Damage Modeling, Scaling and Momentum Enhancement for Asteroid and Comet Nucleus Deflection

Abstract

In the previous symposium, it was demonstrated that extrapolation of momentum enhancement β data from small laboratory tests to larger asteroid and comet nucleus deflection scenarios predicts large β values due to the fact that β does not scale with size. The big question in the extrapolation to larger scales is whether the damage process in the crater formation saturates at some scale – i.e., is there a size beyond which the momentum enhancement does scale, and thus the large scale large β values are not realized. In this work we take the data from the NASA Ames gun in the 1960s by Denardo and Nysmith [1] and examine its clear lack of scaling in more detail. We determine the behavior of the ejecta mass. We show that the amount of ejecta mass is proportional to the impact velocity squared times the square root of the projectile diameter, a quantity which has the dimensions of fracture toughness. Thus, it is likely that the mass liberation process depends on fracture toughness, which contrasts with the fact that the crater size depends on target material strength. Thus, a small fracture toughness leads to large ejecta mass, and that in turn leads to large momentum enhancement. The appearance of the dimensions of fracture toughness implies that classical failure scaling is at work. Classical fracture mechanics is a damage process that likely will not saturate and that we then are able to extrapolate to large sizes. We discuss impactors that would be used to deflect asteroids or comet nuclei for planetary defense or for engineering and exploration purposes, and what expected momentum enhancements would be for impacts into asteroids or comet nuclei comprised of consolidated materials.