EVOLUTION EQUATIONS OF THE RESTRICTED THREE-BODY PROBLEM WITH VARIABLE MASSES

. In classical celestial mechanics, the theory of perturbation based on Keplerian motion iswell developed. Various kinds of perturbed motion equations are described by canonical equations,Lagrange equations and Newton's equations. The masses of bodies are assumed constant and the bodies arepoint or spherical. Classical perturbation theory is a basic tool in the study of many astronomical problems.Observational astronomy shows that the masses of real cosmic bodies change over time. Real celestialbodies are neither spherical nor solid. Celestial bodies are non-stationary and their masses, sizes, shapes andstructures change over time as they evolve. There are now a number of studies with a communitybibliography of papers on the celestial mechanics of bodies of variable mass. However, the perturbationtheory for unsteady space systems is not sufficiently developed. Therefore, we considered a gravitationalsystem consisting of three spherical celestial bodies, with spherical density distributions, with variablemasses in the restricted formulation. We have considered the general case where the masses of the bodieschange non-isotropically at different rates, in the presence of reactive forces. We will assume that a bodywith infinitesimal mass has no effect on the motions of the two main bodies. The problem was investigatedby methods of perturbation theory based on aperiodic motion along the quasi-conic section developed fornonstationary gravitating systems. Evolution motion equations of a less massive body and a small body inoscillating elements, in the relative coordinate system, have been obtained.