Structural integrity of rubble asteroidal satellites

Abstract

We investigate the structural integrity of asynchronous, rubble asteroidal satellites, which may or may not be in synchronous motion, by identifying necessary conditions for the structural equilibrium of such objects. Asynchronous motion may occur when the satellite’s rotation rate about its mass center does not match its orbital angular velocity about the asteroid. The asteroid’s shape is modeled as a triaxial ellipsoid to account for variability in asteroid shapes. The satellites are considered to be oblate or prolate objects, whose rubble interiors are modeled as a rigid-plastic, cohesive material obeying the Drucker–Prager yield criterion. We employ volume-averaging to obtain average stresses in the satellite, which are combined with the yield criterion to obtain necessary conditions for the satellite’s structural equilibrium. Structural equilibrium regions are obtained in terms of the satellite’s shape through the extent of its flattening/elongation, the satellite’s orientation and orbital location with respect to the central asteroid, as characterized by the lead angle of the satellite’s long axis, and an equivalent radius, which accounts for the asteroid’s irregular shape and possibly different density from the satellite. When required, the satellite’s orbital angular velocity is estimated from its distance from the asteroid, assuming that satellite’s orbit is circular. We demonstrate that necessary conditions for the satellite’s structural integrity can be discussed in terms of two particular configurations, viz. the long- and intermediate axis configurations in which the satellite’s long and intermediate axis point towards the asteroid. This reduces a complex dynamical analysis to a simpler quasi-static one. The effects of inter-grain cohesion are explicitly included, as cohesion can play an important role in the extremely low-gravity environments of asteroidal satellites. The final results are applied to recently discovered asteroidal satellites to support or refute the possibility them being rubble piles.