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 (A stick figure representing a human being.) 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 light of the Sun reaching the Earth and Moon in roughly parallel rays, approaching the Earth and eight models of the Moon showing its position along its orbit in its eight phases. The Earth and each model Moon are shown illuminated on the side facing towards the Sun. Labels indicate the time of day or night on Earth at which each model Moon would lie most directly overhead.

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, which can be observed over a period of 29.5 days. 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 The full Moon, with a fully illuminated disk. The waning gibbous Moon, almost three-quarters illuminated from left to right. The third quarter Moon, half illuminated from left to right. The waning crescent Moon, slightly illuminated on the left side. The new Moon, with a dark disk. The waxing crescent Moon, slightly illuminated on the right side. The first quarter Moon, half illuminated from right to left. The waxing gibbous Moon, almost three-quarters illuminated from right to left.
Overhead @ 12 am 3 am 6 am 9 am 12 pm 3 pm 6 pm 9 pm

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

[NMSU, N. Vogt]