Collision rates and impact velocities in the main asteroid belt

Abstract

We have computed, using G.W. Wetherill's (1967, J. Geophys. Res. 72, 2429–2444) algorithm, mutual collision probabilities and impact velocities for a set of 682 asteroids of diameter > 50 km, intended to represent a bias-free sample of asteroid orbits. For every asteroid, we have obtained the intrinsic collision probability, P i, the average collision velocity, V, and the number of projectile orbits which can intersect the target asteroid's orbit, N cross, using the proper orbital elements of A. Milani and Z. Knežević (1990, Celest. Mech. 49, 247–411). The average values and the corresponding standard deviations for the whole asteroid sample are: 〈 P i〉 = 2.85 ± 0.66 × 10 −18 km −2 year −1, 〈 V〉 = 5.81 ± 1.88 km/sec, 〈 N cross〉 = 601 (88% of the existing orbit pairs). No significant differences were found in the average values of P i, V, or N cross using osculating elements instead of proper elements, although results for individual asteroids could change by ≈10%. A running box mean of the intrinsic collision probability with semimajor axis shows a peak near 2.7 AU with 〈 P i〉 = 3.4 × 10 −18 km −2 year −1 followed by a nearly monotonic decrease to 〈 P i〉 = 1.8 × 10 −18 km −2 year −1 at 3.3 AU. Collision probabilities are nearly independent of eccentricities but show a significant decrease with larger inclinations. As expected, collisional velocities grow rapidly with increasing orbital eccentricities and inclinations, but they show surprisingly little variation across the asteroid belt. Family asteroids undergo collisions with other members of the same family two to three times more frequently than with nonfamily projectiles, but the relative speed of these intrafamily impacts is comparatively low for the Koronis and Themis families.