Asteroid orbits in mixed resonances: some numerical experiments

Dynamics of orbits of minor planets in mixed resonances “Jupiter–Saturn–Asteroid” of low order is investigated with the help of different numerical experiments. Several thousands of fictitious asteroids with different initial eccentricities and inclinations are integrated numerically with the simultaneous computation of Lyapunov–Exponent in models with two (Jupiter and Saturn) and one (Jupiter or Saturn) disturbing bodies in order to analyse, under 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 the middle part of the main asteroid belt the joint perturbations from Jupiter and Saturn lead to the phenomenon of “stable chaos” in asteroid motion. In the inner part of the asteroid belt the large variations in eccentricity appear in the model with two disturbing bodies for orbits with small inclinations. These variations can lead to close encounters of asteroids with Mars, that makes this region very unstable.