Asteroid orbits in mixed resonances: some numerical experiments

Dynamics of orbits of minor planets in mixed resonances "Jupiter-Saturn-Ast eroid" of low order is investigated with the help of different numerical ex periments. Several thousands of fictitious asteroids with different initial eccentricities and inclinations are integrated numerically with the simult aneous computation of Lyapunov-Exponent in models with two (Jupiter and Sat urn) and one (Jupiter or Saturn) disturbing bodies in order to analyse, und er what conditions the joint perturbations from Jupiter and Saturn can lead to the origin of chaos in motion of minor planets. It is shown, that in th e middle part of the main asteroid belt the joint perturbations from Jupite r and Saturn lead to the phenomenon of "stable chaos" in asteroid motion. I n the inner part of the asteroid belt the large variations in eccentricity appear in the model with two disturbing bodies for orbits with small inclin ations. These variations can lead to close encounters of asteroids with Mar s, that makes this region very unstable. (C) 2001 Elsevier Science Ltd. All rights reserved.