To look up the phase of the moon for any (Common Era) date,
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The waxing moon.

At 01:01:33 UT Thursday 24 June 2021
the moon’s phase was

WAXING GIBBOUS (99.21% full)


Some factors that go into this equation:

Universal Time is 1.0425 in decimal hours.
The Julian date was 2459390.49205081.
The sun’s ecliptic longitude was 92.763468507319 degrees.
Its mean anomaly was 169.6509987902 degrees.
The moon’s mean longitude on 00 January 1990 was 318.351648 degrees.

These calculations incorporate the switch to the English New Style (N.S.)—i.e., Gregorian— calendar after Wednesday, 02 September 1752; the next day became Thursday, 14 September, skipping eleven days. (Please also note that, while fairly accurate, these calculations remain a bit buggy.)

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