Is the Moon's rotation affected by Earth's?

Question

There is a lot written on the moon affecting the Earth's rotation but not so much the other way around. I know that moon has its own rotation:

Tidal locking is the phenomenon by which a body has the same rotational period as its orbital period around a partner.

Is there any math calculation that explains the Earth rotation not affecting the moon's? I expect it does have and it's probably minimal but I'd like to know a time-frame in which we might start seeing some rotation. Or will the moon always follow the tidal locking?

Note: this is a similar question but it doesn't answer why Earth's rotation has no effect on the moon's which what is I'm asking here.

Answer 1

For a satellite (such as a moon) a state of being tidally locked is a state of lowest energy. Before reaching the state of tidal lock there was energy to dissipate. Tidal lock is the state where all the energy that could be dissipated was dissipated, so once a satelite reaches a state of tidal lock that is the end of it.

More generally, with any binary system both celestiial bodies will eventually end up in tidal lock with the overall orbital period.

As you know, the process of evolving towards tidal lock is a process of conversion of rotational potential energy to heat.

In the case of our Moon:
the Moon still has some rotational kinetic energy because it is still rotating; one revolution per month. So overall the Moon is not at it lowest possible state of energy. However, in the context of the Earth-Moon system it is the lowest possible state of energy since there is no way for the remaining rotational kinetic energy to dissipate.

Incidentally, there is another tidal effect going on. The moon is very gradually slowing down the Earth. In that process the Earth is pulling the Moon ever so slightly ahead, so that very gradually the Moon is pulled to a higher orbit. A higher orbit means a larger period of revolution. Since the Moon will remain in tidal lock, the lengthening of the period of revolution means that the Moon will get to dissipate a little bit more rotational energy.

If memory serves me: the Earth won't make it to tidal lock with the Moon. Our Sun will become a red giant in 5 billion years, engulfing the iner planets, including the Earth. By that time the Earth will not yet have reached tidal lock.

Answer 2

Phrased more generally, you raise the following question: can the rotation of one celestial body affect the state of rotation of another celestial body?

To discuss that, let me make a comparison that will allow me to refer to tabletop demonstrations. The comparison: Gravity and the electrostatic force. Both are spherically symmetric inverse square laws.

We can readily look up tabletop sized demonstrations of electrostatic force. For example when two spheres are electrostatically charged then there is a measurable electrostatic force between the spheres.

Let's take such a setup, and add the following element: all else being kept the same, give one sphere a rotation. Will that rotation affect the other sphere?

I assume you will agree with me that introducing a rotation of one sphere will not have any effect on the other sphere. The reason for that: when a charged sphere rotates around its axis the overall distribution of charge remains the same. Therefore the electrostatic field around the charged sphere does not change in any way.

(It may be that you disagree, and that in fact you expect rotation of one charged sphere to induce rotation of a nearby charged sphere. If that is what you believe I recommend that you go ahead and construct such a setup. It can be done as a tabletop setup; cost can be kept down. If you can demonstrate such an effect heads will turn.)

Back to celestical mechanics:
Astronomical observations inform us that the Sun turns around its own axis. Solar observatories track Sun spots, the Sun spots are seen to revolve; from that observation the Sun's rotation rate is inferred.

Note that there is no way to infer the Sun's rotation from any observation of other bodies. That's because the Sun's rotation affects only the Sun itself, the Sun's rotation does not affect other celestical bodies. Only the overall gravity from the Sun is affecting the other celestial bodies of the solar system.