Could you explain what causes the Moon's synchronous rotation?

The tidal force of the Earth's gravitational field raises solid-body tides on the Moon causing the Moon to be deformed into a non-spherical body resembling a football. The magnitude of this effect is about 20 times the solid-body tide caused by the Moon upon the Earth which is about 20x20 centimeters or 4 meters. When the Moon was first formed, it was closer to the Earth than it is now, so the tidal amplitude was quite a bit greater, moreover, the Moon was molten and so it responded even more strongly to the tidal deformation imposed upon it by the Earth's gravitational field. As a result, the shape of the Moon is very far from being spherical. The Moon was originally rotating faster than it is now so that 3-4 billion years ago it was not orbiting the Earth as fast as it was rotating about its axis.

Below is a figure which shows how deformed the moons shape is from a perfect sphere based on orbital data from the Clementine 1 spacecraft. The color indates how many kilometers different from a perfect sphere the different regiosn are. Red means that the surface is bulged outwards. Blue means it is bulged inwards from the spherical shape. The side facing earth is bulged outwards.

Over the years, however, the gravitational tidal forces acting upon the non-spherical body of the Moon have modified its non-spherical shape, and caused a systematic dissipation of the Moon's rotational energy via friction. It costs a lot of energy to deform the Moon, and this energy is lost through the internal friction of rock rubbing against rock within the Moon to raise the solid body tides. Because the Moon may already have solidified into a football-shaped non-spherical body, there is a portion of the Moon that is always slightly closer to the Earth than other portions of the Moon. This becomes a 'handle' that the gravitational field of the Earth can 'grab onto' to apply a slightly greater force upon the Moon that at other times during the lunar orbit around the Earth. A similar deformity exists in Mercury which has aided the Sun in synchronizing Mercury into a 2:3 spin-orbit resonance. For the Moon, and the larger satellites of the other planets, a similar deformity leads to a 1:1 resonance so that the same side of the satellite always faces the planet.

So, a combination of the Moon's initial deformation when it was molten and solidified in the Earth's tidal gravitational field, together with the on-going tidal deformation, leads to a preferred orientation to the Moon in its orbit which the system relaxes to over billions of years.

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