We have applied the frequency map analysis on the problem of asteroidal motion in the 2/1 mean-motion resonance with Jupiter. Laskar's technique was adapted for the particular use in this dynamical system. The method was then applied to the planar three-body model. We have shown the most detailed correct reproduction of the low-eccentricity chaotic region and investigated the chaos produced by the high-order secondary resonances. We compared their position with that predicted by the semi-numerical method in the circular problem. The narrow chaotic layers were found to be localized in the vicinity of their separatrices. The region around the low-eccentricity chaos is sensible to the value of Jupiter's eccentricity, the chaos grown for but still left a great portion of the phase space regular. The regularity disappeared when the variations of Jupiter's orbit were included and the moderate eccentricity region became chaotic. The effect of the slow chaotic diffusion in moderate eccentricities was then studied on the basis of several 10 Myr integrations with Saturn. It has not yet been possible to make any statistic conclusions about the diffusion effect over much longer time spans. But it seems clear, as the observed changes of several integrated trajectories were so important, that a prolongation of the time interval by two orders of magnitude would allow at least some portion of asteroids to enter the fast low-eccentricity chaos or to reach directly the large eccentricities allowing close encounters with the planets.
© European Southern Observatory (ESO) 1997
Online publication: June 30, 1998