temperature and size. Multiple Choice: 19, 27, 28, 29, 30, 35, 36, 40 Short Answer: 13 Illustrate how a stellar spectrum reveals the star’s chemical composition. Multiple Choice: 21, 32, 33, 34 Short Answer: 12 13.3 Measuring the Masses of Stars in Binary Systems Show how Kepler’s laws and orbital velocities are used to determine the masses of binary stars. Multiple Choice: 42, 45, 46, 48, 51 Short Answer: 20 Differentiate between the observational information and methods used to determine stellar

masses in visual binaries, eclipsing binaries, and spectroscopic binaries. Multiple Choice: 44, 49, 50 Short Answer: 18, 19, 21 13.4 The Hertzsprung-Russell Diagram Is the Key to Understanding Stars Define the axes of the H-R diagram, and the direction in which each axis increases. Multiple Choice: 52, 53, 60 Short Answer: 28 Compare the temperature, luminosity, spectral type, color, and size of stars at different positions on the H-R diagram. Multiple Choice: 54, 55, 56, 57, 62 Short Answer: 15, 27 Illustrate how the H-R diagram is used to determine the distance to a star. Explain how the luminosity class of a star effects the use of spectroscopic parallax. Short Answer: 24, 25, 26 Use the mass-luminosity relationship to determine the luminosity of main-sequence stars. Multiple Choice: 61, 64, 65, 66, 67, 68, 69 Short Answer: 22, 23, 29, 30 Relate how common main-sequence stars are relative to other stars in the galaxy. Multiple Choice: 58, 59 Short Answer: 31 Compare and contrast the habitable zones around different types of stars. Multiple Choice: 63, 70 Short Answer: 32

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Working It Out 13.1 Compute the distance of a star given its parallax. Multiple Choice: 5 Short Answer: 4 Working It Out 13.2 Relate magnitude to the brightness of a star. Multiple Choice: 16, 17 Short Answer: 6, 7 Compare and contrast apparent and absolute magnitude. Working It Out 13.3 Use the Stefan-Boltzmann law to find the size of a star from its temperature and luminosity. Multiple Choice: 37, 38, 39 Short Answer: 14 Working It Out 13.4 Use Keplerâ&#x20AC;&#x2122;s Laws and orbital velocities to measure the masses of binary stars. Multiple Choice: 41, 43, 47 Short Answer: 16, 17 MULTIPLE CHOICE 1. What advantage do you gain by having two eyes that are separated on your face, rather than being very close together? a. better collecting area, which allows you to see dimmer objects b. double vision, which allows you to see multiple objects at once c. color vision, which allows you to determine temperatures

d. stereoscopic vision, which allows you to determine distances e. better magnification, which allows you to see smaller objects ANS: D

DIF: Medium

REF: Section 13.1

MSC: Understanding OBJ: Illustrate how parallax is used to measure the distance to nearby stars. 2. To measure the parallax of the most distant stars measurable, we would make two measurements of the star’s position on the sky separated by a. 6 hours. b. 12 hours. c. 24 hours. d. 6 months. e. 12 months. ANS: D

DIF: Easy

REF: Section 13.1

MSC: Understanding OBJ: Illustrate how parallax is used to measure the distance to nearby stars. 3. Parallax is used to measure a star’s a. distance, b. velocity, c. luminosity, d. mass, e. radius, ANS: A

DIF: Easy

REF: Section 13.1

MSC: Understanding

OBJ: Illustrate how parallax is used to measure the distance to nearby stars. 4. How is the distance to a star related to its parallax? a. Distance is directly proportional to parallax. b. Distance is inversely proportional to parallax. c. Distance is directly proportional to parallax squared. d. Distance is inversely proportional to parallax squared. e. Distance and parallax are not related to each other at all. ANS: B

DIF: Medium

REF: Section 13.1

MSC: Understanding OBJ: Illustrate how parallax is used to measure the distance to nearby stars. 5. If a star’s measured parallax is 0.2 arcsec, what is its distance? a. 2 pc b. 5 pc c. 20 pc d. 40 pc e. 50 pc ANS: B

DIF: Medium

REF: Working It Out 13.1

MSC: Applying OBJ: Compute the distance of a star given its parallax. 6. If a star’s distance is 10 pc, what is its parallax? a. 0.01 arcsec b. 0.05 arcsec c. 0.1 arcsec

d. 0.5 arcsec e. 1 arcsec ANS: C

DIF: Medium

REF: Section 13.1

MSC: Applying OBJ: Illustrate how parallax is used to measure the distance to nearby stars. 7. How many arcseconds are there in 1 degree? a. 60 b. 360 c. 3,600 d. 6,000 e. 36,000 ANS: C

DIF: Easy

REF: Section 13.1

MSC: Remembering OBJ: Illustrate how parallax is used to measure the distance to nearby stars. 8. With today’s advanced technology, what is the maximum distance to which we can measure a star’s distance using its parallax? a. about 100,000 parsecs b. about 10,000 parsecs c. about 1000 parsecs d. about 100 parsecs ANS: C

DIF: Easy

REF: Section 13.1

MSC: Applying OBJ: Illustrate how parallax is used to measure the distance to nearby stars.

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9. A parsec is a measure of a. time. b. size. c. distance. d. both b. and c. ANS: D

DIF: Medium

REF: Section 13.1

MSC: Remembering OBJ: Illustrate how parallax is used to measure the distance to nearby stars. 10. Stars with a larger brightness must be a. closer to us than fainter stars. b. larger in size than fainter stars. c. intrinsically brighter than fainter stars. d. any combination of the above. ANS: D

DIF: Easy

REF: Section 13.1

MSC: Remembering OBJ: Illustrate how parallax is used to measure the distance to nearby stars. 11. The absolute magnitude of a star is a measure of its a. luminosity. b. composition. c. distance. d. color. ANS: A

DIF: Medium

REF: Section 13.1

MSC: Remembering

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OBJ: Relate luminosity, brightness, and distance. 12. Star A and star B appear equally bright, but star A is twice as far away from us as star B. Which of the following is true? a. Star A is twice as luminous as star B. b. Star A is four times as luminous as star B. c. Star B is twice as luminous as star A. d. Star B is four times as luminous as star B. e. Star A and star B have the same luminosity because they have the same brightness. ANS: B

DIF: Medium

REF: Section 13.1

MSC: Applying OBJ: Relate luminosity, brightness, and distance. 13. Two main-sequence stars have the same temperature. If star A is four times brighter than star B, then a. star B is two times farther away than star A. b. star B is four times farther away than star A. c. star B is eight times farther away than star A. d. star B and star A lie at the same distance from us. e. it is impossible to determine their relative distances from the information given. ANS: A

DIF: Medium

REF: Section 13.1

MSC: Applying OBJ: Relate luminosity, brightness, and distance. 14. What is the difference between brightness and luminosity? a. These are different names for the same property.

b. Luminosity is how much light we see from a star; brightness is how much light it emits. c. Brightness is how much light we see from a star; luminosity is how much light it emits. d. Luminosity measures size; brightness measures temperature. e. Brightness measure size; luminosity measures temperature. ANS: C

DIF: Easy

REF: Section 13.1

MSC: Understanding OBJ: Relate luminosity, brightness, and distance. 15. Star A is a red star. Star B is a blue star. You are able to determine that both stars are the same size. Which star is brighter? a. Star A is brighter. b. Star B is brighter. c. They have the same brightness. d. We also need to know the distance of the stars to determine their brightness. e. Color is not related to brightness at all. ANS: D

DIF: Medium

REF: Section 13.1

MSC: Applying OBJ: Relate luminosity, brightness, and distance. 16. The star named Capella has an apparent magnitude of 0, while the star named Polaris has an apparent magnitude of 2. This means that Capella is _________ than Polaris. a. 18 times fainter b. 6 times fainter c. 2 times fainter d. 2 times brighter

e. 6 times brighter ANS: E

DIF: Medium

REF: Working It Out 13.2

MSC: Applying OBJ: Relate magnitude to the brightness of a star. 17. Star A and star B both have the same temperature but different sizes and distances. As a result, star A is more luminous than star B, but star B is brighter than star A. Which of these statements about the absolute and apparent magnitudes of the two stars is correct? a. Star A has a larger apparent magnitude and a larger absolute magnitude. b. Star A has a larger apparent magnitude, while star B has a larger absolute magnitude. c. Star B has a larger apparent magnitude and a larger absolute magnitude. d. Star B has a larger apparent magnitude, while star A has a larger absolute magnitude. e. Both stars have the same apparent and absolute magnitudes. ANS: B

DIF: Medium

REF: Working It Out 13.2

MSC: Applying OBJ: Relate magnitude to the brightness of a star. 18. You observe two stars in a visual binary system using a blue filter that is centered at a wavelength of 550 nm and a red filter that is centered at a wavelength of 650 nm. Star A has a temperature of 10,000 K, while star B has a temperature of 4000 K, and you know that both stars are the same size. Which star will be the brightest in each filter? a. Star A is the brightest in the blue filter, and star B is the brightest in the red filter. b. Star B is the brightest in the blue filter, and star A is the brightest in the red filter. c. Star A is the brightest in both filters. d. Star B is the brightest in both filters.

e. Both stars have the same brightness in each filter. ANS: C

DIF: Difficult

REF: Section 13.2

MSC: Applying OBJ: Explain how the spectrum or color of a star is used to determine its temperature. 19. Stars that have spectral type B ___________ in temperature compared with stars that have spectral type M. a. are cooler b. are hotter c. are the same d. are sometimes hotter and sometimes cooler ANS: B

DIF: Medium

REF: Section 13.2

MSC: Remembering OBJ: Relate the spectral type of a star to its temperature. 20. Which spectral type has the strongest hydrogen absorption lines? a. O b. B c. A d. M ANS: C

DIF: Medium

REF: Section 13.2

MSC: Remembering OBJ: Explain why stars of different temperatures have different spectral lines. 21. Which of the following is not directly measurable from the absorption lines of a star? a. the surface temperature of the star

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b. the identity of an atom producing a given absorption line c. the ionization stage of the atom producing a given absorption line d. the distance to the star ANS: D

DIF: Medium

REF: Section 13.2

MSC: Understanding OBJ: Illustrate how a stellar spectrum reveals the starâ&#x20AC;&#x2122;s chemical composition. 22. Which stars show the largest amount of absorption from molecules such as TiO and CN? a. the least massive main-sequence stars b. the most massive main-sequence stars c. only main-sequence stars with masses close to 1 solar mass d. only red giant stars ANS: A

DIF: Difficult

REF: Section 13.2

MSC: Remembering OBJ: Explain why stars of different temperatures have different spectral lines. 23. Star A is a red star. Star B is a blue star. Which star is hotter? a. Star A is hotter. b. Star B is hotter. c. They are the same temperature. d. We also need to know the luminosities of the stars to determine their temperatures. e. Color is not related to temperature at all. ANS: B

DIF: Easy

REF: Section 13.2

MSC: Applying OBJ: Explain how the spectrum or color of a star is used to determine its temperature.

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24. Star A is a red star. Star B is a blue star. You are able to determine that both stars are the same size. Which star is more luminous? a. Star A is more luminous. b. Star B is more luminous. c. They have the same luminosities. d. We also need to know the distance of the stars to determine their luminosity. e. We cannot tell because color is not related to luminosity. ANS: B

DIF: Easy

REF: Section 13.2

MSC: Applying OBJ: Explain how the spectrum or color of a star is used to determine its temperature. 25. What type of spectrum do most stars produce? a. an absorption spectrum on top of a blackbody spectrum b. an emission spectrum on top of a blackbody spectrum c. an absorption spectrum on top of an emission spectrum d. a pure emission spectrum e. a pure blackbody spectrum ANS: A

DIF: Easy

REF: Section 13.2

MSC: Remembering OBJ: Explain how the spectrum or color of a star is used to determine its temperature. 26. Which sequence correctly lists the spectral classes of stars in order from hottest to coolest? a. A B F G K M O b. O A B G F M K c. A F O B M G K

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d. O B A F G K M e. M K G F A B O ANS: D

DIF: Medium

REF: Section 13.2

MSC: Remembering OBJ: List the spectral types of stars in order of decreasing temperature. 27. The spectral class of a star is related to its a. luminosity. b. brightness. c. radius. d. mass. e. temperature. ANS: E

DIF: Easy

REF: Section 13.2

MSC: Remembering OBJ: Relate the spectral type of a star to its temperature and size. 28. What spectral class is the Sun? a. A0 b. B7 c. F5 d. M3 e. G2 ANS: E

DIF: Easy

REF: Section 13.2

MSC: Remembering OBJ: Relate the spectral type of a star to its temperature and size.

29. Two stars with similar temperatures but different sizes will have a. similar spectral types but different luminosities. b. similar luminosities but different brightnesses. c. similar brightnesses but different distances. d. similar distances but different masses. e. similar masses but different spectral types. ANS: A

DIF: Medium

REF: Section 13.2

MSC: Applying OBJ: Relate the spectral type of a star to its temperature and size. 30. A star classified as a K0III star is a. a giant that is cooler than the Sun. b. a supergiant that is hotter than the Sun. c. a main-sequence star that is hotter than the Sun. d. a subgiant that is cooler than the Sun. e. a dwarf that is hotter than the Sun. ANS: A

DIF: Difficult

REF: Section 13.4

MSC: Remembering OBJ: Relate the spectral type of a star to its temperature and size. 31. Why do O- and B-type stars have weaker hydrogen absorption lines than A-type stars? a. O- and B-type stars are cooler than A-type stars. b. O- and B-type stars are smaller than A-type stars. c. A larger fraction of hydrogen atoms in O- and B-type stars is ionized. d. O- and B-type stars have converted much more of their hydrogen into heavier elements.

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e. A-type stars have a higher mass than O- and B-type stars, so they have more hydrogen. ANS: C

DIF: Difficult

REF: Section 13.2

MSC: Understanding OBJ: Explain why stars of different temperatures have different spectral lines. 32. When astronomers refer to “heavy elements,” which elements are they talking about? a. all elements b. all elements more massive than hydrogen c. all elements more massive than helium d. all elements more massive than carbon e. all elements more massive than iron ANS: C

DIF: Easy

REF: Section 13.2

MSC: Remembering OBJ: Illustrate how a stellar spectrum reveals the star’s chemical composition. 33. Stars are made mostly of a. helium. b. oxygen. c. hydrogen. d. nitrogen. e. carbon. ANS: C

DIF: Easy

REF: Section 13.2

MSC: Remembering OBJ: Illustrate how a stellar spectrum reveals the star’s chemical composition. 34. The fraction of the Sun’s mass that is made of heavy elements is

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a. 0.5 percent. b. 2 percent. c. 10 percent. d. 20 percent. e. 50 percent. ANS: B

DIF: Medium

REF: Section 13.2

MSC: Remembering OBJ: Illustrate how a stellar spectrum reveals the starâ&#x20AC;&#x2122;s chemical composition. 35. If we know the temperature and luminosity of a star, we can also calculate its a. radius. b. mass. c. chemical composition. d. brightness. e. all of the above ANS: A

DIF: Easy

REF: Section 13.2

MSC: Applying OBJ: Relate the spectral type of a star to its temperature and size. 36. Star C is a red star. Star D is a blue star. Which has a larger radius? a. Star C has a larger radius. b. Star D has a larger radius. c. Stars C and D have the same radius. d. We also need to know the luminosities of the stars to determine their radii. e. We cannot determine the radii because color is not related to the radius.

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ANS: D

DIF: Medium

REF: Section 13.2

MSC: Applying OBJ: Relate the spectral type of a star to its temperature and size. 37. Star E is the same temperature as star F, but star E is four times as luminous as star F. How do the radii of the stars compare? a. The radius of star E is twice that of star F. b. The radius of star E is four times that of star F. c. The radius of star F is twice that of star E. d. The radius of star F is four times that of star E. e. The radii are the same length. ANS: A

DIF: Difficult

REF: Working It Out 13.3

MSC: Applying OBJ: Use the Stefan-Boltzmann law to find the size of a star from its temperature and luminosity. 38. If star A has a temperature that is twice as hot as the Sun, but it has the same luminosity as the Sun, the diameter of star A must be _________ times the diameter of the Sun. a. 16 b. 4 c. 2 d.

Q u ic k T im e ™ a n d a d e c o mp re s s o r a re n e e d e d to s e e th is p ic tu re .

ANS: E

DIF: Difficult

REF: Working It Out 13.3

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MSC: Applying OBJ: Use the Stefan-Boltzmann law to find the size of a star from its temperature and luminosity. 39. The bright star named Rigel has a luminosity of 66,000 L⊙and a temperature of 11,000 K. What is its radius? Note that the temperature of the Sun is 5,800 K. a. 5 R⊙ b. 30 R⊙ c. 70 R⊙ d. 135 R⊙ e. 190 R⊙ ANS: C

DIF: Difficult

REF: Working It Out 13.3

MSC: Applying OBJ: Use the Stefan-Boltzmann law to find the size of a star from its temperature and luminosity. 40. Which stars are the most common? a. Stars with a mass and a radius larger than the Sun’s are the most common. b. Stars with a smaller mass and radius than the Sun’s are most common. c. Stars with a mass larger than the Sun’s and a radius smaller than the Sun’s are the most common. d. Stars with a mass smaller than the Sun’s and a radius larger than the Sun’s are the most common. e. All of the above are equally common. ANS: B

DIF: Easy

MSC: Remembering OBJ: Relate the spectral type of a star to its temperature and size. 41. Star X and star Y are 5 AU apart from each other. Star X is four times as massive as star Y. The center of mass of this system is _________ AU away from star X and _________ AU away from star Y. a. 3; 2 b. 2; 3 c. 2.5; 2.5 d. 1; 4 e. 4; 1 ANS: D

DIF: Difficult

REF: Working It Out 13.4

MSC: Applying OBJ: Use Kepler’s Laws and orbital velocities to measure the masses of binary stars. 42. The faster-moving star in a binary is the a. less massive star. b. more massive star. c. smaller radius star. d. larger radius star. e. lower temperature star. ANS: A

DIF: Medium

REF: Section 13.3

MSC: Applying OBJ: Show how Kepler’s laws and orbital velocities are used to determine the masses of binary stars.

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43. In a binary star system that contains stars with 2M⊙ and 1M⊙, the velocity of the 2M⊙ star will be _________ times the velocity of the 1M⊙ star. a. 0.2 b. 0.5 c. 1 d. 2 e. 3 ANS: B

DIF: Medium

REF: Working It Out 13.4

MSC: Applying OBJ: Use Kepler’s Laws and orbital velocities to measure the masses of binary stars. 44. Which of the following properties are NOT useful in determining the masses of stars in a typical binary system? a. The period of the orbits of the two stars is not useful. b. The average separation between the two stars is not useful. c. The radii of the two stars are not useful. d. The velocities of the two stars are not useful. e. All of the above are useful for determining the masses of stars in a binary. ANS: C

DIF: Medium

REF: Section 13.3

MSC: Applying OBJ: Differentiate between the observational information and methods used to determine stellar masses in visual binaries, eclipsing binaries, and spectroscopic binaries. 45. Binary star systems are extremely useful in studying stars because they allow us to determine

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a. the stars’ temperatures. b. the stars’ sizes. c. the stars’ masses. d. the stars’ distances. ANS: C

DIF: Easy

REF: Section 13.3

MSC: Understanding OBJ: Show how Kepler’s laws and orbital velocities are used to determine the masses of binary stars. 46. Which of the following methods is not useful for determining masses of a binary star system having an orbital plane entirely in the plane of the sky as seen from Earth? a. eclipses b. the Doppler effect c. measuring the wobble of a visual binary’s path d. both a. and b. ANS: D

DIF: Medium

REF: Section 13.3

MSC: Understanding OBJ: Show how Kepler’s laws and orbital velocities are used to determine the masses of binary stars. 47. You discover a binary star system in which star A has a velocity of 10 km/s and star B has a velocity of 30 km/s. If you study the system further and find out that the orbital period is 30 days and the orbital separation is a constant 0.3 AU, then what are the masses of stars A and B? a. Star A is 3M⊙, and star B is 1M⊙.

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b. Star A is 1M⊙, and star B is 0.3M⊙. c. Star A is 6M⊙, and star B is 2M⊙. d. Star A is 2M⊙, and star B is 0.5M⊙. e. Star A is 0.3M⊙, and star B is 1M⊙. ANS: A DIF: Difficult REF: Working It Out 13.4 MSC: Applying OBJ: Use Kepler’s Laws and orbital velocities to measure the masses of binary stars. 48. Astronomers can measure the speed of the stars in a binary system by measuring the _________ of the stars. a. temperatures b. luminosities c. distance d. colors e. spectra ANS: E

DIF: Easy

REF: Section 13.3

MSC: Remembering OBJ: Show how Kepler’s laws and orbital velocities are used to determine the masses of binary stars. 49. For which type of binary system are astronomers able to resolve each of the two stars individually? a. eclipsing binary b. spectroscopic binary c. visual binary Copyright © 2015 Pearson Canada Inc.

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d. binaries in which the two stars have the same mass e. binaries in which the two stars have the same luminosity ANS: C

DIF: Easy

REF: Section 13.3

MSC: Remembering OBJ: Differentiate between the observational information and methods used to determine stellar masses in visual binaries, eclipsing binaries, and spectroscopic binaries. 50. Eclipsing binary systems a. orbit in the plane of the sky. b. exhibit large radial velocity shifts. c. contain equal mass stars. d. contain stars that pass in front of one another during their orbit. e. contain stars that can be resolved as two separate stars. ANS: D

DIF: Medium

REF: Section 13.3

MSC: Remembering OBJ: Differentiate between the observational information and methods used to determine stellar masses in visual binaries, eclipsing binaries, and spectroscopic binaries. 51. Main-sequence stars range in mass from approximately a. 0.5 to 10 M⊙. b. 0.08 to 150 M⊙. c. 1 to 100 M⊙. d. to 75 M⊙. e. 5 to 50 M⊙. ANS: B

DIF: Easy

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MSC: Remembering OBJ: Show how Keplerâ&#x20AC;&#x2122;s laws and orbital velocities are used to determine the masses of binary stars. 52. The Hertzsprung-Russell diagram is a graph of _________ for stars. a. mass versus brightness b. size versus mass c. luminosity versus temperature d. mass versus spectral type e. luminosity versus brightness ANS: C

DIF: Easy

REF: Section 13.4

MSC: Remembering OBJ: Define the axes of the H-R diagram, and the direction in which each axis increases. 53. Any of the following properties could be plotted on the horizontal axis of an H-R diagram except for: a. Color b. Luminosity c. Temperature d. Spectral class e. All of the above are plotted on the horizontal axis of an H-R diagram. ANS: B

DIF: Easy

REF: Section 13.4

MSC: Remembering OBJ: Define the axes of the H-R diagram, and the direction in which each axis increases. 54. The figure below shows an H-R diagram, with five stars labeled A through E. Which star

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has the highest temperature? a. A b. B c. C d. D e. E ANS: A

DIF: Easy

REF: Section 13.4

MSC: Applying OBJ: Compare the temperature, luminosity, spectral type, color, and size of stars at different positions on the H-R diagram. 55. The figure below shows an H-R diagram, with five stars labeled A through E. Which star has the highest luminosity? a. A b. B c. C d. D e. E ANS: B

DIF: Easy

REF: Section 13.4

MSC: Applying OBJ: Compare the temperature, luminosity, spectral type, color, and size of stars at different positions on the H-R diagram. 56. The figure below shows an H-R diagram, with five stars labeled A through E. Which star has the smallest radius?

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a. A b. B c. C d. D e. E ANS: D

DIF: Medium

REF: Section 13.4

MSC: Applying OBJ: Compare the temperature, luminosity, spectral type, color, and size of stars at different positions on the H-R diagram. 57. On a typical H-R diagram, where are the stars with the largest radii located? a. in the upper left corner b. in the upper right corner c. in the center d. in the lower left corner e. in the lower right corner ANS: B

DIF: Medium

REF: Section 13.4

MSC: Applying OBJ: Compare the temperature, luminosity, spectral type, color, and size of stars at different positions on the H-R diagram. 58. What type of star is most common in the solar neighborhood? a. subgiants b. supergiant c. white dwarf

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d. giant e. main-sequence ANS: E

DIF: Easy

REF: Section 13.4

MSC: Remembering OBJ: Relate how common main-sequence stars are relative to other stars in the galaxy. 59. Roughly what percentage of stars in our galaxy are main-sequence stars? a. 10 percent b. 25 percent c. 50 percent d. 75 percent e. 90 percent ANS: E

DIF: Medium

REF: Section 13.4

MSC: Remembering OBJ: Relate how common main-sequence stars are relative to other stars in the galaxy. 60. A star’s position in the H-R diagram is determined by its a. temperature and size. b. temperature and distance. c. brightness and size. d. mass and distance. ANS: A

DIF: Difficult

REF: Section 13.4

MSC: Understanding OBJ: Define the axes of the H-R diagram, and the direction in which each axis increases. 61. A star’s location on the main sequence is determined entirely by its

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a. mass. b. composition. c. distance. d. size. ANS: A

DIF: Medium

REF: Section 13.4

MSC: Understanding OBJ: Use the mass-luminosity relationship to determine the luminosity of main-sequence stars. 62. The stars that have the largest radii are classified as a. main sequence stars. b. blue supergiants. c. red supergiants. d. white dwarfs. ANS: C

DIF: Easy

REF: Section 13.4

MSC: Understanding OBJ: Compare the temperature, luminosity, spectral type, color, and size of stars at different positions on the H-R diagram. 63. In which region of an H-R diagram would you find the main-sequence stars with the widest habitable zones? a. upper left b. upper right c. center d. lower left

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e. lower right ANS: A

DIF: Medium

REF: Section 13.4

MSC: Applying OBJ: Compare and contrast the habitable zones around different types of stars. 64. The figure below shows an H-R diagram, with five stars labeled A through E. Which of the main-sequence stars has the smallest mass? a. A b. B c. C d. D e. E ANS: E

DIF: Medium

REF: Section 13.4

MSC: Applying OBJ: Use the mass-luminosity relationship to determine the luminosity of main-sequence stars. 65. What is the approximate luminosity of a 5 M⊙ main-sequence star? a. 50 L⊙ b. 80 L⊙ c. 150 L⊙ d. 280 L⊙ e. 510 L⊙ ANS: D

DIF: Medium

REF: Section 13.4

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MSC: Applying OBJ: Use the mass-luminosity relationship to determine the luminosity of main-sequence stars. 66. What is the approximate luminosity of a 0.5 M⊙main-sequence star? a. 0.09 L⊙ b. 0.01 L⊙ c. 0.2 L⊙ d. 0.5 L⊙ e. 0.7 L⊙ ANS: A

DIF: Medium

REF: Section 13.4

MSC: Applying OBJ: Use the mass-luminosity relationship to determine the luminosity of main-sequence stars. 67. The one property of a main-sequence star that determines all its other properties is its a. luminosity. b. mass. c. temperature. d. spectral type. e. brightness. ANS: B

DIF: Easy

REF: Section 13.4

MSC: Understanding OBJ: Use the mass-luminosity relationship to determine the luminosity of main-sequence

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stars. 68. The stars that have the largest radii are classified as a. giants. b. ultragiants. c. supergiants. d. megagiants. e. supernovae. ANS: C

DIF: Easy

REF: Section 13.4

MSC: Remembering OBJ: Use the mass-luminosity relationship to determine the luminosity of main-sequence stars. 69. The brightest stars in the sky also tend to be a. the highest-mass stars. b. the hottest stars in the sky. c. very near to us (within 5 parsecs). d. very luminous. e. all of the above ANS: D

DIF: Difficult

REF: Section 13.4

MSC: Applying OBJ: Use the mass-luminosity relationship to determine the luminosity of main-sequence stars. 70. The habitable zone for the Sun covers the area that is between _________ from the Sun. a. 0 to 0.8 AU

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b. 0.5 to 10 AU c. 1.2 to 4.2 AU d. 0.9 to 1.4 AU e. 0.2 to 10.2 AU ANS: D

DIF: Medium

REF: Section 13.4

MSC: Remembering OBJ: Compare and contrast the habitable zones around different types of stars . SHORT ANSWER 1. If a star’s parallax is measured using identical telescopes, one on Earth and the other on Mars, which planet’s telescope would measure the biggest parallax? Explain your answer. ANS: The telescope on Mars would measure a larger parallax. Because Mars has a larger orbit than the Earth, it will have a greater distance between the two parallax observations. This greater distance between observations for the telescope on Mars will lead to a greater apparent motion of a star. DIF: Difficult REF: Section 13.1 MSC: Understanding OBJ: Illustrate how parallax is used to measure the distance to nearby stars. 2. If you want to measure the distance to a star via measuring its parallax, how far apart should your observations of the star ideally be, and why? ANS: Ideally one would want to observe the star at two positions as far apart as possible for ease in measuring its parallax. For Earth, this means your observations should be when the Earth is on opposite sides of the Sun, such that the two measurement points are separated by 2 AU, the diameter of Earth’s orbit. This occurs for the two points that are six months apart

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from one another. DIF: Medium REF: Section 13.1 MSC: Understanding OBJ: Illustrate how parallax is used to measure the distance to nearby stars. 3. Star A is exactly the same color as star B and appears equally bright. Through stellar parallax measurements, we find that star B is twice as far away from us as star A. Determine which star has the largest radius and how much larger it is. ANS: For stars of equal brightness, luminosity is directly proportional to their distance squared. If star B is twice as far away, then it must be four times as luminous as star A. Second, if the two stars are exactly the same color, then they are also the same temperature. For stars of the same temperature, luminosity is directly proportional to the square of the radius. If star B is four times as luminous, it must be twice as big as star A. DIF: Difficult REF: Section 13.1 MSC: Applying OBJ: Relate luminosity, brightness, and distance. 4. A star with a stellar parallax of 0.025 arcsecond has a distance of how many parsecs? ANS: The inverse of stellar parallax given in arcsec-onds is its distance in parsecs:

Quic kTime™ and a dec ompre s s or are needed to s ee this pic ture .

arcseconds = 40 parsecs. DIF: Medium REF: Working It Out 13.1 MSC: Applying OBJ: Compute the distance of a star given its parallax. 5. How is the unit of length known as a parsec defined? ANS: The parsec is defined such that an object at a distance of 1 parsec has a parallax

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exactly equal to 1 arcsecond. DIF: Easy REF: Section 13.1 MSC: Remembering OBJ: Illustrate how parallax is used to measure the distance to nearby stars. 6. Rigel is a star with an apparent magnitude of +0.1, and Betelgeuse is a star with an apparent magnitude of +0.4. Which star appears brighter, and what is the ratio of their brightnesses? ANS: Rigel is brighter than Betelgeuse by a factor of 2.512(0.4–0.1) = 1.32. Thus, Rigel is 32 percent brighter than Betelgeuse. DIF: Difficult REF: Working It Out 13.2 MSC: Applying OBJ: Relate magnitude to the brightness of a star. 7. If the Hubble space telescope can see stars as faint as magnitude 27, how much fainter are these stars than the faintest ones you can see in a very dark night sky, which have magnitude 6? ANS: The Hubble space telescope can see objects that are 2.512(27–6) = 2.5 × 108 = 250 million times fainter than the stars you can see in a dark night sky. DIF: Medium REF: Working It Out 13.2 MSC: Applying OBJ: Relate magnitude to the brightness of a star. 8. Explain how astronomers can use the blue and visible filters to determine the temperatures of stars. ANS: Astronomers compare the relative intensities of light measured through each filter. Stars with more blue than visual light are hotter, whereas stars with more visual than blue

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light are cooler. DIF: Easy REF: Section 13.2 MSC: Understanding OBJ: Explain how the spectrum or color of a star is used to determine its temperature. 9. The sequence of stellar spectral types is shown in the figure below. Explain why the hottest star (O5) has so little emission in the visible portion of the spectrum (450-700 nm), spectral types F-K show the most emission in the visible band, and still cooler stars (M type) once again show very little in the visible band. ANS: O stars are very hot blackbodies (40,000 K), so, based on Wien’s law, their emission peaks in the UV band, at wavelengths shorter than 350 nm. As a result, most of the light from O stars is not emitted in the visible band. On the other hand, the blackbody peak from stars of spectral type F-K (4000-7000 K) peaks in the visible band between 350 and 700 nm, so they are bright throughout the visible band. M stars (3,000 K), in contrast produce blackbody radiation peaking in the infrared band, at wavelengths longer than 700 nm. As a result, most of their emission is not visible to us. In addition, molecular absorption lines from species such as TiO in M stars absorb much of the emission in the optical. DIF: Difficult REF: Section 13.2 MS: Applying OBJ: Explain how the spectrum or color of a star is used to determine its temperature. 10. The blackbody spectra of a star with a temperature of 6000 K and a star with a temperature of 4000 K are shown in the figure below. An astronomer uses a telescope to observe each of these two stars in both the blue and red filters. The blue filter is centered at 450 nm, while the red filter is centered at 660 nm. For each of the two stars, indicate through which filter that star will be the brightest. Explain

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your answer. ANS: Looking at the blackbody curves, the 6000 K star emits more light at 450 nm than it does at 660 nm, so it will be brighter when using the blue filter than it will be when using the red filter. For the 4000 K star, the opposite is true, so it will appear brighter through the red filter than it will through the blue filter. DIF: Medium REF: Section 13.2 MSC: Applying OBJ: Explain how the spectrum or color of a star is used to determine its temperature. 11. What is the spectral type of star that has the strongest hydrogen absorption lines? Why do stars that are hotter than these have weaker hydrogen lines? ANS: The A-type star has the strongest hydrogen absorption lines in its spectra. O- and Btype stars are hotter than A stars, so the hydrogen in O and B stars becomes ionized. Electrons not in atoms do little absorbing, so the hydrogen absorption lines in O and B stars are weaker than those in A stars. DIF: Difficult REF: Section 13.2 MSC: Applying OBJ: Explain why stars of different temperatures have different spectral lines. 12. What are the two main chemical elements that make up the Sun? How much of the mass of the Sun is composed of elements other than these two? ANS: By mass, the Sun is made up of 74.5 percent hydrogen and 23.7 percent helium. All the other elements in the periodic table make up only about 2 percent of the mass of the Sun. DIF: Medium REF: Section 13.2

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MSC: Remembering OBJ: Illustrate how a stellar spectrum reveals the star’s chemical composition. 13. If we measure a star’s luminosity and temperature, what other property of the star can we calculate? Explain how. ANS: If we measure the luminosity L and temperature T of a star, then we can use the Stefan-Boltzmann law that says L/4 πR2 = σT4 to calculate the star’s radius R. DIF: Medium REF: Section 13.2 MSC: Applying OBJ: Relate the spectral type of a star to its temperature and size. 14. The bright star Arcturus has a luminosity of 210 L⊙ and a temperature of 4300 K. What is its radius? Note that the Sun has a temperature of 5800 K. ANS: Using the Stefan-Boltzmann law and solving for the radius we get

Comparing Arcturus to the Sun, we find

QuickTime™ and a decompressor are needed to see this picture.

Thus the radius of

Arcturus is 26 R⊙ DIF: Difficult REF: Working It Out 13.3 MSC: Applying OBJ: Use the Stefan-Boltzmann law to find the size of a star from its temperature and luminosity. 15. Star A emits its peak energy at a wavelength of 500 nm, and star B emits its peak energy at a wavelength of 750 nm. If both stars have the same radii, which star is hotter and by how much?

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ANS: By Wien’s law, the temperature of a star is inversely proportional to the wavelength

of its peak emission: λpeakA/λpeakB =

Qu ickTime™ and a d ecompressor are n eed ed t o see th is p ict u re.

. This means that star A is

Q u ic k T ime ™a n d a d e c o mp re s s o r a re n e e d e d o t s e e th is p ic u t re .

= 1.5 times hotter

than star B. DIF: Difficult REF: Section 13.2 MSC: Applying OBJ: Compare the temperature, luminosity, spectral type, color, and size of stars at different positions on the H-R diagram. 16. You observe a binary star system and find that star 1 has a velocity of 10 m/s while star 2 has a velocity of 35 m/s. What is the ratio of masses of the two stars (M1/M2)? ANS: The ratio of masses of stars in a binary system is inversely proportional to the ratio of velocities: M1/M2 = v2/v1 = (35 m/s)/(10 m/s) = 3.5. Therefore, star 1 is 3.5 times as massive as star 2. DIF: Medium REF: Working It Out 13.4 MSC: Applying OBJ: Use Kepler’s Laws and orbital velocities to measure the masses of binary stars. 17. You observe a binary star system and find that star 1 has a velocity of 20 m/s while star 2 has a velocity of 40 m/s. What is the ratio of masses of the two stars (M1/M2)? If you find that the separation of the two stars is 0.5 AU and the orbital period is 70 days, then what are the individual masses of the two stars? ANS: The ratio of masses of stars in a binary system is simply inversely proportional to the ratio of velocities: M1/M2 = v2/v1 = 40 m/s / 20 m/s = 2. Therefore, M1 = 2M2. Using Kepler’s third law, we can calculate the sum of the masses: Copyright © 2015 Pearson Canada Inc.

P = 70 days × 24 hr/day × 3,600 s/hr = 6.0 × 106 s (M1 + M2) = 4 π2A3/GP2 = 4π2 (0.5 × 1.5 × 1011 m)3 / (6.7 × 10−11 Nm2/kg × (6.0 × 106 s)2) (M1 + M2) = 6.9 × 1030 kg × 1 M⊙/2 × 1030 kg = 3.5 M⊙. Solving for the individual masses gives (2M2 + M2) = 3M2 = 3.5M⊙or M2 = 1.1 M⊙, and M1 = 2.2 M⊙. DIF: Difficult REF: Working It Out 13.4 MSC: Applying OBJ: Use Kepler’s Laws and orbital velocities to measure the masses of binary stars. 18. What is the physical difference between an eclipsing binary system and a spectroscopic binary system? ANS: The only real difference is the tilt of the stars’ orbits relative to the Earth’s position (also known as the inclination angle). For an eclipsing binary system, the stars are aligned in a way so that one star passes directly between the Earth and the other star. For a spectroscopic binary, the stars’ orbits do not line up exactly with the Earth’s position. DIF: Easy REF: Section 13.3 MSC: Understanding OBJ: Differentiate between the observational information and methods used to determine stellar masses in visual binaries, eclipsing binaries, and spectroscopic binaries. 19. The figure below shows the light curve of an eclipsing binary system consisting of two main sequence stars. The dip in observed light is stronger when the cooler star passes in front of the hotter star than when the cooler star is behind the hotter star. Why? ANS: Cooler main sequence stars are by definition also smaller than hotter main sequence stars, so they have a lower luminosity and contribute less to the combined light of the stars. Since we observe the combined light of the two stars (they can’t be resolved in the Copyright © 2015 Pearson Canada Inc.

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telescope), the cooler star passing in front of the hotter star causes a larger fraction of the total light to be blocked than when the cooler star passes behind the hotter star, so the corresponding dip is larger for the former than for the latter. DIF: Difficult REF: Section 13.3 MSC: Understanding OBJ: Differentiate between the observational information and methods used to determine stellar masses in visual binaries, eclipsing binaries, and spectroscopic binaries. 20. A main sequence star follows a circular orbit around its companion with a speed of 22 km/s. Its orbital period is 1.3 years. What is the radius of its orbit? ANS: We know that the circumference of a circle is 2πR, where R is its radius, while the velocity v of the star in a circular orbit is just distance / time, or v = 2πR / P, where P is its period. So solving this for R, we have R = Pv / 2π = (1.3 yr) × (3.15 × 107 s/yr) × (22 km/s) / 2π = 1.44×108 km. DIF: Difficult REF: Section 13.3 MSC: Applying OBJ: Show how Kepler’s laws and orbital velocities are used to determine the masses of binary stars. 21. Suppose you observe the visual binary pair Alpha Cen A and Alpha Cen B, as seen in the figure shown below. Assuming that it can be observed repeatedly over a period of time, what two orbital parameters can be measured from the image? ANS: The semi-major axis can be measured from the angular separation of the two stars, while the orbital period can be estimated by observing how long the binary takes to return to its original separation and orientation on the sky. Copyright © 2015 Pearson Canada Inc.

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DIF: Medium REF: Section 13.3 MSC: Applying OBJ: Differentiate between the observational information and methods used to determine stellar masses in visual binaries, eclipsing binaries, and spectroscopic binaries. 22. What is the main property of a main-sequence star that determines all its other properties? ANS: The star’s mass has the most effect on all its other properties. DIF: Easy REF: Section 13.4 MSC: Remembering OBJ: Use the mass-luminosity relationship to determine the luminosity of main-sequence stars. 23. When main-sequence stars are plotted on an HR diagram (luminosity vs. temperature), they fall along a swath running diagonally from the upper left to the lower right. Why don’t they fall in arbitrary locations on the HR diagram? ANS: The mass of a star determines both its temperature and radius, so arbitrary combinations of radius and temperature can’t occur. DIF: Difficult REF: Section 13.4 MSC: Understanding OBJ: Use the mass-luminosity relationship to determine the luminosity of main-sequence stars. 24. Explain how we can use spectroscopic parallax to determine the distance to a star farther away than a few hundred light-years. ANS: First, we can determine the temperature of the star based on its absorption line spectrum, as well as determine whether the star is a main-sequence star. If the star is a main-

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sequence star, and if we know the temperature of the star, we can simply read off its luminosity from the diagram. We then measure how bright the star appears and use the inverse square law of radiation to determine its distance. DIF: Medium REF: Section 13.4 MSC: Understanding OBJ: Explain how the luminosity class of a star affects the use of spectroscopic parallax. 25. Suppose you take images of star SBD 1256 in different filters and find that, by comparing the brightness of the star through the different filters, it’s an F5 star. You assume the star is on the main sequence (F5V), and then use the HR diagram to figure out that it’s at a distance of 120 parsecs. A few months later you take a spectrum of SBD 1256 and notice that its absorption lines are very narrow, indicating that it’s not an F5V main-sequence star but rather a giant F5III star. Explain how this now affects the distance estimate and why. ANS: Because the star is now found to be a giant, this means it’s intrinsically more luminous that it would be if it were on the main sequence. So to get the observed brightness of the star, it must now be farther away than 120 parsecs. DIF: Difficult REF: Section 13.4 MSC: Applying OBJ: Explain how the luminosity class of a star affects the use of spectroscopic parallax. 26. Suppose you take a spectrum of a yellow star and, based on the shape of its blackbody curve as well as its absorption lines, that it is of spectral type K3. However, you do not know its distance. How can you then determine whether it is a main-sequence star or a giant star? ANS: If it is a main-sequence star, it will have a radius smaller than that a giant star of the same temperature. The greater compactness of the star means it will have a higher surface

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gravity, so its absorption lines will be broader due to increased Doppler motion of the atoms in the stronger gravitational field. If it were a giant star, on the other hand, its absorption lines would be narrower due to its larger size and lower surface gravity. DIF: Difficult REF: Section 13.4 MSC: Understanding OBJ: Explain how the luminosity class of a star affects the use of spectroscopic parallax. 27. Imagine you are observing a nearby star. You know that it is a main-sequence star but don’t know anything else about it. If you had access to any telescope equipment you wanted, explain how you would determine this star’s temperature, luminosity, distance, and radius. ANS: You could measure the temperature either by determining its color using different filters, or by taking a spectrum to determine its spectral type. Once you know the color of a main-sequence star, you can use an H-R diagram to read off the luminosity of that temperature star. Then, since you know the luminosity, measuring the brightness of this star tells you the distance, using the equation B = L/(4πd 2). Alternatively, if the star was relatively nearby, you could measure the distance to it using parallax and then use the brightness equation to determine the luminosity. Finally, since you already know the temperature and luminosity of the star, you can use the Stefan-Boltzmann equation L = 4πR2σT4 to calculate its radius. DIF: Difficult REF: Section 13.4 MSC: Applying OBJ: Compare the temperature, luminosity, spectral type, color, and size of stars at different positions on the H-R diagram. 28. Along the main sequence, how do the luminosity, temperature, radius, and mass of stars

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change as you go from the upper-left to the lower-right corners of the H-R diagram? ANS: Stars near the upper-left end of the main sequence are very luminous, hot, large, and massive stars. Stars near the lower-right end of the main sequence are low-luminosity, cool, small, and low-mass stars. DIF: Medium REF: Section 13.4 MSC: Understanding OBJ: Define the axes of the H-R diagram, and the direction in which each axis increases. 29. Based on the mass-luminosity diagram for main sequence stars shown in the figure below, approximately how many more time luminous is a 25 M⊙ star compared with a 0.3 M⊙ star? ANS: From the graph, the luminosity of a 25 M⊙ star is approximately 104 L⊙, while that of a 0.3 M⊙ star is approximately 10-2 L⊙. Therefore the more massive star is 104 / 10-2 = 106 times more luminous that the less massive star. DIF: Medium REF: Section 13.4 MSC: Understanding OBJ: Use the mass-luminosity relationship to determine the luminosity of main-sequence stars. 30. Based on the figure shown below, approximately how many more time luminous is a mainsequence star having a radius of 10 R⊙ compared with a star having a radius of 1 R⊙? ANS: From the mass-radius graph, the mass of a star having a radius 10 R⊙ is approximately 25 M⊙. Turning now to the mass-luminosity graph, a 25 M⊙ star has a luminosity of approximately 104 L⊙. Doing this same procedure for the 1 R⊙ star, its mass must 1 M⊙, so that translates to a luminosity of 1 L⊙. The ratio of the two is 104L⊙/ 10 L⊙ = 104, so a main-

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sequence star of radius 10 R⊙is 10,000 times more luminous than the Sun. DIF: Difficult REF: Section 13.4 MSC: Understanding OBJ: Use the mass-luminosity relationship to determine the luminosity of main-sequence stars. 31. Based on the figure shown below, which shows the relative number of stars as a function of stellar luminosity, how common are stars having 0.01 L⊙ compared with those having a luminosity of 100 L⊙? ANS: Drawing a line vertically from the horizontal axis at 10-2 L⊙, the relative number of stars at that luminosity is 4 stars for every solar mass star. Similarly, drawing a line vertically from the horizontal axis at 100 L⊙, the relative number of stars at that luminosity is around 0.05 star for every solar mass star. The ratio of these is 4 / 0.05 = 80, so stars having a luminosity 1/100th that of the Sun are 80 times more common than those having a luminosity 100 times that of the Sun. DIF: Medium REF: Section 13.4 MSC: Understanding OBJ: Relate how common main-sequence stars are relative to other stars in the galaxy. 32. How does the size and distance of a habitable zone depend on the spectral type of the star? ANS: Habitable zones (distances from the star where water can exist as liquid) are both wider and farther from the star when it is hotter and narrower and closer to the star when the star is cooler. So the habitable zone narrows and moves closer to the star as one goes from spectral type O to spectral type M.

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DIF: Medium REF: Section 13.4 MSC: Applying OBJ: Compare and contrast the habitable zones around different types of stars.

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