Structural stability of rubble-pile asteroids

Granular aggregates, like fluids, do not admit all manners of shapes and rotation rates. It is hoped that an analysis of a suspected granular asteroid’s equilibrium shape and its structural stability will help confirm its rubble-pile nature, and, perhaps, even constrain the asteroid’s material parameters. Equilibrium shapes have been analyzed in the past by several investigators (Holsapple, K.A. [2001]. Icarus 154, 432–448; Harris, A.W., Fahnestock, E.G., Pravec, P. [2009]. Icarus 199, 310–318; Sharma, I., Jenkins, J.T., Burns, J.A. [2009]. Icarus 200, 304–322). Here, we extend the classical Lagrange–Dirichlet stability theorem to the case of self-gravitating granular aggregates. This stability test is then applied to probe the stability of several near-Earth asteroids, and explore the influence of material parameters such as internal friction angle and plastic bulk modulus. Finally, we consider their structural stability to close planetary encounters. We find that it is possible for asteroids to be stable to small perturbations, but unstable to strong and/or extended perturbations as experienced during close flybys. Conversely, assuming stability in certain situations, it is possible to estimate material properties of some asteroids like, for example, 1943 Anteros.