Low-speed impacts between rubble piles modeled as collections of polyhedra, 2

Abstract

We present the results of additional calculations involving the collisions of km-scale rubble piles. In new work, we used the Open Dynamics Engine (ODE), an open-source library for the simulation of rigid-body dynamics that incorporates a sophisticated collision-detection and resolution routine. We found that using ODE resulted in a speed-up of approximately a factor of 30 compared with previous code. In this paper we report on the results of almost 1200 separate runs, the bulk of which were carried out with 1000–2000 elements. We carried out calculations with three different combinations of the coefficients of friction η and (normal) restitution ϵ : low ( η = 0 , ϵ = 0.8 ) , medium ( η = 0 , ϵ = 0.5 ) , and high ( η = 0.5 , ϵ = 0.5 ) dissipation. For target objects of ∼1 km in radius, we found reduced critical disruption energy values Q RD ∗ in head-on collisions from 2 to 100 J kg −1 depending on dissipation and impactor/target mass ratio. Monodisperse objects disrupted somewhat more easily than power-law objects in general. For oblique collisions of equal-mass objects, mildly off-center collisions ( b / b 0 = 0.5 ) seemed to be as efficient or possibly more efficient at collisional disruption as head-on collisions. More oblique collisions were less efficient and the most oblique collisions we tried ( b / b 0 = 0.866 ) required up to ∼200 J kg −1 for high-dissipation power-law objects. For calculations with smaller numbers of elements (total impactor n i + target n T = 20 or 200 elements) we found that collisions were more efficient for smaller numbers of more massive elements, with Q RD ∗ values as low as 0.4 J kg - 1 for low-dissipation cases. We also analyzed our results in terms of the relations proposed by Stewart and Leinhardt [Stewart, S.T., Leinhardt, Z.M., 2009. Astrophys. J. 691, L133–L137] where m 1 / ( m i + m T ) = 1 - Q R / 2 Q RD ∗ where Q R is the impact kinetic energy per unit total mass m i + m T . Although there is a significant amount of scatter, our results generally bear out the suggested relation.