How long was a lunar month in ancient times?

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.

• There are various types of lunar month. I assume you mean some kind of synodic month (the period of the cycle of the phases). Commented Dec 6, 2020 at 15:07
• 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. Commented Dec 6, 2020 at 15:16
• @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. Commented Dec 7, 2020 at 4:46