## Motions of the Moon

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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.

If you watch the Moon throughout the year, you will 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 you is that the Moon turns exactly once on its axis each time that it goes around the Earth. Later on you will find out how tidal forces have caused this face-to-face dance of the Earth and Moon. The Moon 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?
4. Why did the Apollo missions to the Moon always have landings on the same side of the Moon?

### 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, the phases of new moon, first quarter, full moon, third quarter occur nearly one week apart from each other.

Select this link to find the phase for any date and time between 1800--2199. A picture of the Moon will be shown.

The phases are due to how the Sun illuminates the Moon and the relative positioning of the Earth, Moon, and Sun. You will 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 you see illuminated. When the angle is within about 6 degrees you see it in a new phase. Sometimes that angle = 0 degrees and you 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 you see illuminated. Around 180 degrees angular separation, you see the Moon in full phase. Sometimes (about twice a year) the Sun-Moon angle is exactly 180 degrees and you see the Earth's shadow covering the Moon---a lunar eclipse.

Select here for a nice simulation of the moon phases. Be sure to choose ``both'' for the point of view pop-up list.

You can use the illustration of the lunar phases above 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., Los Angeles, 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). The person at position (C) (e.g., Zahedan, Iran) is at the midnight position (half a turn, 12 hours, ahead of position (A)) and the person at position (D) (e.g., Sydney, Australia) is experiencing sunrise (three-quarters of a turn, 18 hours, ahead of position (A)). If the Moon was at its new phase position, person (D) would see the new moon rising, person (A) would see the new moon on the meridian, and person (B) would see the new moon setting within a few minutes of sunset.

If the Moon was at its first quarter position, person (A) would see the Moon beginning to rise, person (B) would see the Moon on his meridian at sunset, and person (C) would the first quarter moon setting because it is already midnight at her position. Using the same method, you can see that the full moon is rising for person (B) at sunset, is on the meridian at midnight for person (C) opposite the Sun, and is setting for the person (D) at sunrise. Now try to figure out when the third quarter moon will rise, cross the meridian, and set using this method. Remember that each of the persons A, B, C, D are each six hours apart from each other.

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
(eastern sky)
Crosses Meridian
(southern sky)
Sets
(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 eclipses actually happen only twice a year. You can see why if you 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 exactly at the new or full phase. Usually, the Moon crosses the ecliptic plane at another phase instead of exactly at new or full phase during its approximately month-long orbit around the Earth.

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 is exactly at full or new phase when it crosses the ecliptic. 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. The figure above shows another complication---the elliptical orbit of the Moon around the Earth means that the new moon can occur at different distances from the Earth and the Moon's shadow may not reach the Earth if it is too far away.

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 you see different phases all depending on the relative positions of the Earth-Moon-Sun. Another possible model was presented by highly-esteemed Harvard seniors at their graduation. They seriously proposed that the dark part of the Moon is the result of portions of the Moon lying in the shadow of the Earth. Many other people have also explained the phases with this Earth shadow model, but I will call this the ``Harvard model'' below.

Since the Moon would need to be opposite the Sun for it to be in the Earth's shadow, the ``Harvard model'' predicts Sun-Moon angles that are very different from the observed angles. In addition, the model predicts that the Moon would need to be one-half a rotation (or 12 hours) away from the Sun. The Moon should rise 12 hours after sunrise, cross the meridian 12 hours after the Sun, and set 12 hours after sunset for all of the phases except full. How is this different from what is observed?

### 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. If the Moon was full 7 nights ago, what time of day (night) should you look for the Moon to be up high in the sky in the south today? Explain your answer.
4. What are the positions of the Earth-Moon-Sun during an eclipse?
5. 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?
6. What are the real angular separations for New and Gibbous phase?
7. 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?
8. About how much difference in time is there between moonset and sunset at new phase?
9. If the Earth's shadow caused the lunar phases, what would be the difference in time between moonrise and sunrise at new and first quarter phases?
11. The Moon is low in the western sky at sunrise, what is its phase? Explain!
12. Why don't we have eclipses every month?

### 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, an observer on the Moon would not be able to see the Sun at all---she would observe a solar eclipse! An observer on the Earth looking at the Moon 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 observer on the Moon would see the Sun only partially covered up---a partial solar eclipse. The observer on the Earth would see the Moon only partially dimmed---a partial lunar eclipse.

During a total lunar eclipse you 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. The dust in the air is also why the Sun appears redder at sunset on Earth. The observer on the Moon would see a reddish ring around the Earth even at mid-eclipse!

### Eclipse Details: Solar Eclipse

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

Select the image to get information about this image of the July 11, 1991 solar eclipse taken by Fred Espenak

In a total solar eclipse the bright disk of the Sun is completely covered up by the Moon and you can 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 at most 270 kilometers [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. A bright ring will be visible around the Moon when it is lined up with the Sun---an annular eclipse (because of the annulus or ring of light around the Moon).

### Eclipse Web Sites

The following sites are probably the best and most complete ones on the web. You'll find eclipse predictions, photographs, observing instructions, and fairly complete indexes of all high-quality eclipse sites on the web. Between these three you should find whatever you may be interested in with regard to eclipses.
1. NASA's Eclipse Bulletins.
2. Fred Espenak's eclipse site. A less technical version of the NASA site. Fred Espenak is also the main contributer to the NASA site.
3. Sky & Telescope's eclipse site.

### 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 does a new phase occur every month but a lunar eclipse occurs only twice a year?
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? Explain your answer.
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 just the naked eye (i.e., 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. This tells you something about of the orientation of the planet orbit planes with respect to the ecliptic---the figure below shows how flat the solar system is when viewed along the ecliptic plane. The planet positions, of course, do change as they orbit the Sun, but the orbit orientations remain the same.

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. As viewed from the Earth, 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. This tells you something about the size of their orbits in relation to the Earth's orbit size. When Venus and/or Mercury are east of the Sun, they will set after sunset so they are called 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; you see them by reflected sunlight. True stars produce their own visible light. The planets inside the Earth's orbit are called the ``inferior'' planets because their distance from the Sun is less than (or inferior to) the Earth's distance from the Sun. Their closeness to the Sun enables us to see them go through a complete set of phases. Because they can get between us and the Sun, Venus and Mercury can be seen in a crescent or new phase. This also explains why the planets outside the Earth's orbit, called the ``superior planets'', are never seen in a crescent or new phase. When Venus is in crescent phase, it is the brightest object in the sky besides the Moon and the Sun. Even though you see a small fraction of its sunlit side, it is so close to us that you see it appear quite bright. At these times, Venus is bright enough to create a shadow! The fact that you can see Venus and Mercury in gibbous and nearly full phase proved to be a critical observation in deciding between a Earth-centered model and a Sun-centered model for the solar system.

Because Mercury and Venus are closer to the Sun than we are, they are never visible at around midnight (or opposite the Sun). The superior planets can be visible at midnight. At midnight you are pointed directly away from the Sun so you see solar system objects above the horizon that are further out from the Sun than we are. If you want to see where the planets are in their orbits today or any other date, then go to the Solar System Live site.

Ordinarily the planets ``wander'' eastward among the stars (though staying close to the ecliptic). But 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, then halt and move eastward again. The planet executes a loop against the stars! When a planet is moving backward it is said to be executing retrograde motion. Perhaps it seemed to the ancients that the planets wanted to take another look at the stars they had just passed by.

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. You will investigate the question when you look at geocentric (Earth-centered) models of the universe and heliocentric (Sun-centered) models of the universe in the next chapter.

### Review Questions

1. How do the planets move with respect to the stars?
2. What does the fact that all of the planets move within 7ƒ of the ecliptic imply about the alignment of their orbital planes? What would an edge-on view of our solar system look like?
3. Why are Venus, and Mercury never seen at midnight while the other planets can be visible then?
4. What phase would Venus be in when it is almost directly between us and the Sun? Where would it be in its orbit if we see in a gibbous phase?
5. Are the planet motions random all over the sky or are they restricted in some way?
Go to Time and Seasons section

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last update: 25 January 1999

Nick Strobel -- Email: strobel@lightspeed.net

(661) 395-4526
Bakersfield College
Physical Science Dept.
1801 Panorama Drive
Bakersfield, CA 93305-1219