We are looking down on the solar system, from above the North Pole. The Earth rotates on its own axis counterclockwise once a day (you can verify this by checking that the Sun will appear to rise in the east at dawn and set in the west at dusk), and the Moon orbits counterclockwise around the Earth once a month.

The Moon has been drawn in its eight major phases. In each case, a figure () placed below the Moon on the surface of the Earth shows where one would stand to see the Moon directly overhead, and the time of day or night is identified. You can imagine that the Earth is the center of a gigantic clock, and as you stand on it you sweep through 24 (not 12!) hours with every full circle, forming our night and day cycle.

The Moon is always half illuminated (the side facing the Sun), and half in shadow (the side hidden from the Sun). Where must the Moon be (relative to the Earth) so that we see the fraction of the illuminated side corresponding to the correct lunar phase? What time is it if you are on the side of the Earth directly underneath this point?

The following table lists the eight major phases of the Moon. It shows the appearance of the Moon from Earth, and the time of night or day at which the Moon will be directly overhead for each phase. Test your understanding by looking at each phase, and comparing the appearance of the Moon in the table with the fraction of the Moon which is illuminated which can be seen from Earth (as deduced from the above figure).

Lunar PhaseFull Waning gibbous Third quarter Waning crescent New Waxing crescent First quarter Waxing gibbous
Appearance
Overhead @ 12am 3am 6am 9am 12pm 3pm 6pm 9pm

You may assume that it is noon when the Sun is directly overhead in the sky, 6pm at sunset, midnight when the Sun is most hidden behind the Earth, and 6am at sunrise. (Don't worry about daylight savings time, and remember that 12pm is noon, and 12am is midnight.)

When considering rising and setting times, you need to think about when the Moon will appear on the horizon. It is important to realize that in the figure above, we have drawn the Earth and the Moon much larger than they really are so that they will be easy to see.

In the figure below, this strategy is repeated on the left. In the figure on the right, however, we have drawn the Earth and Moon at their actual size (keeping the distance between the Earth and the Moon constant). If you only looked at the figure on the left, you might be tempted to say that the person needed to rotate back a few degrees (rather then standing straight up), as is shown, in order to see the Moon on the horizon. The figure on the right should reassure you that because the Earth and Moon are both much smaller than the distance between them, you can see the Moon on the horizon when it lies a full quarter-turn away from you.

You can assume that the Moon will lie above the horizon for twelve hours out of every day, and will be hidden on the other side of the Earth for twelve hours out of every day. It appears on the eastern horizon, slowly rises through the sky for six hours until it reaches its maximum height in the sky (transits), and then slowly sets for six hours until it falls below the western horizon. The Moon will lie overhead six hours after rising, and will set six hours after it is overhead.

We trace this this pattern out for the full Moon below. It rises majestically above the eastern horizon at around dusk, ascends through the sky until transiting at midnight, and then slowly sets toward the western horizon, reaching it at dawn.