# Moon Motions

## Motions of the Moon

The moon moves rapidly with respect to the background stars. It moves about 13 degrees (26 times its apparent diameter) in 24 hours (slightly greater than its own diameter in one hour)! Its rapid motion has given it a unique role in the history of astronomy. For thousands of years it has been used as the basis of calendars. Isaac Newton got crucial information from the Moon's motion around the Earth for his law of gravity.

Almost everyone has noted that we see the same face of the Moon all of the time. It's the ``man in the moon'', ``woman in the moon'', ``rabbit in the moon'' etc. One thing this shows us is that the moon turns exactly once on its axis each time that it goes around the Earth. Later on we'll find out how tidal forces have caused this face-to-face dance of the Earth and Moon. It drifts eastward with respect to the background stars (or it lags behind the stars). It returns to the same position with respect to the background stars every 27.323 days. This is its sidereal period.

sidereal period

### Review Questions

1. How does the Moon move with respect to the stars?
2. How does the fact that we always see one side of the Moon prove that the Moon rotates once every orbital period?
3. In a particular year the Moon is in the constellation Aries on June 1st. What date will it be in Aries the next time?

### Phases and Eclipses

One of the most familiar things about the Moon is that it goes through phases from new (all shadow) to first quarter (1/2 appears to be in shadow) to full (all lit up) to third quarter (opposite to the first quarter) and back to new. This cycle takes about 29.53 days. This time period is known as the Moon's synodic period. Because the moon moves through its phases in about four weeks, new moon, first quarter, full moon, third quarter, and new moon occur at nearly one-week intervals.

We know that the phases are due to how the Sun illuminates the Moon and the relative positioning of the Earth, Moon, and Sun. We observe that not much of the Moon is illuminated when it is close to the Sun. In fact, the smaller the angular distance between the Moon and the Sun, the less we see illuminated. When the angle is within about 6 degrees we see it in a new phase. Sometimes that angle = 0 degrees and we have a solar eclipse-the moon is in new phase and it is covering up the Sun. Conversely, the greater the angular distance is between the Moon and the Sun, the more we see illuminated. Around 180 degrees we see the Moon in full phase. Sometimes (about twice a year) the Moon-Sun angle is exactly 180 degrees and we see the Earth's shadow covering the Moon-a lunar eclipse.

We can use the illustration of the lunar phases to the left to find out the time of day when the Moon will be visible. The Sun is at the right of the figure so a person at position (A) on the Earth (e.g., Bakersfield, CA) sees the Sun on the meridian. The Earth rotates in the counterclockwise direction (A to B to C to D). A person at position (B) (e.g., Sao Mateus in the Azores) sees the Sun setting since he is one-quarter turn (6 hours) ahead of the person at position (A). If the Moon was at its new phase position, person (B) would ``see'' the New Moon setting, but if the Moon was at its first quarter position, he would see the Moon on his meridian at sunset. A person at position (C) (e.g., Zahedan, Iran) would see the First Quarter Moon setting because she is 6 hours (one-quarter turn) ahead of person (B). It is midnight at her location (the Sun is directly behind her). She would see the Full Moon on her meridian at midnight when then Moon moves one-quarter of the around in its orbit from its first quarter position. The person at position (D) (e.g., Sydney, Australia) 6 hours ahead of person (C) sees the Sun rising. The New Moon would also be rising while the Moon at Full phase would be setting. The third quarter phase would be on her meridian, but person (A) sees the third quarter phase setting.

It may be a little difficult to visualize this right away so give yourself some time to develop the picture in your mind. Use the table below to get the key points. The table gives a summary of about when the Moon is visible and where to look. Some readers will be surprised to find out that the Moon is sometimes visible in broad daylight!
Phase Time Rises Crosses Meridian Sets
(ahead/behind) (eastern sky) (southern sky) (western sky)
New within few minutes Sunrise Noon Sunset
First Quarter 6 hrs behind Noon Sunset Midnight
Full 12 hrs behind Sunset Midnight Sunrise
Third Quarter 6 hrs ahead Midnight Sunrise Noon

The phase diagram seems to show that a solar and lunar eclipse should happen every month but we know that eclipses happen only twice a year. We can see why if we look at the Moon's orbit from close to edge-on. The Moon's orbit is tilted by 5 degrees with respect to the Earth's orbital plane (the ecliptic). In order for an eclipse to occur, the Moon must be in the ecliptic plane AND at the new or full phase.

During a year the Moon's orbit is oriented in very nearly the same direction in space. The position of the Earth and Moon with respect to the Sun changes while the Moon's orbit direction is approximately fixed. So in one month the Moon will be below the ecliptic at full phase and above the ecliptic at full phase about six months later. Though the Moon crosses the ecliptic twice a month an eclipse will happen only when it at full or new phase when it crosses. The tilt of the Moon's orbit explains why eclipses happen only twice a year.

The direction of the Moon's orbit slowly shifts (precesses) over time. Because the Moon's orbit precesses, eclipses will occur on different dates in successive years. However, even if there was no precession, eclipses would still happen only twice a year.

Why are the synodic and sidereal periods not equal to each other? For a reason similar to the reason why the solar day and sidereal day are not the same. Remember that a solar day was slightly longer than a sidereal day because of the Sun's apparent motion around the Earth (which is really due to the Earth's motion around the Sun). The Sun's eastward drift against the stars also means that the Moon's synodic period is longer than its sidereal period.

At new moon, the Sun and Moon are seen from the Earth against the same background stars. One sidereal period later, the Moon has returned to the same place in its orbit and to the same place among the stars, but in the meantime, the Sun has been moving eastward, so the Moon has not yet caught up to the Sun. The Moon must travel a little over two more days to reach the Sun and establish the new moon geometry again.

The modern model has the moon going around the Earth with the Sun far away. At different positions in its orbit we see different phases all depending on the relative positions of the Earth-Moon-Sun. Another possible model was presented by the highly-esteemed Harvard graduates. They proposed that the dark part of the moon is the result of portions of the moon lying in the shadow of the Earth.

### Vocabulary

lunar eclipse solar eclipse synodic period

### Review Questions

1. Why does the Moon have phases?
2. Why are New Moon phases longer than a sidereal period (27.3 days) apart from each other?
3. What are the positions of the Earth-Moon-Sun during an eclipse?
4. What would the Sun-Moon angular separation be for the New Moon if the Earth's shadow caused the lunar phases? How about Gibbous phase?
5. What are the real angular separations for New and Gibbous phase?
6. About how much difference in time is there between moonset and sunset at first quarter phase? Does the Moon set before or after the Sun at that phase?
7. About when will the Waxing Crescent Moon be on the meridian?
8. The Moon is low in the western sky at sunrise, what its phase?
9. Why don't we have eclipses every month?

### Relationship of Tides and Lunar Phases

When you look in the paper at the section containing the tide tables, you'll often see the phase of the moon indicated as well. That's because the ocean tides are caused by different strengths of the Moon's gravity at different points on the Earth. We'll go into the nitty-gritty details of gravity a little later, but now you just need to know that gravity depends on mass and distance--greater distance means less gravity.

The side of the Earth facing the moon is about 4000 miles closer to the Moon than the center of the Earth is, and the Moon's gravity pulls on the near side of the Earth more strongly than on the Earth's center. This produces a tidal bulge on the side of the Earth facing the Moon. The Earth rock is not perfectly rigid; the side facing the Moon responds by rising toward the Moon by a few centimeters on the near side. The more fluid seawater responds by flowing into a bulge on the side of the Earth facing the moon. That bulge is the high tide.

At the same time the Moon exerts an attractive force on the Earth's center that is stronger than that exerted on the side away from the Moon. The Moon pulls the Earth away from the oceans on the far side, which flow into a bulge on the far side, producing a second high tide on the far side.

These tidal bulges are always along the Earth-Moon line and the Earth rotates beneath the tidal bulge. When the part of the Earth where you are located sweeps under the bulges, you will notice a high tide; when it passes under one of the depressions, you experience a low tide. An ideal coast should experience the rise and fall of the tides twice a day. In reality, the tidal cycle also depends on the latitude of the site, the shape of the shore, winds, etc.

The Sun's gravity also produces tides that are about half as strong as the Moon's and produces its own pair of tidal bulges. They combine with the lunar tides. At new and full moon, the Sun and Moon produce tidal bulges that add together to produce extreme tides. These are called spring tides (the waters really spring up!). When the Moon and Sun are at right angles to each other (1st & 3rd quarter), the solar tides reduce the lunar tides and we have neap tides.

### Tides Slow Earth Rotation

As the Earth rotates beneath the tidal bulges, it attempts to drag the bulges along with it. A large amount of friction is produced which slows down the Earth's spin. The day has been getting longer and longer by about 0.0016 seconds each century.

Over the course of time this effect can have a noticeable effect. Astronomers trying to compare ancient solar eclipse records with their predictions found that they were off by a significant amount. But when they took the slowing down of the Earth's rotation into account, their predictions agreed with the solar eclipse records. Also growth rings in ancient corals about 400 hundred million years old show that the day was only 22 hours long so that there were over 400 days in a year. In July 1996 a research study reported evidence, from several sedimentary rock records providing an indicator of tidal periods, that the day was only 18 hours long 900 million years ago.

Eventually the Earth's rotation will slow down to where it keeps only one face toward the Moon. Gravity acts both ways so the Earth has been creating tidal bulges on the Moon and has slowed it's rotation down so much that it rotates once every orbital period. The Moon keeps one face always toward the Earth.

Several people have asked me for references about the evidence for the slowing down of the Earth's rotation so here's a list:

1. Growth Rhythms and the History of the Earth's rotation, edited by G.D. Rosenberg and S.K. Runcorn (Wiley: New York, 1975). An excellent source on the eclipse records and the biology of coral and their use as chronometers.
2. Tidal Friction and the Earth's Rotation, edited by P. Brosche and J. Sündermann (Springer Verlag, 1978). The second volume put out in 1982 does not talk about eclipse records or the use of coral but, instead, goes into the astrophysics of the Earth-Moon dynamics and geophysics of internal Earth processes effects on the Earth's rotation.
3. Earth's Rotation from Eons to Days, edited by P. Brosche and J. Sündermann (Springer Verlag, 1990). Has several articles about the use of ancient Chinese observations.
4. Richard Monastersky 1994, Ancient tidal fossils unlock lunar secrets in Science News vol. 146, no. 11, p. 165 of the 10 Sept 1994 issue.
5. C. P. Sonett, E. P. Kvale, A. Zakharian, Marjorie A. Chan, T. M. Demko 1996, Late Proterozoic and Paleozoic Tides, Retreat of the Moon, and Rotation of the Earth in Science vol 273, no. 5271, p. 100 of the 05 July 1996 issue.

### Tides Enlarge Moon Orbit

Friction with the ocean beds drags the tidal bulges eastward out of a direct Earth-Moon line and since these bulges contain a lot of mass, their gravity pulls the moon forward in its orbit. The Moon's orbit is growing larger, receding from the Earth at about 3 cm per year. We have been able to measure this slow spiralling out with lasers bouncing off reflectors left by the Apollo astronauts on the lunar surface.

The consequence of the Moon's recession from the Earth because of the slowing down of the Earth's rotation is also an example of the conservation of angular momentum. Angular momentum is the amount of spin motion an object or group of objects has. It depends on the geometric size of the object or group of objects, how fast the object (or group of objects) is moving, and the mass of the object (or the group). The concept of angular momentum is discussed in the Angular Momentum web document and we will encounter the implications of angular momentum in several other topics in the course.

The slow spiralling out of the Moon means that there will come a time in the future when the angular size of the Moon will be smaller than the Sun's and we won't have any more total solar eclipses! Fifty billion years in the future the Earth day will equal 47 of our current days and the Moon will take 47 of our current days to orbit the Earth. Both will be locked with only one side facing the other--people on one side of the Earth will always see the Moon while people on the other side will only have legends about the Moon that left their pleasant sky.

### Tidal Effects Elsewhere

Tidal effects are larger for more massive objects and at closer distances. The Sun produces a tidal bulge on the planet Mercury (the planet closest to the Sun) and has slowed that planet's rotation period so it rotates three times for every two times it orbits the Sun (a ``3--2 spin-orbit resonance''). Jupiter's moon, Io, orbits at about the same distance from Jupiter's center as the Earth's moon. Jupiter is much more massive than the Earth, so Jupiter's tidal effect on Io is much greater than the Earth's tidal effect on the Moon. Io is stretched by varying amounts as it orbits Jupiter in its elliptical orbit. This tidal flexing of the rock material creates huge amounts of heat from friction in Io's interior which in turn is released in many volcanic eruptions seen on Io. Galaxies passing close to each other can be severely stretched and sometimes pulled apart by mutual tidal effects.

### Vocabulary

conservation of angular momentum neap tide spring tide

### Review Questions

1. What causes the tides?
2. How are tides related to the position of the Moon and Sun with respect to the Earth?
3. Why are there two high tides roughly every 12.5 hours? Explain why there are two tidal bulges AND why they are over 12 hours apart.
4. At what phases do spring tides occur?
5. At what phases do neap tides occur?
6. How are tides responsible for the slowing down of the Earth's spin and the Moon's spiralling away from us?
7. Where are some other places that tides play a significant role in the appearance and motion of objects?

### Eclipse Details: Lunar Eclipse

Let's explore a little more about lunar and solar eclipses. Remember that an eclipse happens when an object passes through another object's shadow. Any shadow consists of two parts: an umbra which is the region of total shadow and the penumbra which is the outer region of partial shadow. If the Moon were to pass through the Earth's umbra, a Moon observer would not be able to see the Sun at all-she would observe a solar eclipse! An Earth observer would see a total lunar eclipse. The Earth's shadow is pretty big compared to the Moon so a total lunar eclipse lasts about 1 hour 45 minutes.

If the Moon only passed through the outer part of the shadow (the penumbra) then the Moon observer would see the Sun only partially covered up---a partial solar eclipse. The Earth observer would see the Moon only partially dimmed-a partial lunar eclipse.

During a total lunar eclipse we see another interesting effect---the Moon turns a coppery (or bloody) red. This is due to sunlight refracting or bending through the Earth's atmosphere. Dust particles in the Earth's atmosphere have removed much of the bluer colors in the sunlight so only the redder colors make it to the Moon. The amount of dust determines the deepness of the red colors. This is also why the Sun appear redder at sunset on Earth. The Moon observer would see a reddish ring around the Earth.

### Eclipse Details: Solar Eclipse

The Moon's shadow also has an umbra and penumbra. The shadow is much smaller than the Earth's. Only if the Moon is in the ecliptic plane when it is exactly New Moon will we have the Moon's shadow hitting the Earth. Where the umbra hits the Earth, we'll see a total solar eclipse. Where the penumbra hits the Earth, we'll see a partial solar eclipse.

In a total solar eclipse the bright disk of the Sun is completely covered up by the Moon and we see the other parts of the Sun like the corona, chromosphere, and prominences. Unfortunately, only the tip of the Moon's umbra reaches the Earth (the tip hitting the Earth is 270 km [168 miles] in diameter) and it zips along the Earth's surface at over 1600 kph (1000 mph) as the Moon moves around the rotating Earth. This means that a total solar eclipse can last a maximum of only 7.5 minutes. Usually total solar eclipses last only 3-4 minutes. Because of the orbital motion of the Moon and the rotation of the Earth, the umbra makes a long, narrow path of totality.

Sometimes the umbra does not reach the Earth at all (only the penumbra) even though the Moon is on the ecliptic and it is exactly in New Moon phase. We see a bright ring around the Moon when it is lined up with the Sun---an annular eclipse (because of the annulus of light around the Moon). NASA publishes excellent information about upcoming eclipses on the world-wide-web: the February 26, 1998 eclipse visible in South America and the Caribbean is at http://umbra.nascom.nasa.gov/eclipse/980226/rp.html.

### Vocabulary

annular eclipse penumbra refraction
umbra

### Review Questions

1. What are the two parts of a shadow and in which part is the Sun partially visible?
2. Why don't we have eclipses every month?
3. Why is the path of totality of a solar eclipse different each time? Why does the latitude of the path vary?
4. Why does the Moon turn orange-red during a total lunar eclipse?
5. Would a person on the Moon ever experience an annular solar eclipse?
6. Why don't we have just annular solar eclipses or just total solar eclipses when the Moon and Sun are exactly lined up?

## Planetary Motions

There are other celestial objects that drift eastward with respect to the stars. They are the planets (Greek for ``wanderers''). There is much to be learned from observing the planetary motions with the naked eye (no telescope). There are 5 planets visible without a telescope, Mercury, Venus, Mars, Jupiter, and Saturn (6 if you include Uranus for those with sharp eyes!). All of them move within 7 degrees of the ecliptic.

The arrow pointing to Polaris in the solar system picture is tilted by 23.5 degrees because the Earth's rotation axis is tilted by 23.5 degrees with respect to the ecliptic. Two of the planets (Mercury and Venus) are never far from the Sun. Venus can get about 48 degrees from the Sun, while Mercury can only manage a 27.5 degrees separation from the Sun. When Venus and/or Mercury are east of the Sun, they will set after sunset so we'll see them as an ``evening star'' even though they are not stars at all. When either of them is west of the Sun they will rise before sunrise and they are called a ``morning star''.

Planets produce no visible light of their own; we see them by reflected sunlight. True stars produce their own visible light. Venus can be the brightest of all the planets, sometimes getting so bright that it can create a shadow! Mercury and Venus are never visible at around midnight (or opposite the Sun), the other planets can be visible at midnight because they orbit further out from the Sun than the Earth does.

Sometimes a strange thing happens---a planet will slow down its eastward drift among the stars, halt, and then back up and head westward for a few weeks or months (retrograde motion), then halt and move eastward again. The planet executes a loop against the stars! The figure below shows Mars' retrograde loop happening at the beginning of 1997. Mars' position is plotted every 7 days from October 22, 1996 (the position on November 12, 1996 is noted) and the positions at the beginning and end of the retrograde loop (February 4 and April 29, 1997) are noted. What causes retrograde motion? The answer to that question involved a long process of cultural evolution, political strife, and paradigm shifts. We'll investigate the question when we look at geocentric (Earth-centered) models of the universe and heliocentric (Sun-centered) models of the universe.