If the Earth and the moon became tidally locked, would this last theoretically forever (assuming no external gravitational force modifies their orbits, for example, ignoring the effects caused by the Sun)? Or would their orbits would change?
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2$\begingroup$ "forever" is long time. The sun will turn into a red giant and the Earht and moon may be swallowed... But I feel that isn't what you are asking about. $\endgroup$– James KApr 13, 2022 at 19:34
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$\begingroup$ @JamesK I feel like we'd have to relinquish such considerations for this question, especially since the sun will turn into a red giant before the Earth and Moon tidally lock... $\endgroup$– zephyrApr 13, 2022 at 20:14
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$\begingroup$ @JamesK I am asking if it is theoretically possible, not practically possible, so in my scenario the Sun basically does not exist. So if we ignore the Sun effects, and no other body distorts the orbits (here we are only considering the Earth and the Moon) would this situation keep forever? Or would they change the orbits even without external influences? $\endgroup$– vengaqApr 13, 2022 at 20:55
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$\begingroup$ @zephyr exactly. When I said "ignoring the effects caused by the Sun" I was basically saying that the Sun would not influence in any manner the Earth-Moon system in this exercise, as if it did not exist basically $\endgroup$– vengaqApr 13, 2022 at 20:56
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$\begingroup$ I suspect the "will it last forever" the answer is almost always, no. But your scenario is a crazy-long timescale. How long will it take for gravitational waves to lead to the decay of an orbit . . . That would be many orders of magnitude. I wouldn't even want to try to calculate, but it would be shorter than forever. If the Earth and Moon orbit the white-dwarf our sun becomes, then the 3 body system could be stable for maybe trillions or hundreds of trillions of years, but given enough time, the tidal forces would probably destabilize it or another planet or rogue object could. $\endgroup$– userLTKApr 17, 2022 at 21:07
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If the Earth or Moon are still slightly non-spherical (due to rotation and the fixed tide) then if any fractionation occurs (heavy stuff sinking towards the middle) then the orbit will expand very slightly.
I suppose, theoretically, the Earth-Moon will radiate gravitational waves which will reduce the energy of the system and cause the orbit to shrink. But I wouldn't hold your breath waiting for that to happen.
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$\begingroup$ and when the orbit would shrink could it expand again somehow (without any external influence like some gravitational force by another planet)? @RogerWood $\endgroup$– vengaqApr 16, 2022 at 2:53
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$\begingroup$ @vengaq Maybe there will eventually be a Big Rip en.wikipedia.org/wiki/Big_Rip $\endgroup$ Apr 16, 2022 at 3:00
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$\begingroup$ Again, as this is purely theoretical and I am not considering other conditions outside the earth-moon system I am ignoring the possible Big Rip, Big Freeze, Big Crunch...etc that might happen @RogerWood $\endgroup$– vengaqApr 16, 2022 at 11:12