SECULAR RESONANCES IN MEAN MOTION COMMENSURABILITIES - THE 4/1, 3/1, 5/2, AND 7/3 CASES

With this paper we complete our review on the dynamics in mean motion resonances. Here we investigate the 4/1, 3/1, 5/2, and 7/3 commensurabilities and show that, due to the interaction between the nu(5) and nu(6) secular resonances, chaotic motion is present almost everywhere in the phase space. This chaotic motion is responsible for the large jumps in the eccentricity (up to 0.8 or more) that one usually observes in the realistic numerical simulations, which force the asteroids to cross the orbits not only of Mars, but even of Earth. In this way we achieve a better understanding of the effective mechanisms for the depletion of the 3/1, 5/2, and 4/1 resonances, and we are able to explain, for the first time, the existence of the gap associated with the 7/3 mean motion commensurability. (C) 1995 Academic Press, Inc.