Many recent observations have shown that resonances have a wide variety of effects in planetary rings: spiral waves, gaps, confinement, sharp edges, arcs. While resonances are known to be associated with such structures, the role of inter-particle collisions is still poorly understood, although necessary to explain the long term evolution of the rings.
In an effort to better understand the associated dynamics, we have performed numerical simulations of colliding particles orbiting a massive central planet. The code simulates the 3-D motion of 100 identical spherical particles orbiting a massive cental body and suffering inelastic collisions while being perturbed by one or more satellites.
We used this code to explore in more details the dynamics of are rings, and to explain in particular the reeent observations of are structures around Neptune. Clusters of particles at a satellite’s Lagrangian point {L4 or L5) are shown to be dispersed by dissipative effects. However, a second satellite can stabilize the system by providing sufficient energy through a Lindblaďs
resonance m±l:m. Other dynamically equivalent configurations (e.g. only one satellite, but with an eccentric orbit) can also stabilize are sytems, in accord with current analytical models.
We examine the roles of collisions at Lindblad and corotation resonances in various cases. Arcs remain at the potential maxima created by the corotations. However, stability requires that the satellites’ masses be within a limited range: small satellites cannot provide enough energy while large ones give too much, so the arc can disperse.
Despite all the new data, the nature of planetary rings is stíII
controversial. We don't know why each planetary ring is so different from the others and we have no idea of the nature of a single partícle ring, The large number of structures observed in planetary rings seems to indicate that many different physícal mechanisms are simultaneously at work. We are not yet able to include all of them in a single model. Resonances with nearby satellites play an ímportant role, but through complex mechanisms. Appropriate observations and more sophísticated models are needed to improve our understanding of rings and to identify the main physícal mechanisms involved.