THE INFLUENCE OF THE GRAVITATIONAL PERTURBATIONS OF THE SOLAR SYSTEM PLANETS ON THE EVOLUTION OF THEIR ORBITS’ ECCENTRICITIES AND INCLINATIONS

Abstract

In the paper the classic problem of N bodies is treated as if the mass of one body (the Sun) is much larger than the mass of the rest mutually gravitating bodies. We take as the unperturbed motion the movement of a planet in an elliptical orbit, with the Sun being in one of its foci. A set of equations of motion are derived in barycentric coordinates using the canonical Delaunay variables. Applying the motion equation averaged system we define the functions for describing the evolution of a single planet orbit’s eccentricity and inclination caused by the other planets’ mutual gravitation. The numerical estimations of the eccentricity and orbital inclination change rate for each of the Solar system’s planets have been obtained.

Keywords

• n-bodies problems
• barycenter
• delaunay variables
• orbit elements
• perturbed motion
• averaging method