Instability and Chaotic Motion for Some Fictitious Satellites of Venus and Mars

Abstract

Among the remarkable differences between inner and outer planets, we can mention the striking scenario of their satellite system : while in general, the giant planets have a rich satellite system, the inner planets are very poor. In order to explain this situation, many authors have invoked the effects of the tides which could have been decisive to provoke the disappearance or the fall of such satellites. Usually, it is well agreed that the time scale for tides is not so short. In this work, just considering gravitational effects ( solar perturbation and the oblateness of the mother planet), it is possible to show the existence of strong instability and chaotic motion that may occur in a very short time (some thousand of years). The conditions under which this occurs is dictated by some special high values of the obliquity of the ecliptic (ε) and the distance of the satellite from the planet. As shown by Laskar, Touma and Wisdom, the obliquity of the ecliptic of the! inner planets is not primordial. According to them, ε might have varied up to very large inclinations. Therefore considering some high ε and provided that the distance of the satellite is usually in the neighbourhood of a critical value, a strong chaotic motion with big increase of eccentricity and inclination can occur in a very short time.