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At 23:47:24 EDT* Thursday 18 August 1720
the waning moon’s phase was
*03:47:24 Universal Time, Sunday, 19 August 1720
Universal Time (UT) was 03:47:24, Sunday, 08/19/1720.
(That’s 3.80666666666666 in decimal hours.)
The Julian date was 2349507.63550238.
The sun’s ecliptic longitude was -60683.1099248897 degrees.
Its mean anomaly was -60964.2961741968 degrees.
The moon’s true longitude was -1162686.29141844 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.)