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If I remember correctly, the amount of time it takes for the moon to rotate around Earth is getting longer over time. Is this true, and if so or the opposite is true and a lunar month is getting shorter, is there a way to estimate how long a lunar month will be in the far future?

Doing a worldbuilding project that takes place 53 million years in the future, and trying to figure out how many months they'd put in a year.

Edit: Specifically trying to figure out the length of the synodic month, not the sidereal month.

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    $\begingroup$ astronomy.stackexchange.com/questions/49039/… This question is relevant. It gives that in just over 70 million years, the rotation of the Earth will have slowed to 360 days in a year, and at the same time the orbital time of the moon will have increased by about 8 hours. So in 40 million years you might get 4 to 5 hour increase in the length of the month. $\endgroup$
    – James K
    Oct 15, 2023 at 21:49
  • $\begingroup$ Curious, do you mean the length of a synodic or sidereal month? Would the increase in time be about the same amount of hours? $\endgroup$ Oct 15, 2023 at 23:03
  • $\begingroup$ *same amount of hours for each type of month? $\endgroup$ Oct 15, 2023 at 23:14
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    $\begingroup$ I think that is about sidereal but the synodic month willy increase by the same amount, more or less, since the earth orbit about the sun isn't going to change substantially over such a short time. $\endgroup$
    – James K
    Oct 16, 2023 at 5:22
  • $\begingroup$ Nice question! (+1). I think that since the Moon is receding away from us at a rate of 3.8 cm per year, it would be continuously increasing as gravity is an inverse square force field, so accounting for that increasing rater, by inserting the rate into Kepler's 3rd law of planetary motion along with masses of the primary and secondary body, we could get to know the sidereal month, which would give a very close answer to the actual synodic month as @JamesK suggested. Perhaps you could account for the milankovitch eccentricity cycles to precisely know the change in Earth's radius vector. Thanks! $\endgroup$
    – Arjun
    Oct 16, 2023 at 16:55

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In that future, some of the angular momentum of the Earth's rotation will have been transferred to the moon by tides.

So there will be less then the current 365.2422 days in a year, perhaps about 362 days. An the month will be a little longer. It is currently about 8.085% of a year (or 12.368 synoptic months per year) By about four hours or so.

These factors combined will mean that there will be about 12.1 to 12.2 months per year. There are lots of ways to design a calendar with about 362.xxx days and about 12.15 months per year. This might involve 12 named months (and no fixed link to the moon) or a cycle of 12 lunations per year (and no fixed link to the annual cycle, or the insertion of intercalendary days, or an extra month twice every 13 years. . .

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