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 (every 29 days).

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
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.)