Features of Space Debris Migration in the Earth-Moon System

The possibility of capturing and releasing cosmic masses is considered within the framework of a plane hyperbolic three-body problem, as well as within the framework of a plane parabolic three-body problem. A mathematical model is proposed that allows us to explain the formation of nonspherical satellites of planets, similar to the Martian satellites Phobos and Deimos, due to the interception or exchange of cosmic masses, and also allows us to understand why there is no space debris of extraterrestrial origin in near-Earth and lunar space. The effect of accumulation of artificial debris in the Earth-Moon system is being studied. The present study is based on a numerical and analytical analysis of certain Chazy classification schemes for final motions in the three-body problem. The three-body boundary value problem is considered, the possibility of the existence of a solution to this problem is shown, and the conditions for the final hyperbolic-ellipticity of motion are obtained. The analytical results are illustrated by numerical simulations.