[syhprum (OP)]

A vast amount of energy is stored in the rotation of a planet and the only way I can see that it losses it is by the conversion of this energy to heat by the action of tide which it then radiates away or by the radiation of gravitational waves that only amount to a few dozen Watts.
I have seen it suggested that the Earth has slowed to one quarter of its speed since the collision that created the Moon but the moon has slowed by much more despite being a solid body with no tides.

[Kryptid]

- The Moon has far less mass than the Earth does and so can be slowed much more easily.
- The Moon does have tides of a sort, via the flexing of its crust as it moves closer to and further away from the Earth.
- As I understand it, the Moon is "lop-sided" in terms of its center-of-gravity: the crust facing us is much thinner than the crust facing away from us. That would probably have sped up tidal-locking.
- Perhaps the initial rotation rate for the Moon was already low.

[evan_au]

I agree that gravitational waves are far too weak to detectably affect the dynamics of the Earth-Moon system (or even the Earth-Sun system).

the Earth has slowed to one quarter of its speed

The Earth's angular momentum has been transferred into the Moon, which is receding from the Earth

the moon has slowed by much more despite being a solid body with no tides

You can't say there are no tides from the Moon's rotation - because that is only true after it is tidally locked.

Before an orbiting body is tidally locked, it rotates, and dissipates energy in the deformation of its rocks/ice etc. So the rotation rate slows at a slowing rate, until eventually it doesn't have enough momentum to make a complete rotation relative to the parent body.

There are many examples of tidally locked moons in the Solar system - and when we look at exoplanets, there are many exoplanets that must also be tidally locked because they are so close to their parent star.

Tidal locking occurs more quickly when:
- The parent body is massive (induces strong tides in the orbiting body)
- The orbiting body is much smaller (little angular momentum)
- The orbital radius is small (tidal forces follow an inverse-cube law - and the Moon was much closer in the past)

See: https://en.wikipedia.org/wiki/Tidal_locking#Moons

[rmolnav]

Perhaps the initial rotation rate for the Moon was already low.

The initial rotation rate was much higher than now, and the Moon was much, much closer ... Tidal effects were big.
Earth was also rotating much quickly, and subsequently its days were much shorter.
Energy wasted as heat due to tidal frictions made both celestial bodies rotate progressively slower, and The Moon, being much smaller, got tidal locked relatively soon.