# On the transfer of angular momentum in the Earth and Moon system

Tides cause friction in the Earth and are slowing its rotation with a rythm of 2 milliseconds per century. Due to this, and following the conservation of the angular momentum of the entire system Earth plus Moon, we have that the Moon moves away from the Earth, very slowly. I saw a calculation of this in Paul Nahin's excellent "In Praise of Simple Physics", and sure it can be found in many other places.

My question is: if we consider the isolated system of a spinning Earth + spinning Moon + rotating Moon around the Earth, which is reasonable to a high degree of approximation, the angular momentum, as it was said, is constant:

$$L_{\text{spin Earth}}+L_{\text{rot Moon}}+L_{\text{spin Moon}}=\text{constant}$$

It seems that the decrease in $$L_{\text{spin Earth}}$$ is totally transferred to an increase in $$L_{\text{rot Moon}}$$ (Nahin), nothing to $$L_{\text{spin Moon}}$$ (and reasoning this way you admirably reproduce the measured 2 milliseconds per century.

Why? One could say that this is what it's observed, that the Moon does not increment its speed of rotation around its axis, but then, again, why? If it's due to tidal locking, then what's the reason the Moon's spin is privileged to not receive momentum?

• I finally deleted my answer. Forgot about it. Have a great day Jul 30, 2021 at 14:12