Icarus 165 (2003) 355–370 www.elsevier.com/locate/icarus Interacting ellipsoids: a minimal model for the dynamics of rubble-pile bodies F. Roig, a,∗ R. Duffard, a P. Penteado, a D. Lazzaro, a and T. Kodama b a Observatório Nacional–MCT, Rua Gal. José Cristino 77, Rio de Janeiro, 20921-400 RJ, Brazil b Instituto de Física–UFRJ, Cx. Postal 68528, Rio de Janeiro, 21945-970 RJ, Brazil Received 13 March 2003; revised 7 July 2003 Abstract A simple mechanical model is formulated to study the dynamics of rubble-pile asteroids, formed by the gravitational re-accumulation of fragments after the collisional breakup of a parent body. In this model, a rubble-pile consists of N interacting fragments represented by rigid ellipsoids, and the equations of motion explicitly incorporate the minimal degrees of freedom necessary to describe the attitude and rotational state of each fragment. In spite of its simplicity, our numerical examples indicate that the overall behavior of our model is in line with several known properties of collisional events, like the energy and angular momentum partition during high velocity impacts. Therefore, it may be considered as a well defined minimal model.  2003 Elsevier Inc. All rights reserved. Keywords: Collisional physics; Impact processes; Rotational dynamics; Asteroids 1. Introduction Rubble-pile asteroids are believe to be the outcomes of the re-accumulation of fragments after the catastrophic dis- ruption of a large asteroid. They would be basically consti- tuted by a cluster of several monolithic bodies, which are kept together by their mutual gravitational attraction, with- out any additional cohesive forces between them. Among several evidences, the actual existence of a large number of these cohesion-less bodies in the asteroid belt is suggested by: (i) the rather low mass densities (∼ 1–2 g cm -3 ) mea- sured on some large asteroids (e.g., Merline et al., 1999; Veverka et al., 1997; Viateau, 2000; Yeomans et al., 1997, 1999); (ii) the notable absence of kilometer-sized and larger bod- ies with rotational periods shorter than ∼ 2 h (e.g., Harris and Burns, 1979; Pravec and Harris, 2000; Wei- denschilling, 1981); * Corresponding author. E-mail address: froig@on.br (F. Roig). (iii) the unusual observed shapes of some asteroids (e.g., Bottke et al., 1999; Kwiatkowski, 1995; Miller et al., 2002; Thomas et al., 2002); (iv) the presence of giant craters and grooves on the sur- faces of some asteroids recently revealed by the NEAR Shoemaker probe (e.g., Veverka et al., 1997); and (v) the existence of small asteroidal satellites and binary asteroids (e.g., Chapman et al., 1995; Merline et al., 1999). Many collisional processes in the Solar System, like the formation of asteroid families, the tidal disruption of comets and NEAs, and the formation of asteroid satellites, may in- volve parent bodies with a rubble pile structure. Thus, the precise understandings of the collisional dynamics of rubble- piles would give important insight about these processes. One of the crucial questions about the formation of asteroid families is how the incident collisional energy is transferred into the rotational energies of the ejected fragments. The pur- pose of this paper is to introduce a minimal model to study such problems. This model aims to describe the macro- scopic behavior of different quantities—like energy, angular momentum, escape velocities and spins—during the course of the dynamical processes involving rubble-pile asteroids, 0019-1035/$ – see front matter  2003 Elsevier Inc. All rights reserved. doi:10.1016/S0019-1035(03)00216-1