The Velocity-Size Relationship for Members of Asteroid Families and Implications for the Physics of Catastrophic Collisions

An extensive analysis of the size-ejection velocity relationship for members of several of the most important asteroid families identified in the Main Belt is presented. We have found a well defined behavior, with smaller fragments having on the average higher ejection velocities. The results provide useful constraints to current models of catastrophic breakup processes and lead also to a new estimate of the transition limit in largest remnant/parent body mass ratio, distinguishing cratering, and shattering regimes. Moreover, we have now available a practical method for estimating fragment ejection velocities in interasteroid collisional events. This can be easily implemented in numerical models of the collisional evolution of the asteroid belt. In particular, it should be possible to undertake a more quantitative assessment of the efficiency of collisional events in the Main Belt as the sources of near Earth asteroids of different sizes.