Stability time-scale prediction for main-belt asteroids using neural networks

Many asteroids move in the belt between the orbits of Mars and Jupiter under the gravitational attraction of the Sun and planets in the Solar system. If one of these asteroids does not leave the belt during a period, it is considered to be temporarily stable on that time-scale. This paper aims to study the time-scales on which asteroids could stay in the main belt. A simplified situation is studied in which the initial orbital inclinations and the longitudes of the ascending nodes of the asteroids are set to zero. Numerical integration is used to study the temporal stability of the main-belt asteroids. In the integration, the distribution of the instability time for randomly generated particles can be fitted with a function. Thus a reasonable method is presented to choose an integration time-scale based on the percentage of the already unstable particles in relation to all unstable particles. A total of 151 000 particles are generated and then integrated for 8.09 × 106 yr. The integration data are used to train the probabilistic neural networks to predict the stability of particles. A temporal stability map in the a-e plane is obtained from the prediction results of the neural networks.