What was the synodical period of the Moon 5000 years ago, and is there a simple formula for finding it?

You can calculate this by using the following formula: 

Month = 29.5305882 + 0.00000016xT   days
where T is the number of centuries from 1900. For 5000 years ago, this is -50 centuries so the synodical month is 29.5305882 + 0.00000016 x (-50) = 29.5305802 days. The difference is 0.0000008 days or 0.069 seconds. So the time between Full Moon and Full Moon was 0.069 seconds SHORTER around 3100 BC. Similarly, in 5000 years fron now ( +50 centuries) the Synodic Month will be 0.069 seconds LONGER than it is today.
Copyright 1997 Dr. Sten Odenwald
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