ВЫХОД КОСМИЧЕСКИХ МАСС ИЗ ОКРЕСТНОСТЕЙ МАССИВНОГО ТЕЛА ПОД ВОЗДЕЙСТВИЕМ ВНЕШНЕГО ГРАВИТАЦИОННОГО ВОЗМУЩЕНИЯ

The accumulation of space debris in Earth's orbit has given rise to a number of problems, and the required solution is to remove it from near-Earth space as efficiently as possible. In order to achieve this, it is necessary to study the formation of large groups of these artificial particles, their evolution in shape and in orbit, as well as the possibility of their change in movement influenced by the gravity of a massive body such as the Moon. In order to solve the problem of space debris in near-Earth orbit, a mathematical model predicting the behavior of cosmic masses is proposed in this paper. It uses the Chazy classification of final motions in the three-body problem and helps consider the case of the final hyperbolic-ellipticity of the motion of cosmic masses. Possible removal of space debris from near-Earth orbit via the Hill's Sphere model is discussed; at a certain point, when the debris particle is between the Earth and the Moon, it can either exit the Earth-Moon system along a hyperbolic trajectory, or begin orbiting the Moon instead of the Earth. The proposed mathematical model gives insight into the question of space debris of extra-terrestrial origin in the orbital space between the Earth and the Moon. A theorem is derived to describe the necessary conditions for the final hyperbolic-ellipticity of the motion of cosmic masses. A number of simulations is carried out according to the theorem in order to find the optimal orbits of particles. The paper concludes with the orbital parameters of space debris required to meet these conditions.