Rotation of an elastic sphere about its mass center in the gravitational field of two attracting points

A planet model as a uniform elastic sphere in the gravitational field of two mass points whose mutual motion causes tidal deformations is considered. The sphere rotation about its mass center is studied with consideration of its deformations caused by the centrifugal force field and the gradient fields of gravitational forces. The sphere’s inertia tensor whose components are time dependent is found. The sphere’s angular velocity projections onto the axes associated with the sphere according to an integral law are determined. The results obtained are illustrated for the case of the Earth. For this case, the equivalent values of the elasticity modulus and Poisson’s ratio and the angular velocity disturbances are found.