Evolution of motion of a double planet in the gravitational field of a massive viscoelastic body

The motion of a double planet in the gravitational force field of a massive planet modeled by a viscoelastic body is studied. The double planet is modeled by a viscoelastic body and a material point. The viscoelastic bodies are homogeneous, isotropic and, in their undeformed state, occupy spherical regions in the three-dimensional Euclidean space. The problem is solved in the framework of the linear theory of viscoelasticity. The motion separation method and the averaging method are applied to derive an approximate system of equations describing the evolution of translational-rotational motion for the mechanical system under study. The Earth–Moon system is considered in the gravitational force field of the Sun as an example of a double planet.