Dynamical behaviour of the primitive asteroid belt

In this paper we consider the dynamical evolution and orbital stability of objects in the asteroid belt. A simple physical model, including full gravitational perturbations from both giant planets, is used to compute the dynamical evolution of 1000 test particles simulating the primitive asteroids. The criterion of planet crossing (or close approach in the case of resonant objects) is used to reject particles from the simulation. 44 per cent of the particles survived for the whole time-span covered by the numerical integration (similar to 10(9) yr). The 4:1, 3:1 and to a lesser extent the 2:1 Kirkwood gaps are formed in similar to 10(7) yr of evolution, representing direct numerical evidence about their gravitational origin. We found that the rms eccentricity and inclination of the sample experience a fast increase during the first 10(6) yr. The final rms eccentricity is 0.11, similar to 60 per cent smaller than the present rms eccentricity (0.17). Nevertheless, the gravitational action of the giant planets suffices to prevent the formation of large objects, allowing catastrophic collisions and the subsequent depletion of material from this zone of the Solar system. The excited eccentricity by Jupiter and Saturn may favour mutual encounters and the further increase of the relative velocities up to their present values.