Application of average equations for investigation of orbit evolution of space debris bodies

Mathematical modeling of the unobservable fraction of space debris in the near-Earth environment is based on investigating time evolution of motions of a large set of space bodies with various orbits. A means of fast and precise calculation of a body orbit is needed for such investigating, at that the calculation must take into account the main disturbing factors: Earth oblateness, atmosphere drag, gravitation of Moon and Sun, solar radiation pressure. The most abundant means of the orbit evolution study is an averaged system of differential equations for osculating orbital elements. In recent time there are a lot of such systems of various forms. Our task consisted in a choice of the most suitable ones. We describe and investigate in this paper the averaged systems that are well adapted to integrating by numerical methods. We evaluate the accuracy of those systems by comparing their solutions with solutions of appropriate full equations of body motion. At that we make such comparing for some sets of disturbing factors.