Collisional outcomes in the asteroid belt

In order to study the outcomes of the major collisions endured by asteroids of different sizes, the projectile's kinetic energy (PKE) is compared with the energy needed to overcome the target's solid-state cohesion (expressed as SM, where M is target mass and the critical specific energy S ranges from 100,000 to 100 million erg/g, depending on the material properties) plus the target's self-gravitational energy. This latter is multiplied by a factor gamma, to account for energy losses due to dissipative processes. It is predicted that catastrophic fragmentation occurs and that a substantial part of the target's mass is dispersed to infinity when PKE SM + (3 gamma/5) (GMsq/R) where R is target radius. It is concluded that almost all asteroids are outcomes of catastrophic collisions, that caused either complete fragmentation of the target objects or, at least, drastic readjustments of their internal structure, shape and spin rate.