Secular perturbations in the three-body problem with masses changing anisotropically at the different rates

Abstract

In this article we investigate the three-body problem with variable masses changing non-isotropically at the diferent rates in the general case. In this case due to non-isotropically mass changes appear reactive forces. Using the methods of the perturbation theory are obtained the canonical equations of secular perturbations of the three-body problem with masses changing non-isotropically at the diferent rates. The mass change laws are considered arbitrary. Using Picard’s method in the analogues of the second system of the Poincare elements are found approximate analytical solutions of the equations of secular perturbations. On basis of these solutions is possible to do the analysis of the evolution of the analogues elements of the orbit. It can be used in the analysis of the dynamical evolution of triple gravitating systems with varying anisotropic reactive in the presence of the masses forces.