002.1 Phases of the Moon
The waning Gibbous Moon does not rise until hours after the Sun has set. You might see it in the early morning, however.
Suppose that you go out just after the sun has set and look for the Moon when it is in its Waning Gibbous phase. How long must you wait for it, and where do you first see it?
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You need to wait around 2-4 hours and can expect to see it rise in the East well before midnight. A typical time might be around 10pm.