A celestial-mechanical model for the tidal evolution of the Earth-Moon system treated as a double planet

Abstract

A celestial-mechanical model for the motion of two viscoelastic spheres in the gravitational field of a massive point is considered, treating them as a double planet. The spheres move along quasi-circular orbits in a single plane, with their rotational axes perpendicular to this plane. The deformation of the spheres is described using the classical theory of small deformations. A Kelvin-Voigt model is adopted for the viscous forces. A system of evoutionary equations is obtained and applied to analyze the joint translational-rotational tidal evolution of the Earth and Moon in the gravitational field of the Sun. This system has been numerically integrated several billion years into the past and into the future. The results are compared with the predictions of other theories, paleontological data, and astronomical observations.