002.1 Phases of the Moon
The Waning Quarter Moon rises at midnight. In clear weather, you might see it throughout the morning.
If, one winter night, you see a Moon with one flat side (a quarter Moon in other words) and it is right on the horizon, what time is it?
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Midnight, Solar Time. The Local Time is probably between 11:30pm and 12:30am because Daylight Savings Time is not in effect during the Winter and Local Time is usually within a half hour of Solar Time. If the flat side is on the right, then you see a Waning Quarter Moon rising in the East. If the flat side is on the left, then it is a Waxing Quarter Moon setting in the West.