Dynamical stability in the vicinity of Saturnian small moons: The cases of Aegaeon, Methone, Anthe, and Pallene

Abstract

In this work we analyse the orbital evolution and dynamical stability in the vicinity of the small Saturnian moons Aegaeon, Methone, Anthe, and Pallene. We numerically resolve the exact equations of motions to investigate the orbital motion of thousands of test particles within and near the domain of the 7/6, 14/15, 10/11 mean-motion resonances of Aegaeon, Methone, and Anthe with Mimas, respectively. We show that, for massless small moons, the orbits of particles initially restricted to the resonant domains remain stable for at least 104 yr. We also conduct numerical simulations considering Aegaeon, Methone, Anthe, and Pallene as massive bodies. The results show that most particles undergo significant perturbations in their orbital motions, ultimately destabilizing on time-scales of a few hundreds of years or even less through collisions with the four small moons. In addition, we also simulate the orbital evolution of test particles initially distributed in the form of arcs around Aegaeon, Methone, and Anthe. We show that the initial arcs are dynamically eroded on time-scales of hundreds of years, allowing us to constrain the time-scales on which gravitational forces operate to remove particles from the observed arcs.