LONG-TIME STABILITY FOR THE MAIN PROBLEM OF ARTIFICIAL-SATELLITES

We investigate the significance of long time stability predictions in the light of Nekhoroshev's theory by studying the orbits of artificial satellites. As a simplified model problem we consider the so-called J (2) problem for an earth's satellite, neglecting luni-solar perturbati ons and nonconservative effects. We consider a wide range of orbits, e xcluding those which are too close to the critical inclination. Most o f the orbits turn out to be stable for times larger than the estimated age of the solar system, thus proving that, as far as dissipation can be neglected, stability in Nekhoroshev's sense may be effective for p hysically realistic systems.