Orbital tori in three-dimensional space and time

Abstract

Orbital torus is a spatial figure formed by an elliptical orbit of a small body in a coordinate system rotating around a central body. The conception of orbital tori was introduced by the author about 35 years ago choosing high-apogee orbits of artificial Earth satellites (AES) to study near-Earth space. In this paper, is investigated the evolution of orbital tori in space and time under the influence of external gravitational perturbations. These studies based on qualitative perturbation theory methods developed in the Lidov-Kozai theory (TLK). At the same time, to study the evolution of orbital tori, numerical integration of orbits carried out taking into account various perturbing factors, and TLK used to understand the essence and description of the character of the evolution of orbits and orbital tori. As an illustration of these studies, the evolution of near-Earth orbital tori under the influence of external gravitational perturbations from the Moon and the Sun is used. It shown that the Moon has a more effective influence on the evolution of orbits and orbital tori than the Sun, and the precession of the Moon’s orbit changes the character of the evolution of orbits and orbital tori.