Gravitational potential of a planet modeled by a visco-elastic sphere

Abstract

The paper investigates the gravitational potential of a planet moving in a gravitational field of an attracting center and a satellite. The planet is modeled by a homogeneous isotropic visco-elastic body that in its natural undeformed state has a full sphere shape. The satellite and the attracting center are represented by material points. The planet-satellite system moves relatively to the common center of gravity, which in its turn moves along a Keplerian orbit relatively to a motionless attracting center. Based on the solution of the quasi-static problem of elasticity theory for the current problem, the authors deduced a formula for evaluating the gravitational potential of a planet and also determined the Earth’s gravitational potential, taking into account the Moon and Sun’s tidal effects both in an external point.