Evolution of the Orbital Motion of a Satellite of a Viscoelastic Planet taking into account its Tidal Deformations

This work is dedicated to the study of the orbital motion of an artificial satellite moving in the gravitational field of a viscoelastic planet, which in turn is moving in the gravitational field of a massive attracting center and a satellite. The planet is modeled as a homogeneous isotropic viscoelastic body, while the other celestial bodies are treated as material points. Under the influence of the gravitational fields of the attracting center and the natural satellite, tidal bulges arise in the viscoelastic body of the planet, which affect its gravitational potential and serve as a disturbing factor for the orbital motion of artificial satellites in low-flying orbits. The equations of motion for the artificial satellite are derived in terms of Delaunay canonical variables. A procedure for averaging over the “fast” angular variables is carried out. In the averaged equations, the “slow” Delaunay variables responsible for the evolution of the semimajor axis and the eccentricity of the elliptical orbit remain unchanged. The entire effect of evolution is concentrated in the change of inclination, longitude of the ascending node, and longitude of the perigee from the ascending node. With respect to the specified orbital elements, an evolutionary system of equations is derived. In the zero approximation for the dissipative terms, a closed system of second-order differential equations is identified relative to the inclination and longitude of the ascending node of the satellite’s orbit. Its stationary solutions are determined and their stability is studied. The existence of stable stationary motions for polar satellites and satellites close to equatorial ones is shown.