The relative motion of the core and mantle of a planet in the gravitational field of a point mass

A model of a planet, consisting of two solid bodies – a core and a mantle – between which there is a spherical layer of a viscous incompressible liquid, is considered. The gravitational interaction between the core and the mantle is taken into account. The problem is investigated in a limited formulation, when the mass centre of the planet moves in a fixed elliptical orbit in the gravitational field of a point mass, while the mutual displacements of the core and the mantle are to be determined. The mutual displacements of the core and the mantle of the planet, and also the velocity field of the viscous liquid in the spherical layer, are obtained using multiparameter perturbation theory, where the Reynolds number, the orbit eccentricity and the ratio of the radius of the planet to the distance to its attracting centre are taken as small parameters. In addition, an approximate theory of gyroscopes is used to analyse the equations of motion. The results obtained are illustrated by the example of the motion of the Earth-Moon system.