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The waxing moon.

At 20:38:29 UT Tuesday 02 June 2020
the moon’s phase is

WAXING GIBBOUS (88.20% full)


Some factors that go into this equation:

Universal Time is 20.6580555555556 in decimal hours.
The Julian date is 2459003.38195366.
The sun’s ecliptic longitude is 72.765545998373 degrees.
Its mean anomaly is 149.0110560551 degrees.
The moon’s mean longitude is 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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