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At 23:47:24 UT Sunday 14 August 1720
the waning moon’s phase was
is 23.8066666666667 in decimal hours.
The Julian date was 2349503.09189067.
The sun’s ecliptic longitude was -60688.1003996091 degrees.
Its mean anomaly was -60969.3886855381 degrees.
The moon’s true longitude was -1162748.67420893 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.)