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As the Moon is getting farther and farther from Earth, it's natural that the time it takes to circle around our planet is going to increase, thus the month will be longer.

However, I read that the reason it's straying from us also is causing the Earth to revolve more slowly. As the day is getting longer, maybe a lunar month will remain more or less the same?

Fast rewind it back to billions of years ago, did that hold true too? How many 'days' did it take for the Moon to go around the Earth, say, 4bya? Are there any formulae to calculate this?

I'd appreciate more the answers that consider both the day length of specific ancient times and its conversion to modern day, for easy imagination. Any sources that list several values for different periods in the past would be great, too.

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  • $\begingroup$ There are various types of lunar month. I assume you mean some kind of synodic month (the period of the cycle of the phases). $\endgroup$ – PM 2Ring Dec 6 '20 at 15:07
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    $\begingroup$ BTW, Lunar Theory is complicated, mostly because the Moon is relatively large compared to the Earth (as well as the tidal effects). So it can be tricky to model its motions accurately in the far distant past or future. $\endgroup$ – PM 2Ring Dec 6 '20 at 15:16
  • $\begingroup$ @PM2Ring Well, I want a comparison of a modern month to a distant past month, so actually any type of lunar month will do, as long as we use just that kind for both the present and the past. My preference would be sidereal, if possible. $\endgroup$ – longtry Dec 7 '20 at 4:46
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'Day' is the worst possible unit to measure the revolution of the Moon around Earth as it is the temporal unit which is directly influenced by the tidal friction and deceleration. We can reasonably assume that the length of the year is not impacted by lunar tides and subject to much less variation.

This is only a partial answer as I will have to leave the math to get an actual number for time reasons.

The only measurable quantity for the past is the length-of-day of Earth and the tidal rythm by means of their impact on biorythms and in turn its impact on sediment stratigraphy and growth markers e.g. in fossil shells and similar.

One summary with some values and further references on how the past rotation can be estimated is this paper by Deines & Williams. If you know the length-of-day at a time, you can calculate the yearly angular deceleration of Earth. That knowledge can be employed, using the conservation of angular momentum and calculate the orbit of the moon and thus length of month (thus one full orbit around Earth).

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