Imperfections of Elasticity in the Small Bodies of the Solar System

Abstract

The rough estimate of the damping of the 14-monthly variation of latitude gives two types of solution on the hypothesis of elastic afterworking, in which the times needed to attain the strain for long-continued stress are of the orders of a few weeks and nearly a year. These are applied to tidal friction in the Moon and Mercury. The long scale leads to quantitative difficulties. For the Moon the straightforward application, in which it is supposed that the imperfection of elasticity is elastic afterworking and applies to the whole body, gives satisfactory results, but if it applies only to the inner part it is apparently necessary that the rotation and revolution periods were brought into close coincidence when the Moon was much nearer the Earth than it is now. For Mercury the effect is too small to have produced the required result in the time available, and a greater degree of imperfection of elasticity seems to be required, at least for periods of the order of a day or at some earlier stage of its history. The shorter time scale for the relaxation leads to no serious difficulties. Comparison with satellites of the outer planets shows some peculiar features, but these may be attributed to differences of composition.