Effects of orbital ellipticity on collisional disruptions of rubble-pile asteroids

Abstract

The behavior of debris ejected from asteroids after collisional disruptions has significant implications for asteroid evolution. Analytical approximations of the elliptic restricted three-body system show that the behavior of ejecta varies significantly with the orbital eccentricity and true anomaly of an asteroid. To study these orbital perturbative effects on collision outcomes, we conduct a series of low-speed collision simulations using a combination of an \(N\)-body gravity algorithm and the soft-sphere discrete element method. The asteroid is modeled as a gravitational aggregate, which is one of the plausible structures for asteroids whose sizes are larger than several hundreds of meters. To reduce the effect of complicating factors raised by the mutual interaction between post-collision fragments on the outcomes, a low-resolution model and a set of frictionless material parameters are used in the first step of exploration. The results indicate that orbital perturbations on ejecta arising from the eccentricity and true anomaly of the target asteroid at the time of impact cause larger mass loss and lower the catastrophic disruption threshold (the specific energy required to disperse half the total system mass) in collision events. The “universal law” of catastrophic disruption derived by Stewart and Leinhardt (Astrophys. J. Lett. 691:L133–L137, 2009) can be applied to describe the collision outcomes of asteroids on elliptical heliocentric orbits. Through analyses of ejecta velocity distributions, we develop a semi-analytic description of escape speed from the asteroid’s surface in an elliptic restricted three-body system and show that resulting perturbations have long-term orbital effects on ejecta and can also have an indirect influence on the velocity field of post-fragments through interparticle collisions. Further exploration with a high-resolution model shows that the long-term perturbative effects systematically increase mass loss, regardless of the target’s material parameters and internal configuration, while indirect effect on mass loss is much more complicated and is enhanced when a coarse material or high-porosity model is used.