Synodic month
What is a synodic month?
A synodic month is the time from one full moon to the next, about 29.5 days. It is longer than the Moon’s trip around Earth relative to the stars, because Earth has moved and the Moon must catch up to the same angle with the Sun.
Two months, one Moon
Sidereal month: back to the same stars, about 27.3 days. Synodic month: back to the same phase, about 29.5 days. Calendars and the word “month” follow the phases, so they follow the longer one.
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Why moonrise slips
Earth must turn extra to catch the Moon, which has moved east. That extra is about 50 minutes a day — the same arithmetic as the synodic month spread over 24 hours.