Earth-Moon receding-approaching cycle?

Question

I made the following question in an another more informal forum of discussion on physics:

My question comes after reading this article: https://www.coastreporter.net/in-the-community/the-moon-is-coming-down-to-earth-eventually-3575368 The moon is receding from Earth as it steals angular momentum from our planet. Since energy must be conserved, the Earth slows its rotation and the Moon increases its orbital radius.
In the far future this would reach to a halt where the Earth and the Moon system would become tidally locked for both of them. However, tidal forces from the Sun (ignoring that it would probably have already become a red giant on the time this may happen), would apparently further slow Earth's rotation, so now the system goes out of equilibrium and the Moon starts approaching the Earth, presumably ultimately crashing onto the Earth's or being obliterated by strong tides once it crosses the Roche's limit. However, couldn't this possibly occur in a cyclic manner? I mean, if the Moon approaches the Earth, wouldn't it transfer angular momentum to the Earth, making it rotate faster and faster? And, just as the Earth was rotating faster in the past and the Moon started receding slowing it down in the process, couldn't that happen again, so that the Moon recedes again at some point repeating this cycle as long as the system is unperturbed?

I got an answer by an astrophysicist where he said that in reality what would happen is that the Moon will recede up to the point where the orbit would be unstable and chaotic and therefore 3 scenarios would occur: The moon crashes onto the Earth, the Sun, or is ejected from the system and becomes free

I then asked if my original scenario was impossible then, and he replied:

Highly unlikely. The direction of migration is really governed by the difference between the spin and orbital frequencies. Since tides are an asymptotic process (getting ever closer) it is not going to over shoot the equilibrium state and then need to oscillate back. The only other thing the direction of migration relies on is that whatever processes involved act to dampen the tide. What this means is that the orbital energy is decreasing. There is technically a mechanism that can act opposite to this, that is energy is put into the tide and hence added to the orbital energy. However, it would only occur in stars and I do not believe it would ever physically manifest (note this is not belief as in a casual commentator but a belief from understanding the mechanism extremely well). Essentially what is important is the dissipation of the tidal energy. There are various mechanisms that can dissipate tidal energy. Convection in stars can inhibit the tidal flows. It is possible that convection can also inject energy into the tide but I dont think this will actually really occur.

And also

The Moon orbits would fundamentally become dynamically unstable and either it crashes into the Earth, crashes into the Sun, or is ejected from the system. There could be some in between where it becomes a planet itself but as time tends to infinity one of the three scenarios will play out.

At the end I made a final question but he stopped replying. As I got interested in the discussion I would appreciate if some astrophysicist or anyone with a similar knowledge could answer these questions...

Mmmh... I suppose that you say that it could be that the moon starts orbiting the sun instead for a while. If the moon would change its orbit in the process, then the "new orbit" of the moon would be close to that of the Earth, there could be close encounters where tidal forces are relatively strong?

Also if the process of convection processes in stars giving energy to the tides is unclear, could there be other sources or processes that would be more plausible? Perhaps convection processes ocurring in a black hole (imagine that the Earth-Moon system was orbiting a black hole)?

Is there any answer to these questions?

Answer 1

• "I got an answer by an astrophysicist where he said that in reality what would happen is that the Moon will recede up to the point where the orbit would be unstable and chaotic and therefore 3 scenarios would occur: The moon crashes onto the Earth, the Sun, or is ejected from the system and becomes free."

This answer was wrong, because the mutual synchronisation will be reached before the Moon leaves the reduced Hill sphere. Please see this answer for details.

• You proposed that the solar tides will "further slow Earth's rotation, so now the system goes out of equilibrium and the Moon starts approaching the Earth".

You have made an ingenious guess. The moon indeed will go on an extremely slow descent -- though the mechanism of this descent will be a bit more complex. As you rightly said, the Sun will be applying on the planet a decelerating torque (the solar tidal torque, or simply the solar torque). The Moon will easily neutralise it by applying a compensating accelerating lunar tidal torque (or simply the lunar torque). To make it accelerating, the Moon will have to reduce its semimajor axis by a minuscule amount. Even a minuscule step down will be sufficient to compensate for the solar torque. So, in reality, the Moon's orbit will be synchronised with the Earth rotation not exactly but almost exactly. This will give birth to a torque wherewith the Earth will be acting on the Moon's orbit. As a result of this, the Moon will be extremely slowly descending (like Phobos is descending towards Mars). This machinery is explained in our paper.

You should be commended for your amazing intuition. This is a difficult material, and it took us time and effort to understand these intricacies.