The asteroid belt and its evolution

We have reinvestegated the suggestion that collisional fragmentation in the asteroid belt can account for its present luminosity function. We suggest, based on the usual Boltzmann-type equation for this process, that for the brightest asteroids the time scale for a catastropic collision is 1.2 × 10⁹yr. However, the assumption of molecular chaos is not valid in the asteroid belt and we demonstrate a new method to determine the necessary corrections. We then obtain, using the new procedure, a lower limit for a collision time. For the above sample it is 2 × 10¹¹yr. This, we believe, rules out collisional evolution of the asteroid belt since its formation. Finally, we also show histograms of eccentricity, inclination, absolute magnitude, height above the ecliptic plane, and argument of perihelion for the 2829 asteroids with well-determined orbits. This represents a synthesis of the numbered asteroid and PLS data.