The Moon doesn’t necessarily rise at sunset and go down at sunrise, sometimes it’s up during the day. So what does it do? Are those times varying depending on it’s phase? Is it random? Are they always the same for a same phase? Do they vary across the year like the Sun’s do?
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During a full moon, the moon is on the opposite side of the earth from the sun, so we see its face fully lit. Since it’s on the opposite side of the earth, we’ll see it on the opposite side of the sky: the full moon rises in the east as the sun sets in the west, and vice versa.
During a new moon, the moon is on the same side of the Earth as the sun, so the unlit side faces us. That means that it would appear right next to the Sun in the sky (if we could see it), so it rises as the sun rises, and set as the sun sets.
In general, the Moon orbits the Earth, completing one full circuit from new moon to new moon every 29.5 days. So every every day it moves a little farther in its orbit and appears a little farther to the east in the sky, and every day it rises and sets about 50 minutes later than the day before.
So, for example, the first quarter moon rises and sets about 6 hours after the Sun, the third quarter moon is about 18 hours behind the sun, and so on.
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