Planets in the asteroid belt

The main asteroid belt has lost >99.9% of its solid mass since the time at which the planets were forming, according to models for the protoplanetary nebula. Here we show that the primordial asteroid belt could have been cleared efficiently if much of the original mass accreted to form planet-sized bodies, which were capable of perturbing one another into unstable orbits. We provide results from 25 N-body integrations of up to 200 planets in the asteroid belt, with individual masses in the range 0.017-0.33 Earth masses. In the simulations, these bodies undergo repeated close encounters which scatter one another into unstable resonances with the giant planets, leading to collision with the Sun or ejection from the solar system. In response, the giant planets' orbits migrate radially and become more circular. This reduces the size of the main-belt resonances and the clearing rate, although clearing continues. If similar to3 Earth masses of material was removed from the belt this way, Jupiter and Saturn would initially have had orbital eccentricities almost twice their current values. Such orbits would have made Jupiter and Saturn 10-100x more effective at clearing material from the belt than they are on their current orbits. The time required to remove 90% of the initial mass from the belt depends sensitively on the giant planets' orbits, and weakly on the masses of the asteroidal planets. 18 of the 25 simulations end with no planets left in the belt, and the clearing takes up to several hundred million years. Typically, the last one or two asteroidal planets are removed by interactions with planets in the terrestrial region.