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The astronomical symbol for the Moon is easy to recognize: it’s a crescent moon. Both the crescent and decrescent moon symbols are used to represent the Moon in astronomy, astrology and alchemy.
When the crescent is on the right, this is the first phase of the Moon, as seen by the northern hemisphere. Think about that for a second, when you’re standing in the southern hemisphere, your view of the Moon is reversed. So from a southern perspective, the crescent will be on the left. But for people in the northern hemisphere, when the crescent is on the right, it’s the first quarter, just after the new moon. And when the crescent is on the left, it’s in the last quarter, just before the new Moon.
Calendars often use a different set of symbols for the Moon to designate the different phases.
This is the same symbol used for the Moon in astrology, and represents silver in alchemy.
Here’s more information about the Moon symbol from symbols.com.