Application of average equations of space body for approximation of trajectory measurements

Evaluation of space debris accumulation in the near-Earth space demands investigations of 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 these investigations and the calculation must take into account the main disturbing factors: Earth oblateness, atmosphere drag, gravitation of Moon and Sun, solar radiaton pressure. The most abundant means of the orbit evolution study is an averaged system of differential equations for osculating orbital elements. We evaluate in this paper the accuracy of averaged systemsfor approximation of motion of real Earth satellites that move without any control and are similar in this relation to space debris bodies. We consider two satellites: low-orbiting Foton M-3 and resonance Molniya 2. The different averaged systems are used for description of their motion. We evaluate the accuracy of those systems by two ways. First, we compare solutions of each system with solutions of appropriate full equations of satellite motion. Second, we try to approximate the satellite two line elements by solutions of the averaged and full systems. It turned out, that the averaged systems give a sufficiently precise description of secular variation of satellite orbital elements but give 1.5–2 times greater errors at approximating of two line elements than the full systems.