Stability of rubble-pile satellites

We consider the stability of rubble-pile satellites that are held together by their own gravity. A satellite is said to be stable whenever it is both orbitally and structurally stable to both orbital and structural perturbations. We restrict attention to satellites whose dimensions are small compared to their respective orbital radii and their associated planets' sizes. In this case, we show that a satellite is stable whenever it is orbitally stable to orbital perturbations and structurally stable to structural perturbations. Orbital stability is investigated by a spectral analysis, while structural stability is probed by appropriately extending the work of Sharma [Sharma, I., 2012. Stability of rotating non-smooth complex fluids. J. Fluid Mech. 708, 71-99; Sharma, I., 2013. Structural stability of rubble-pile asteroids. Icarus 223, 367-382]. The stability test is then applied to planetary satellites of the Solar System that are suspected to be granular aggregates, including many of the recently discovered smaller moons of the giant planets.