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 (will display in another window). 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. The figure below shows that as the Moon orbits the Earth, the fraction of its illuminated side that you can see changes. You will observe only a small fraction of the Moon's illuminated side when it is close to the Sun. In fact, the smaller the angular distance between the Moon and the Sun, the less of its illuminated side you see. When the angular distance is less than 90° separation, you will see less than half of the Moon's illuminated side and it will look like a a curved sliver of light---the crescent phase. Because the Moon is spherical, the boundary between light and shadow is curved. Note that the figure of the phase angles shows just one of the angles possible for the crescent phase (at 45°). When the angle is within about 6 degrees you see it in a new phase and is the beginning of the phase cycle. Sometimes that angle = 0 degrees and you have a solar eclipse---the moon is in new phase and it is covering up the Sun. At 90° angular separation you see half of the Moon's illuminated side and the phase is called a quarter phase because you can see a quarter of the Moon's entire surface. The quarter phase a week after the new phase is called first quarter.
The greater the angular distance is between the Moon and the Sun, the more of the Moon's illuminated side you can see. When the angular distance is more than 90° separation, you will more than half of the Moon's illuminated side---the gibbous phase. ``Gibbous'' means a shape that is convex (bulges outward) at both sides. Again note that the figure shows just one of the angles possible for the gibbous phase (at 135°). Around 180° angular separation, you see the entire illuminated side of the Moon---the full phase. 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. Sometimes a descriptive term is added to the crescent and gibbous phases. If the amount of illuminated side you can see increases with time, it is waxing as in waxing crescent or waxing gibbous. If the illuminated fraction decreases with time, it is waning as in waning crescent or waning gibbous.
Select here for a nice simulation of the moon phases (will display in another window). Be sure to choose ``both'' in 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.
If you are having a hard time visualizing this, try using a white ball (e.g., a styrofoam ball) for the Moon, a bright light bulb for the Sun, and your head for the Earth in a room shut off from other lights. When your eyes are facing the bulb, that would be noon. While facing the bulb, move the ball to your left ear so half of it is lit up. That is the first quarter phase. If you move your head counterclockwise 90° so you are facing the half-lit ball, you will see the bulb out of the corner of your right eye (in the ``west'' direction). That would be sunset. Move the ball around so it is opposite the bulb but out of the shadow of your head. You should see all of it lit up---a full phase. If you face the same direction that you faced the half-lit ball, the full phase ball would be visible out of the corner of your left eye (in the ``east'' direction). As you turn your head counterclockwise, you will see the ball ``rise'' and the bulb ``set''. When you face the full-lit ball, that would be midnight. How would you simulate a third quarter phase?
The table gives a summary of approximately when the Moon is visible and where to look (the crescent and gibbous phases are in between the table values). You may be surprised to find out that the Moon is sometimes visible in broad daylight!
| Phase | Time ahead/behind the Sun |
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 (i.e., at sunset), cross the meridian 12 hours after the Sun, and set 12 hours after sunset (i.e., at sunrise) for all of the phases except full. How is this different from what is observed?
| lunar eclipse | solar eclipse | synodic period |
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last updated: 04 May 2001