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.
By rneans of correlation analysis, resonance interaction between Uranian rings and new satellites predicted earlier, is proved, Instability of circular rings relative to the disturbance with the azimuthal number m =1 is shown; it may be the cause of the ring’s eccentricity. This justifies the authors' hypothesis that the formation of eccentric rings of the protodisk around Uranus ia due to unknown Uranian satellites, There is no longer necessity for the hypothesis of the existence of "shepherd"-satellites in Uranian rings which have not been discovered by Voyager-2. A new - accretion instability of the protodisk is described which may háve served as a generator of the birth of a large-scale structure of Saturn’s rings, The discovery of the instability makes it possible to understand the origin of the hierarchic structure of Saturn’s rings, since the mechanisms of formation of narrow ringlets were investigated earlier.
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.
The new observations of planetary rings, including those acquired during the encounters of Voyager with Jupiter, Saturn and Uranus and the discovery of incomplete rings around Neptune, reveal the great importance of resonances in determining the dynamics and the shape of planetary rings. Several types of resonances play a part in planetary rings. Current questions of interest are related to the nonlinear theory of density waves, the confinement of the Uranian rings, and the arcs of rings around Neptune.