Tidal dissipation by solid friction and the resulting orbital evolution

Dissipation of tidal energy in the earth's mantle and the moon was calculated assuming a dissipation factor 1/ Q constant throughout both bodies. In the mantle the dissipation varies from about 2 × 10 −6 / Q erg cm −3 sec −1 near the pole at the bottom of the mantle to about 0.02 × 10 −6 / Q erg cm −3 sec −1 near the surface. The effects of compressibility and inhomogeneity are less than 3%. In a homogeneous moon the dissipation varies from a maximum of about 0.03 × 10 −6 / Q erg cm −3 sec −1 near the center to a minimum of about 0.4 × 10 −9 / Q erg cm −3 sec −1 at the surface. A theory of orbital evolution is developed in which the disturbing function is expressed in a Fourier series with respect to time, so that the effects of variation of dissipation factor 1/ Q , or lag angle ϵ, with amplitude and frequency can be examined. Comparisons with results of other authors are made.