Orbital evolution of asteroids with the effects of mutual gravitational attraction

The effects of the mutual gravitational attraction between asteroids were analyzed by two N-body calculations, in which N=4,516 (the Sun, the nine planets, and 4,506 asteroids). In one calculation the gravity of the asteroids was taken into account, and in the other it was ignored. These calculations were carried out for a time period of about 100 years. The largest difference in the positions of the asteroids between these two calculations is about 10^–3 AU. For the orbital elements of the semimajor axis, the eccentricity, and the inclination, the largest differences were 9 × 10^–6 AU, 4 × 10^–6, and 5 × 10^–4 degrees, respectively. It was found that the distribution of the differences of the semimajor axis between the two calculations is quite similar to the Cauchy distribution.