Motion stability of the system of two bodies and their mass center in an inhomogeneous medium

Within the framework of Newtonian celestial mechanics, a material system is considered. It consists two spherically symmetrical bodies comparable masses moving inside gas dust ball with density distribution medium in it. Problems are formulated and solved. They give an answer to degree influence gravitational field inhomogeneous on motion stability their mass center relative coordinates bodies, center, as well orbital according Lyapunov. Additionally, problems sense Lagrange Poisson proved that symmetrically distributed transforms considered motions, which stable vacuum, into unstable ones Lagrange, Poisson, Some numerical estimates related instabilities presented. show for popular pairs stars galaxies medium, additional displacements order many millions kilometers arise. When dark matter taken account, should not be magnitude greater than last estimate. The noted consequence secular displacement along cycloid or deformed absence barycentric coordinate when taking account (the closed). this system, circular elliptical orbits cannot exist. Instead these orbits, we have “turns” shown figure given article. In planetary systems (such Solar System) immersed centers negligible therefore can assume practically