A numerical study of Saturn's F-ring

Abstract

We study the short-term effects of “shepherding” satellites on narrow rings, in the general case where all bodies move along eccentric orbits. We do this by following numerically a ring of test particles as their orbits evolve under the gravitational perturbations of the shepherds. Planar motion is assumed. Our numerical scheme vastly improves (by a factor of ∼10 4) the computation speed over conventional orbital integration methods by constructing a table of the perturbation integrals and then utilizing it over and over. The approach is applicable to any narrow ring with a nearby satellite, such as a ring confined by the shepherding mechanism of P. Goldreich and S. Tremaine [ Nature 277, 97–99 (1979)] . We arrive at results for a variety of orbital configurations, and then apply these to the F-ring of Saturn. Several features of the numerical integration are reminiscent of the kinks and clumps observed by Voyager. If the ring-to-satellite distance changes significantly due to eccentricities, then the ring can break up into periodic clumps in an azimuthal domain which trails the satellite. This region may lag somewhat in longitude. The perturbations may also cause the ring to vary significantly in width, being narrowest near the point of closest approach of the shepherd and widest at the opposite side. It is as yet unclear whether this effect is, or could be, observed in the Voyager images. And finally, the perturbations of the shepherds can impact a significant, but probably time variable, eccentricity to the ring. The short-term tendency is not toward alignment of ring and satellite apsides; longer time effects have not been explored.