DIFFERENTIAL EQUATIONS OF PLANETARY SYSTEMS

Abstract

In this article will be considered many spherical bodies problem with variable masses, varying non-isotropic at different rates as celestial-mechanical model of non-stationary planetary systems. In this article were obtained differential equations of motions of spherical bodies with variable masses to reach purpose exploration of evolution planetary systems. The scientific importance of the work is exploration to the effects of masses’ variability of the dynamic evolution of the planetary system for a long period of time. According to equation of Mescherskiy, we obtained differential equations of motions of planetary systems in the absolute coordinates system and the relative coordinates system. On the basis of obtained differential equations in the relative coordinates system, we derived equations of motions in osculating elements in form of Lagrange's equations and canonically equations in osculating analogs second systems of Poincare's elements on the base aperiodic motion over the quasi-canonical cross- section.