Study of Secular Perturbations in the Restricted Three-Body Problem of Variable Masses Using Computer Algebra

Abstract

A nonstationary restricted three-body problem for variable masses is considered taking into account the reactive forces arising due to anisotropic variation of masses of the bodies. It is assumed that the bodies are spherically symmetric and interact in accordance with Newton’s law of gravitation. On the basis of the equations of motion of the bodies in the relative system of coordinates, differential equations of aperiodic motion along quasi-conic sections in terms of osculating elements are derived. Equations determining the secular perturbations of the orbital elements are derived in the case of small eccentricities and inclinations of orbits. All symbolic computations are performed using Wolfram Mathematica.