Asteroidal evolution between Jupiter and Saturn region

Abstract

The stability of the Jupiter-Saturn region is analyzed, in the context of the four body problem, by direct numerical integration of the equations of motion of a group of fictitious asteroids. The results indicate that the region is highly unstable with the exception of two resonance points: the 3/2 and the 1/1 Saturn commensurabilities. Two ejection mechanisms were found: one extremely fast (∼ 10² yrs.) produced by direct close encounters with the planets, and in which the orbits of the bodies turn hyperbolic. The other mechanism (∼ 10⁴ yrs.), is due to the existence of regions of chaotic motion formed by resonance relations. In this case, the asteroids suffer secular changes in the eccentricity and, after close encounters with one of the perturbers, finally escapes. The behaviour of the stable points of the region, is totally different. In the S:3/2 resonance, the results show a small region of stability, in which the motion of the bodies is quasi-periodic. The same thing can be said for the S:1/1 resonance, in which the flux of asteroids to the commensurability and the following regularization of their orbits seems to support the idea of possible Troyans associated with Saturn.