New data on the velocity–mass relation in catastrophic disruption

The relationship between fragment velocity and mass following a disruptive impact is of great importance when modelling populations of small bodies such as the asteroid main belt or the more recently observed Edgeworth-Kuiper belt where mutual collisions play an important role in their dynamic evolution. The velocity-mass relation following these mutual collisions strongly affects not only the collisional lifetime of large (gravity dominated) asteroids, but also the rate at which mass is ejected from the belt into resonances, providing a source of resupply for the Earth-crossing asteroid population and, in the case of the Edgeworth-Kuiper Belt, the short period comets. Although considerable work has been done on the subject of the relationship between velocity and mass of fragments from cratering and catastrophic disruption events, it has recently become apparent that there may not be a valid general relationship between these quantities. In this paper I present a summary of size-velocity data obtained from single- and twin-camera films of hypervelocity, highly catastrophic impacts into spherical 21 cm targets of artificial rock with strength and density similar to basalt. The 2D velocities of at least 951 fragments larger than approximately 10 mm have so far been measured in 8 similar experiments. Of these, 69 have been studied in 3D in the recent experiments using two cameras at 60°. The data collected here suggest that in general there is only a weak correlation between mass and velocity, and that the best-fitting exponent varies between 0 and −1\6 with an average value of approximately −1\13.