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At 23:47:24 EDT* Tuesday 16 August 1720
the waning moon’s phase was
*03:47:24 Universal Time, Sunday, 17 August 1720
Universal Time (UT) was 03:47:24, Sunday, 08/17/1720.
(That’s 3.80666666666666 in decimal hours.)
The Julian date was 2349505.88774529.
The sun’s ecliptic longitude was -60686.0090911081 degrees.
Its mean anomaly was -60967.2531162659 degrees.
The moon’s true longitude was -1162723.01877843 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.)