The shapes and rotational dynamics of minor planetary satellites

Statistical analysis of the available data on the sizes and inertial parameters for all hitherto known satellites of the Solar system’s planets is performed. Analytical approximations are derived for the size distribution of satellites. Empirical relations are obtained to approximately estimate the inertial parameters of a satellite from its size. These relations can be used in statistical studies of the possibility of manifestations of various nonstandard rotational modes of planetary satellites. In particular, the probability of the “Amalthea effect” (the presence of two centers of synchronous resonance in the phase space of rotational motion) is shown to be much higher for minor (with diameters smaller than 100 km) satellites moving in close-to-circular orbits than for other satellites.