LARGE ORBITAL ECCENTRICITIES AND CLOSE ENCOUNTERS AT THE 2-1 RESONANCE OF A DYNAMICAL SYSTEM MODELING ASTEROIDAL MOTION

In a recent work (Varvoglis 1991) we proposed the use of a model dynam ical system as a fast and effective method to study the motion of aste roids in the main asteroidal belt. This dynamical system is, essential ly, a modified planar elliptical restricted three-body problem, in whi ch the variation of Jupiter's eccentricity, caused by the perturbation of Saturn, is taken explicitly into account. Here we show that, near the 2: 1 resonance, the (osculating) eccentricity, e, of the trajector ies of this dynamical system may attain high values (e greater-than-or -equal-to 0.6) and that a fictitious asteroid, following such a ''high -e'' trajectory, may undergo a close encounter with Jupiter and be sub sequently removed from the 2:1 resonance region.