# Tidal Friction

The tides in the oceans occur primarily because of the gravitational force of the Moon and secondarily the Sun's tidal force. Tidal forces stretch the Earth in the direction of the tide producing body because of the inverse square law, i.e., the force on the near side is greater than the force on the far side, giving a net stretching force. While more noticeable in the oceans, there is also tidal stretching of the land masses.

The tidal forces on an orbiting body slowly change the character of the orbit. For example, assume an orbiting moon which is also rotating about an axis perpendicular to the orbital plane. The tidal force stretches the moon along the line joining it with the planet, and then that stretching relaxes as that diameter rotates away from the line. There is frictional resistance to the stretching, and energy is dissipated to heat in the stretching and in the relaxing of the deformation, gradually taking energy away from the rotating system.

As the deformed moon rotates away from the connecting line, gravity exerts a torque which acts to diminish the rotational angular momentum of the moon, gradually slowing its rotation rate. This braking effect over a long time period brings the moon's rotation rate relative to the connecting line to zero, so that its rotation period approaches the orbital period and the same face is toward the planet at all times. The Earth's Moon has reached that state so that we always see the same side of the Moon.

The planet Mercury is tidally coupled to the Sun but this does not produce the 1:1 ratio of orbit period to rotation period like the Earth's Moon. From the Mercury planetary data we find that the sidereal period of Mercury around the Sun is 87.969 days but the planet's period of rotation about its axis is 58.646 days. The planet makes an accurate 3/2 rotations in one orbital period of the planet. This is called a "tidal resonance" or a "spin-orbit resonance".

The Moon's tidal force on the Earth likewise influences it so that energy is being dissipated by tidal friction. As the tidal deformation of the Earth rotates away from the connecting line, the asymmetry produced by the slightly elongated shape provides a lever arm for a braking torque that slows the Earth's rotation, currently increasing the length of the day by about 2.3 milliseconds per century. A million years from now the day will be about an hour longer.

 How did the Moon form?

Online references:
Ocean Tides and the Earth's Rotation

Index

References:
Ward & Brownlee
Ch 10

Tidal resonance

Kwon, 3-2 Mercury-Sun

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