Full Moon Cycle - Matching Synodic and Anomalistic Months

Matching Synodic and Anomalistic Months

When tracking by counting cycles of 14 synodic months, a correction of 1 synodic month should take place after 18 cycles:

18×FC = 251×SM = 269×AM, not:
18×14 = 252×SM

The equality of 269 anomalistic months to 251 synodic months was already known to Chaldean astronomers (see Kidinnu). A good longer period spans 55 cycles or rather 767 synodic months, which is not only very close to an integer number of synodic and anomalistic months, but also when reckoned in synodic months is close to an integer number of days and an integer number of years:

767×SM = 822×AM = 22650 days = 55×FC + 2 days = 62 years + 4 days

There are 13.944335 synodic months in a full moon cycle, the 251-month cycle approximates the full moon cycle to 13.944444 synodic months and the 767-month cycle approximates the full moon cycle to 13.9454545 synodic months.

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