Orateur
Description
Rings are made up of countless test particles that can be perturbed by satellites with circular or elliptic orbits. At first sight, resonances effects on the disk can be satisfactorily described in the context of the Planar Restricted Three-Body Problem (PR3BP). However, an essential ingredient is missing in the PR3BP approach: the interactions between particles, either by local inelastic collisions or by long-range gravitational interactions. This gives rise to collective behaviors and leads to counter-intuitive behaviors when considering captures into resonances.
A few situations will be discussed, noting that two main types of resonance come into play: corotation resonances, that confine ring arcs into finite intervals of longitudes, and eccentric resonances that confine radially complete ringlets. A result obtained in the PR3BP framework states that captures into eccentric resonances occur only if the orbits of the particle and the perturber converge. This is not true any longer for rings, as collective behaviors can lead to confinement at the resonance even if the orbits diverge.
Difficulties arise as the corotation and eccentric resonances may occur close to each other, leading to chaotic motion and non-permanent captures. Other difficulties arise when eccentric resonances of orders larger than one are considered, as they lead to self-crossing periodic orbits, thus predicting the destruction of these orbits. However, recent numerical simulations show that collisions may lead to spontaneous re-arrangements of the particle orbits, and eventually to a confinement of the ring. This is a paradoxical results as the ring is at the same time locked into the resonance, but without exhibiting the classical periodic orbits expected at this resonance.