Three-dimensional perturbations of particles in a narrow planetary ring

Abstract

In an effort to understand the observed complex form of Saturn's F ring, we have used Gauss' perturbation equations to numerically model the short-term, three-dimensional dynamics of narrow rings. We consider ring particles that are perturbed by local moonlets orbiting with small ( i ≤ 0°.1) inclination; collisions are ignored. We confirm that, as expected, the distance of closest approach determines the strength of the interaction; this distance depends on the orientation of the orbits, as well as the orbital eccentricity and the separation in semimajor axes of the ring particle from the perturbing satellite. Furthermore the exact geometry of encounter, particularly the relative orientation of the longitude of ascending node to the argument of pericenter, plays an important role in the vertical response of any satellite-ring particle perturbation. We find that, with an appropriate choice of parameters, ring particles can be perturbed to substantial inclinations. We present simulations of a model narrow ring consisting initially of three strands typically with 800 particles apiece, which show the short-term effects of the neighboring moons and the influence of different orientations at encounter. Finally, we demonstrate that a combination of modest vertical and horizontal distortions to three narrow strands, as induced by out-of-plane satellite perturbations comparable to those present in the real ring, produces a structure that looks much like the “braided” F ring.