Tidal dissipation by solid friction and the resulting orbital evolution

TLDR

Tidal dissipation in the Earth’s mantle and Moon varies with depth, ranging from ~2×10⁻⁶/Q to ~0.02×10⁻⁶/Q erg cm⁻³ s⁻¹ in the mantle and from ~0.03×10⁻⁶/Q to ~0.4×10⁻⁹/Q erg cm⁻³ s⁻¹ in a homogeneous Moon, with compressibility and inhomogeneity contributing less than 3%. The study develops an orbital‑evolution theory that uses a time‑Fourier series disturbing function to analyze how variations in the dissipation factor 1/Q or lag angle ε affect the system. The authors compute tidal energy dissipation in the Earth’s mantle and Moon assuming a constant 1/Q, formulate a Fourier‑series disturbing function to study how 1/Q or lag angle variations influence orbital evolution, and compare their results with previous studies.

Abstract

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.