Tidal Deformations of a Viscoelastic Planet

Abstract

This article studies the tidal deformations of a viscoelastic planet in the gravitational field of the attracting center and satellite. The planet is modeled either as a body consisting of a solid core and a viscoelastic shell rigidly attached to it, or as a uniform isotropic viscoelastic ball. The attracting center and the satellite are modeled by material points. The function describing the dependence of the height of the tidal hump at a fixed point on the planet’s surface on time has been found. Graphs of this function were constructed for the planet “Earth” moving in the gravitational field of the Sun and the Moon. To obtain the result, the method of separation of movements developed by V.G. Vilke for mechanical systems with an infinite number of degrees of freedom is used.