Preamble

The Earth rotates in the gravity fields of the Moon and Sun, causing cyclic variations in the gravitational potential. The most obvious consequence is the marine tide but there are also tidal deformations of the solid Earth. These take the form of prolate ellipsoidal extensions, aligned with the Moon or Sun, and the observed tides are caused by the rotation of the Earth in the deformed ‘envelope’. This phenomenon occurs in all rotating astronomical bodies that are not very remote from the gravitational influences of their neighbours. It would merit little more than a footnote in a text of this kind were it not for one crucial effect: tides are dissipative. The dissipation of rotational energy is slight in gaseous bodies, but it strongly influences the behaviour and orbital evolution of solid planets and satellites and in the Earth it is strongest in the oceans.

We present an analysis of tidal potential and deformation as the starting point for a discussion of tidal friction. This has had a major effect on the Earth–Moon system and we suggest also on Venus and Mercury. It may not be important to Mars but it has interesting effects on some of the solid bodies of the outer Solar System. The vigorous volcanism of Jupiter's satellite Io is attributed to heating by tidal dissipation. In this case it is a radial tide, that is, a variation in the amplitude of a tide of constant orientation, because Io has stopped rotating relative to Jupiter.