Moonstruck
Georg Glaeser
Moonstruck The Interplay of Celestial Bodies in Pictures
Preface
5
The Moon really packs a punch You would be hard-pressed to find anyone who does not associate some romantic memories with our faithful companion, the Moon. On a mild full-moon night on the beach after a spectacular sunset, who could blame you for feeling a little moonstruck… The Moon can often be seen during the day, but it is usually in the evening when we start looking for the Moon on the opposite side of the setting Sun. However, we will only find it there on the days of full moon. Before the full moon, we can see the Moon rising in the early evening, before sunset. After full moon, the Moon rises with increasing delay – so much so that only night owls and early birds get to enjoy the stunning sight of the late The Moon in the middle and, to its left,
waning moon.
slightly higher up, the planet Jupiter.
What almost everyone “kind of” knows… We know some “facts” about the Moon, even if we cannot always explain why this is so: The Moon keeps pointing the same face towards us, it affects the ocean tides, and it can cause a solar eclipse. Many ancient civilisations worshipped not only sun gods but also moon gods. The Moon is flipped upside down in the Southern Hemisphere. So much for the “scientific” part. There are also anecdotes of people who experience more restless sleep during full moon and statistics suggesting that car accidents are more common in this period. According to folklore, you should cut your hair during new moon to make it grow more abundantly, but such claims do not stand up to scientific scrutiny. Facts and myths This book will provide a detailed examination of “facts” like the ones listed above. This book is not the right choice for those who seek esoteric wisdom or any other kind of scientifically unfounded knowledge of the Moon. There are already numerous books, calendars, and sources on the Internet offering information on the best lunar phases to repot your plants or cut apples to keep them fresh.
6 Let’s settle one thing right away: The author is a romantic scientist who is also quite “moonstruck”. However, he only believes in things that can be proven, and he aspires to comprehend things well enough to be able to explain them to a lay person. Who is this book for? Just from flipping through the pages of the book, you can tell that this book is (also) a picture book. So, it is definitely suitable for the visually inclined. Close-up shots of the Moon or atmospheric pictures of a romantic moonlit night will hardly leave anyone cold. If you already know a thing or two about the Moon and you would like to learn more about it, you are the ideal reader for this book. Here you will find explanations for various phenomena related to the Moon. If you are drawn to esotericism, you might find yourself vexed by this book at times, because it also aims to dismantle many things that are commonly said about the Moon. Even so, I hope that you will still enjoy the photographs… What else will you find in this book? This book will not limit itself to exploring those parts of the Moon that are visible from Earth. Occasionally, we will also have a look at the so-called far side of the Moon, which faces away from Earth, and at other moons which orbit other planets in our solar system (including dwarf planets, in the case of Pluto). So, you will also learn about the moons of Jupiter. Their discovery at the beginning of the 17th century was a breakthrough that helped confirm the heliocentric model of the universe. Moonstruck is conveniently structured on the double-page principle, which allows you to read the information preIs it the Sun or the Moon behind the clouds? To an observer on Earth, the two celestial bodies appear to have the same size. On a clear day, the Sun is, of course, many thousand times brighter, but when it is covered by clouds, it can be hard to tell if the disc in the photograph is the Sun or the Moon in its full splendour.
sented in this book in an (almost) random order. Even if you already know a little about maths and physics, some double pages might still make you think about the Moon in ways you had not contemplated before. The author hopes that even for readers who are already familiar with the subject, this book will hold some yet unknown insights. If you have no affinity for a particular topic, you can simply skip a double page without losing the thread.
7
Table of Contents 9
The Tidal Forces on Earth . . . . . . . . . .
72
10
The Rhythm of High and Low Tides . . . . . .
74
The “Composite” Full Moon . . . . . . . . .
12
Peculiarities of the Moon’s Motion
. . . . . .
76
Cloudy Atmosphere with the Moon . . . . . .
14
Lunar Precession . . . . . . . . . . . . . .
78
Half an Hour Before Sunset . . . . . . . . .
16
The Rotation of the Terminator . . . . . . . .
18
Looking toward the Sun? . . . . . . . . . . .
20
In Opposition . . . . . . . . . . . . . . . .
22
Full Moon Fascination . . . . . . . . . . . .
24
The “Wrong Inclination” of the Terminator . . .
26
The Sunlit Moon Lunar Phases . . . . . . . . . . . . . . . .
Eclipses and Distortions
81 . . . . . . .
82
The Moon’s Umbra . . . . . . . . . . . . .
84
The Distorted Sphere . . . . . . . . . . . .
86
Egg-Shaped Sunrises and Moonrises . . . . .
88
When the Full Moon Is Eclipsed . . . . . . .
90
29
At Dawn . . . . . . . . . . . . . . . . . .
92
Earth’s Self-Rotation . . . . . . . . . . . . .
30
The Moon’s Brightness
94
Earth’s Self-Rotation – Continued . . . . . . .
32
At Least the Moon Is Shining… . . . . . . . .
96
From East to West
. . . . . . . . . . . . .
34
Sun or Moon?
98
Looking North or South? . . . . . . . . . . .
36
Self-Rotation and Elliptical Orbits
How Long Does a Day on the Moon Last? . . .
38
Blue Moon . . . . . . . . . . . . . . . . .
40
The Temperature on the Moon . . . . . . . .
42
The Lunar Poles
44
. . . . . . . . . . . . . .
Kepler Ellipses and Free Fall
47
Rotation Direction in Our Solar System . . . .
48
Earth’s Obliquity and the Seasons
50
. . . .
Why 27 Days for One Orbit? . . . . . . . . .
The Solar Eclipse Phenomenon
. . . . . . . . . . .
. . . . . . . . . . . . . . .
The Moon’s Impact Underwater . . . . . . . 100 The Other Moons of Our Solar System
103
Where Did Our Moon Come From? . . . . . . 104 Magnetic Field on the Moon?
. . . . . . . . 106
The Moons of Jupiter . . . . . . . . . . . . 108 How Many Moons Does (Did) Mars Have? . . . 110 Titan – a Moon Similar to Earth . . . . . . . . 112 Dwarf Planets – Smaller Than Our Moon . . . 114
Where Is the Moon in the Sky? . . . . . . . .
52 The Moon in Different Cultures 117 54 Stonehenge – Inspired by the Moon? . . . . . 118 56 Archaeological Looting and Lunar Cycles . . . 120 58 Why the Pleiades? . . . . . . . . . . . . . 122 60 The Definition of Easter . . . . . . . . . . . 124
Extreme Orbits . . . . . . . . . . . . . . .
62
From Galileo to the Present
Loops in the Sky
64
The Apollo Landing Sites
The Dark Side of the Moon
. . . . . . . . .
Varying Sizes . . . . . . . . . . . . . . . . Optical Illusion
. . . . . . . . . . . . . .
. . . . . . . . . . . . . .
Precessional Motions The Double Planet
. . . . . . . . . . . . .
Gravity and Centrifugal Force
. . . . . . . .
67 Index 68 Lo 70
. . . . . . . . . 126 . . . . . . . . . . 128 130
9
The Sunlit Moon
10
Lunar Phases
An image series showing different phases of the Moon: The top-left image shows an almost completely full moon which is already slightly waning. In the next four pictures, the Moon gradually wanes until it becomes a new moon. The waxing phase starts with the centre-right image: The new moon first turns into a waxing crescent moon and then into a waxing gibbous moon. In the bottom right image, the Moon has become a full moon once again. The different colours are due to changes in the Earth’s atmosphere.
11 The terminator
Full moon and new moon
The Sun continuously radiates light into space, and at any Two positions of the Moon are particularly simple to expoint it illuminates the Moon in such a way that one half plain: When the Moon reaches the imaginary line beof the Moon is lit while the other is in darkness. Obviously, tween the Earth and the Sun, there is either a full moon the same applies to Earth. The dividing line between light or a new moon. If the Moon moves exactly between the and darkness, also known as the terminator, is a circle Earth and the Sun, then it blocks the Sun relative to the on the Moon. By analogy with the Earth, the lunar termi- Earth and causes a solar eclipse. We will discuss this spenator can also be seen as the line that separates day and cial case in more detail later in the book (see pp. 84f.). If night, though lunar days and their corresponding lunar the Moon’s centre falls exactly on the extension of the axis nights are considerably longer because the Moon’s rota- passing from the Sun through the Earth, then the Earth tion around its own axis is much slower than that of the casts a shadow on the Moon and shrouds it in darkness. Earth: As a result, each point on the Moon has almost 15 This special case will also be examined more thoroughly terrestrial days of sunlight, and after that it goes back to (see pp. 90f.). darkness for about two weeks. As seen from Earth From Earth, we can only see parts of the Moon’s sunlit hemisphere, depending on the position of the Moon on its orbit around Earth. The terminator appears as an ellipse – or in the special case of the half moon, as a straight line. Geometrically speaking, the face of the Moon as seen from Earth is made up of a semicircle plus or minus a semi-ellipse.
The period from one full moon to the next lasts 29.5 days on average. During this time, the Moon cycles through all lunar phases. Another peculiar phase is the new moon, which occurs about 14.25 days after the full moon.
12
The “Composite” Full Moon
Photographs of the full moon are lacking in contrast
reflective walls often act as second, indirect light sources
This is because the Sun – the only light source in this sce- which help give your subject a more sculpted look. nario – shines from the direction of the spectator. How- “Complementary” lunar phases ever, photographers prefer to have a certain amount of If we photograph the Moon when it is not in the full-moon side light, which brings out three-dimensional details. stage, then the surface around the terminator (the When you take a photograph under normal conditions, shadow line) will appear particularly textured.
13
Due to the lack of ambient light, the unilluminated portion tures of complementary lunar phases, which we can comof the Moon is entirely dark.
bine with an image editing software. In most cases, we
Putting together complementary phases
would have to tilt one of the two pictures by a few degrees.
We can use this to our advantage: As moonstruck pho- The final result would be a picture where the Moon aptographers, we have plenty of pictures of the Moon in our pears to be illuminated by two light sources from opposite collection. So, most of us should be able to find two pic- directions.
29
Self-Rotation and Elliptical Orbits
30
Earth’s Self-Rotation If you do not look in the right direction, the movement of the stars will appear quite complex.
The relative movement of the starry sky The Earth rotates around its own axis. However, the spherical shape of the Earth and its rotation are not intuitively obvious to us – just think of how long it took for the original “round-Earthers”, who first proclaimed the Earth to be a rotating sphere, to be no longer dismissed as nutcases and heretics. From the perspective of humans on Earth, it is the sky that appears to move above us. Coming to grips with this movement Let us imagine ourselves back to a time when little was known about the movement of the starry sky. How could we proceed to determine what rules govern its movement? First, we position ourselves on a fixed point at some place with a nice view, as in the picture on the top left. Then, on a drawing sheet, we mark the positions of the stars over the course of several hours. The result will be a maze of paths like the one in the middle image on the left. The stars’ movements seem to be quite complicated… Capturing the rotation By observing the sky over an extended period of time, we will realise, even without prior knowledge of the Earth’s rotation, that the stars rotate around a celestial pole. On the Northern Hemisphere, this celestial pole is currently very close to Polaris. In Ancient Egypt, this pole was known as Thuban (the indestructible). At the Great Pyramid of Giza, priests could determine the pole’s position, for instance, by standing at a certain spot to the south of the pyramid’s centre and then looking up to the capstone, also known as the pyramidion, which was then covered in gold. In the days of Ancient Egypt, the so-called Pole Star appeared in a completely different position from where it is seen today, and there was no distinctive star close to the celestial pole. The movement of the starry sky now seems much simpler: at night, all stars move in uniform counterclockwise circles around the pole (they do the same during the day, which simply cannot be seen due to
31
the light of the Sun). The angle of rotation is almost 15◦ per hour, which amounts to a full angle of 360◦ during a rotation period of 24 hours. Polaris indicates the direction of the Earth’s axis The Earth rotates around its own axis, which passes through the geographical north and south poles. This axis points almost exactly at Polaris – hence the importance of being able to locate the Pole Star: You can find it in the northern direction, at an elevation angle equal to the observer’s latitude. If you are far south, then Polaris appears only slightly above the horizon. In the far north, you will find Polaris almost at the zenith. On the Southern Hemisphere, you must look south, at an elevation angle that equals your latitude, in order to locate the southern celestial pole (there is no distinctive star to mark the location). The orbital period is 4 minutes less than 24 hours During the Earth’s rotation period of 23 hours and 56 minutes, the stars complete one orbit and return to the ex-
act same position as the day before. However, since our clocks are set at exactly 24 hours a day, the stars “overrotate” slightly with each day. So, if you are looking for a distinctive constellation in the night sky, such as Orion, the Pleaides, or Ursa Major, you will find them in the same position four minutes earlier than the night before. At some point, perhaps after some weeks or months, you might be able to see these constellations setting at the horizon at a certain time of the night. The Sun, Moon, and planets are different Up to this point, everything has been quite straightforward: Once we know the direction of the axis of rotation, we can come to grips with the spatial rotation around the Earth’s axis. If we look in the direction of the axis, then all movements can be reduced to a two-dimensional rotation, which is easy to comprehend. However, to understand the movements of the Sun, the Moon, and the planets, we will have to gain more knowledge and read the explanations provided on the next two double pages.
32
Earth’s Self-Rotation – Continued
The constant rotation of the starry sky Galileo Galilei once said, “He who understands geometry, understands anything in the world.” Since there is no such thing as geometry without sketches and drawings, we will use the drawing on the right to illustrate again why the stars rotate around the celestial north pole N (which is located very close to Polaris “at the moment”):
P is our position, and we are situated on a circle of latitude ϕ. From our ground plane (which is represented here by a green circle around P ), we are looking north (red arrow). The red arrow intersects the Earth’s axis in space, and the axis of rotation that runs parallel through P has an elevation angle of ϕ. Let us simplify the situation first! Let us imagine that the Earth rotates around its axis at participate in the rotation, we would have to continuously a constant angular velocity but without orbiting the Sun. move our arm in circles to keep pointing at the body in Then we would rotate on the red circle of latitude “with- the sky. The arm would then rotate around the virtual axis out noticing”. The only difference would be that during of rotation that runs through the celestial pole. It would the day the Sun would revolve above the horizon, and sometimes point higher and at other times lower, always so would the stars at night. The Moon and the planets, following the movements of the celestial bodies. The only whose additional movements we will ignore in our present two places on Earth where the elevation angle of our arm discussion, would also rotate around the imaginary axis would not change are the North Pole and South Pole, bethat runs through Polaris. This rotation would last almost cause the virtual axis of rotation is perpendicular to the exactly 23 hours and 56 minutes.
poles (running through the zenith directly above us).
This means that after this lapse of time, all the stars would Next step: the Earth rotates around the Sun be in the same position as the day before – and so would Taking the model one step further, we will no longer imagthe Sun, the planets, and the Moon in this simplified model! ine the Earth rotating on the spot, but let it wander around The rotation would only be local
the Sun. Its journey around the Sun is generally known to
The rotation would affect only things that are situated on last a year. Though we travel through space at more than Earth. If we wanted to point with an extended arm at some 100,000 km/h, we revolve around the Sun at a rate of only celestial body, which, as we have just noted, does not one degree a day. This has no impact on astronomical
33 Mercury appears to move in loops on the sky. The inclination of Mercury’s orbital plane (exaggerated in this image) complicates things.
As seen from Earth, the inner planets Mercury and Venus appear to “oscillate” around the Sun.
objects that are very distant in space, outside of our solar nation of the Earth’s axis to the ecliptic plane, on which system: Since these objects are so far away (the relatively the Earth orbits around the Sun, the Sun’s elevation annearby star Sirius, for instance, is still 500,000 times far- gle also varies slightly over the course of a year – and as ther away from Earth than the Sun), we can keep pointing a result of this, we get the four seasons. at them with our outstretched arm simply through a par- Things are even more complicated allel shift of the arm’s direction. However, objects in our Exact astronomy is for people with high spatial visualisasolar system are not “infinitely far” away. So, the Sun’s tion ability, because the issue outlined above is far from relative position on any given day will be slightly different resolved: The Earth’s orbit around the Sun is by no means from that on the previous day. Since the Sun is clearly our uniform – it does not even have the exact shape of an elmost important celestial object – moonstruck readers will lipse because it wobbles around the shared barycentre hopefully forgive me for saying so – we define the length with the Moon. For the planets, we must also take into of a day according to the Sun. To ensure that the Sun ap- account their orbits around the Sun: As opposed to the pears in the same position as the previous day, we make stars with their “reliable” motions, they exhibit additional a minor correction to the sidereal day (i.e. the actual time movements (image above). it takes for the Earth to complete one rotation) by adding Most complications, however, are caused by the Moon. about four minutes per day. However, due to the incli- Their discussion requires another double page.
34
From East to West The terminator moves to the east When we look at the Earth along its axis of rotation such that the North Pole appears at the centre, then the Earth revolves in anti-clockwise direction. So, when the rays of the Sun hit the Earth in a fixed direction and the Sun is rising at our current location, then it will start to rise with some delay in places on the same latitude that are to the west of us. We can also say that the terminator, which is the line that separates day and night, moves to the east. Conversely, the Sun also sets earlier at our location than it does in places to the west of us. Does the Sun rise in the east and set in the west? Does this common belief actually hold water? There is at least one region for which this is, in fact, always the case, namely for all the places that are very close to the Earth’s equator, such as Quito, Nairobi, and Kuala Lumpur. The equator is divided by the terminator into two equally long circular arcs. One half of the equator is always on the sunny side, and the other half is on the dark side of the Earth. Since the Earth spins uniformly around its axis, completing one rotation in almost 24 hours, day and night on the equator are each 12 hours long throughout the 365 days of the year. Sunrays through a fixed point For the following thought experiment, which will later be extended to the Moon, we must, once again, draw on our knowledge of geometry. If we point with one arm in the direction of the Earth’s axis (that is, to the Pole Star), the position of our arm will remain unchanged throughout the day. However, if we point the other arm at the Sun, then the second arm will rotate around the fixed first arm – this is due to the Earth’s rotation around its axis. The angle that is enclosed by the two arms remains constant because the Earth’s relative position to the Sun changes only minimally within a single day (the Earth rotates only one degree around the Sun each day).
35 The cone to the Sun
east to west and reach its noon climax in the south. Dur-
Instead of our arms, let us now imagine two straight lines ing sunrise our arm must only point approximately to the through a fixed point. The angle that is formed by all pos- east, and during sunset it need not point exactly to the sible sunrays that pass through this point in the course of west – unless we are at the equator. a day is (nearly) constant. It measures 90 degrees on an In anti-clockwise direction on the Southern Hemisphere annual average, but due to the inclination of the Earth’s In the Southern Hemisphere the Sun is located in the axis (about 23 degrees), the actual angle varies between north. So, if we turn to the north, our arm will also wan90 minus 23 degrees and 90 plus 23 degrees.
der from east to west – but it will do so in “anti-clockwise”
In clockwise direction
direction and reach its noon climax in the north. So, the
If we trace the fictional trajectory of the Sun with our arm, crucial point here is not that everything on the Southern our arm will rotate along a cone. We should look towards Hemisphere is “upside down”, but that you have to look the south because our arm will then glide clockwise from for the Sun in the opposite direction.
direction Pole Star
ϕ
ϕ 10h 12h
10h 12h
N
N
The Sun’s and the Moon’s paths on the sky are very similar aside from being time-delayed with respect to each other. Divergences in their trajectories are due to the inclination of
ϕ
the Moon’s orbital plane, which is tilted by about 5 degrees
10h 12h
from the orbital plane of the Sun. N
Looking North or South?
36
It depends on where we are
tempting in its simplicity, but we must consider this ques-
When we are on the Northern Hemisphere, we look for the tion in a more differentiated manner. For instance, where Sun and the Moon in the south. On the Southern Hemi- would we have to look if we were at the equator? As seen sphere, we will look for them in the north. This idea is from there, the Sun appears in the south for one half of the year and in the north for the other half.
moonset
moonrise
Looking south (Northern Hemisphere): Over the course of a day, the Moon orbits in clockwise dieast
rection. It has the shape of a “D” and is waxing.
Moon below the horizon
west
37 Things are even more complicated with the Moon be- tion. The “CD rule”, with which we can determine if the cause its path can deviate by up to 5◦ from the Sun’s.
Moon is currently waning or waxing, is reversed on this
Always from east to west
page. The images on both pages show a waxing moon
The Sun and the Moon always travel in the same direc- that turns into a half moon over the course of a day.
moonset
moonrise
Looking north (Southern Hemisphere): Over the course of a day, the Moon orbits in anti-clockwise west
direction. It has the shape of a “C” and is waxing.
Moon below the horizon
east
40
Blue Moon
41 The romantic variety The famous song “Blue Moon” by Richard Rodgers and Lorenz Hart (1934) was interpreted, among others, by Billie Holiday, Elvis Presley, Frank Sinatra, Bob Dylan, and Rod Stewart. It is a song that evokes strong emotions in many people. The Moon can, in fact, take on a bluish hue under certain atmospheric conditions.
The different inclinations of the terminator can be used as an indicator to determine the different times at which the three photographs were taken. Actually just a matter of statistics Statistically speaking, a second full moon in a calendar month occurs once every 2.4 years on average: We know that the average time from one full moon to the next is
Another variety: two full moons in the same month The term “blue moon” is also used in a figurative sense, to refer to phenomena that have no connection with the colour blue. In astronomy, it denotes the third of the four full moons in one season. In the vernacular, however, the term is more commonly used to refer to a second full moon in a calendar month, which is a fairly rare occurrence.
29.5 days. The lunar cycle is, thus, only slightly shorter than most calendar months. The lengths of the months in our common calendar is 31, 28 (29), 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 days. If a full moon occurs in the early morning hours of the first day of a month, there could potentially be a second full moon in every month except February. If the full moon occurs in the late evening of the first, then there can only be a second full moon in a month of 31 days. A full moon that occurs on the 31st of a month is always a blue moon. Once every 30 years on average, we get a full moon on New Year’s Eve. Once in a blue moon Due to the rare occurrence of these phenomena, we use the phrase “once in a blue moon” to talk about extraordinary events, like the (interpersonal) situations described in the aforementioned song.
The author prefers to talk about the blue moon that is characterised by its colour. The three photographs on this double page have been taken in the course of a few days during which the Moon illuminated the sky in a bluish hue. The colour may have been the result of light refractions in the humid air. In the left-hand image on this double page, you can almost make out a lunar atmosphere.
42
The Temperature on the Moon
Extreme temperature differences during its long nights
around on lunar rovers have had a remarkable impact
In general, the following rule applies: The longer a part of on the temperature around the landing sites, which were the surface remains in darkness, the colder it becomes. A originally covered with a uniform layer of fine powdery lunar night lasts almost 15 days. These two weeks without dust (regolith): The structural changes caused by the asany source of heat, and especially without an insulating tronauts’ movements have brought large areas of dark atmosphere, lead to an extreme drop in temperature. The lunar soil to the surface. These dark areas now absorb average temperature in space is about −270◦ Celsius!
higher amounts of solar energy. Scientists have deter-
The landing sites of the manned Moon missions…
mined that as a result of these changes in the Moon’s
…were all close to the equator. In this area, the Moon’s surface, the maximum temperature in these areas has surface is subject to strong solar heating. The tempera- increased by two degrees. ture rises up to 130◦ C. During the lunar night, it then Long nights: a comparison with Mercury drops to frosty −160◦ . However, the astronauts of the Let us make a comparison with Mercury, which is not only Apollo missions always landed during the “twilight hours”, the smallest planet in our solar system but also the closest which are considerably longer than those on Earth. Space planet to the Sun. Its diameter is only 40% wider than that suits are, of course, designed to have extremely high insu- of the Moon, and there is also no atmosphere. A night on lating properties, but high temperature generally causes Mercury lasts twice as long as the planet’s orbit around more problems than low temperature. the Sun (Mercury is almost “tidally locked”). Despite its The “dusty dozen”
much greater proximity to the Sun, night-time tempera-
The presence and the traces of the twelve astronauts that tures also drop to −170◦ . The side facing the Sun is 600◦ have so far walked on the Moon’s surface and driven warmer though… Picture above:
https://commons.wikimedia.org/wiki/File:Apollo_15_Lunar_Rover_and_Irwin.jpg (July 1971)
43 The frosty poles Since the Moon’s rotational axis is minimally inclined to the ecliptic, the lunar poles are barely grazed by sunlight. The Sun’s rays never reach the insides of the craters on the surface of the poles. It is much colder here than in the areas around the equator, and the temperatures are constant at −250◦ C. Deep-frozen water on the poles Water is omnipresent in outer space, especially on celestial bodies like comets and meteorites. It has been proven that there is a fairly high amount of water inside the craters of the two lunar poles – but this water has obviously frozen due to extremely low temperature. It is now possible to detect water molecules by using infrared radiation at certain wavelengths. The Indian lunar probe Chandrayaan 1, which made 3,400 orbits around the Moon, confirmed the existence of water all across the Moon’s surface, albeit trapped beneath the surface. It is also worth noting that there is a steep increase in water concentration at the lunar poles.
A comparison with the Earth’s poles As opposed to the Moon’s rotational axis, the axis of Earth is tilted at 23.4◦ relative to the planet’s orbital plane. This is actually a lucky coincidence, because it is thanks to this tilt that the Earth experiences four seasons as it orbits around the Sun. Even at the poles, the Sun reaches an elevation angle of 23.4◦ during their respective summers and – at least on cloudless days – it remains continuously visible in this season, shining for 24 hours. That is why the temperatures at the North Pole are “relatively warm” during summer. The situation is a little different at the South Pole for two reasons: one being that, around the South Pole, there is a continent with mountains that are up to 5,000 metres high, and the second being that this landmass is covered in a massive ice sheet with a thickness of up to 2,800 metres. The South Pole itself lies about 3,000 metres above sea level, which makes it one of the coldest places on Earth.
For billions of years, the lunar poles have received only grazing sunlight. As a result, the temperatures there never rise above −250◦ .
52
Why 27 Days for One Orbit?
Today the Moon takes about 27.3 days to revolve around the Earth. Billions of years ago, the Moon was 40% closer to the Earth – and hence took significantly less time to complete one orbit.
Could it be quicker? The Moon takes almost four weeks to orbit the Earth. The moons of other planets take less time to do so. For instance, Io and Europa, two of the inner moons of Jupiter, are about the same size as our Moon, but they only take 1.8 and 3.6 days respectively to complete an orbit. Could this be due to Jupiter’s mass? Or due to their distance to the parent planet? Or is this to do with the respective masses of the moons? There are clear rules underlying free fall According to the general theory of relativity, a satellite or moon moves on its orbit “in free fall” through the gravitational field. At any point during their movement, the gravitational force and the centrifugal force cancel each other. The gravitational pull of a planet is determined by its mass and decreases with the square of the distance to the planet. So, the Jupiter moons orbit so speedily around their parent planet because, first of all, Jupiter has an enormous mass and, second, they are closer to
Jupiter. If a moon’s mass is quite small compared to that of its parent planet, it does not have much of an impact on the orbital period. A quick estimation But let’s get back to our own satellite. Compared to the mass of Earth, the Moon’s mass is just slightly more than one percent (1/81). So, we need not take it into account in our estimations: A weather satellite, which appears to hover 36,000 km above the equator by following the Earth’s rotation as exactly as possible, takes one day to complete an orbit. Its distance to the Earth’s centre is 42,000 km (flight altitude plus Earth radius). At an average distance of 384,000 km, the Moon is about nine times farther from the Earth’s centre. In accordance with Kepler’s third law, the ratio of the squares of the orbital periods is equal to the ratio of the cubes of their mean then distances. If T is the Moon’s orbital period in days, √ T 2 : 1 = 93 : 1 applies. This means that T = 93 = 33 = 27. This has worked marvellously well!
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Kepler’s laws of planetary motion apply to the entire solar system. The greater a planet’s distance from the Sun, the longer its orbital period. Mercury takes only one quarter of a year to complete its orbit, Venus 5/8 of a year, Mars almost two years, Jupiter 12 years, and Saturn 29 years.
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The Dark Side of the Moon
We only know one side of the Moon – and we are well familiar with its changing appearance during the Moon’s different phases: from the new moon, to the waxing gibbous moon, to the full moon, and finally the waning moon. Due to the Moon’s wagging motion, which is a result of its
varying orbital velocity and the rotation of its orbital plane, we can see almost 60% of its surface area from our position on Earth. However, up until the mid-1960s, nobody knew what the far side of the Moon looked like. In 1967, the probe Lunar Orbiter 4 took high-resolution images of
3/4 of the Moon’s far side and its entire near side. The first humans to have seen the far side of the Moon with their own eyes were the crew members of Apollo 8, which was the first spacecraft to orbit the Moon at the end of 1968.
In July 1969, Apollo 11 astronaut Neil Armstrong took his legendary first steps on the Moon, at the so-called “Sea of Tranquillity” (lat. Mare Tranquillitatis). Before landing, the crew had completed five lunar orbits.
55 In 1973, rock band Pink Floyd got their most successful album, The Dark Side of the Moon, into the charts. The release of the album inevitably led to debates over the significance of the title. In an interview, the former doorman of the Abbey Road Studios famously said: “There
is no dark side of the moon, really; as a matter of fact, it’s all dark. The only thing that makes it look light is the Sun.” Of course, we know better: The side of the Moon that faces away from Earth goes through the same lunar phases as the side that faces Earth.
As might be expected, the Moon’s far side does not look a fine layer of dark dust). The two images on this double exactly the same as its near side. It is more rugged, and page are computer-generated. They are based on data there are barely any “seas” (that is, giant craters which from the NASA Goddard Space Flight Center, Maryland. were originally filled with lava and were later coated with
Extreme Orbits
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winter solstice (December 2021, 48◦ NL) orbit of full moon
orbit of crescent moon
orbit of Sun
Horizontal and elevation angles Let us look at the pictures on this double page: They were created with a computer and are not real photos. Marked in yellow is the trajectory of the Sun, in grey the paths of the full moon and the waxing crescent moon. The individual positions of the celestial bodies are defined by horizontal angles and elevation angles. Classic example: Polaris has a horizontal angle a = 0◦ and an elevation angle h = ϕ◦ , where ϕ is the latitude at the location. When the Sun sets exactly in the west (it does so at the equinoxes), it is at a position a = 270◦ , h = 0◦ . If you plot the values of a celestial body over the course of a day in a two-dimensional coordinate system, you get a curve
that, to some extent, gives you an idea of how the body moves. Stroboscopic panoramic photos If you distort the elevation angle like it is done in a photograph with the horizontal axis but plot the horizontal angles undistorted, the result will basically be a panoramic photograph of the sky where you rotate slowly about a vertical axis while keeping the object in the centre of the picture. Then you can visualise the orbital curves quite well, although it is not exactly the same as using a rigid lens (in which case the left and right sides of the photograph would be additionally stretched outwards).
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Note on the background photo: The sky was yellowish on this summer day due to dust from the Sahara!
summer solstice (June 2021, 48◦ NL) orbit of Sun
orbit of crescent moon orbit of full moon
Comparison of the two images (December and June) We draw a picture of the Moon every day exactly at sunset (see pp. 26f.). This gives us a nice impression of how it “falls behind” every day. At other times of the day, the crescent needs to be rotated by about 15◦ per hour due to the Earth’s rotation. Role swap Sun ↔ full moon In principle, the two images are very similar. The only noticeable difference is the fact that the Sun and the full moon have swapped roles. The orbit of the crescent moon is somewhere between the orbit of the Sun and the orbit of the Moon. The orbit of the new moon is not pictured at all because it is almost identical to the orbit of the Sun.
The Moon varies much faster The Sun reaches its absolute maximum or minimum altitude every half year. The Moon goes through this process in just under 15 days, with the associated values being extreme around the solstice. The winter full moon can rise extremely high The elevation angle of the full moon can exceed or fall below the absolute maximum elevation of the Sun by ±5.2◦ because the plane in which the Moon’s orbit lies deviates from the ecliptic by this value. In this particular case, the full moon rises particularly high. Such peculiarities were already noticed by humans during the Neolithic Age (see pp. 118f.).