To look up the phase of the moon for any (Common Era) date,
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At 13:30:41 UT Tuesday 07 September 2021
the moon was
is 13.5280555555556 in decimal hours.
The Julian date was 2459464.50342013.
The sun’s ecliptic longitude was 165.13311759648 degrees.
Its mean anomaly was 244.0873153036 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.)