Mathematics
Scientific paper
Oct 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994icar..111..514s&link_type=abstract
Icarus (ISSN 0019-1035), vol. 111, no. 2, p. 514-535
Mathematics
6
Eccentric Orbits, Gaps, Gravitational Effects, Moonlets, Planetary Rings, Ring Structures, Wakes, Analysis (Mathematics), Chaos, Computerized Simulation, Equations Of Motion, Kinetics, Laminar Flow, Mass Distribution
Scientific paper
We have extended previous one-dimensional kinematic investigations about the gravitational influence of satellites embedded in planetary rings on the surface mass density to two spatial dimensions, radius r and azimuth phi. The trajectories of 219 = 524288 test particles have been integrated numerically using a Connection Machine. This large number of test particles allowed us to make simulations for the first time simultaneously in three types of regions showing different structures which were investigated separately by different authors: (1) the region of density wakes (Showalter et al., 1986), (2) gaps limited by the wakes (Petit and Henon, 1988), (3) a ringlet covering the orbit of the moonlet. For eccentric orbits (em not = 0), the density field sigma (r, phi) has been found to depend sensitivity on the azimuthal longitude phi of the model ring. The librating gravitational perturbations of the moonlet cause azimuthal variations in the border regions of the gaps (2) and in the inner ringlet (3). The numerical experiments have yielded interferences of the wakes showing mirror symmetry with respect to the longitude of the moonlet. In order to interpret the formation of the structures found in the wake region (1) as well as in the ringlet (3) we have modified the streamline approach in the simplest case of a circular revolving moonlet (em tends to 0). Concerning the wake interferences, a model has been developed where the damping of the wakes has been neglected. In this way we have been able to reproduce the interference of the wakes, and also the axisymmetric density profile of the ringlet. Besides the interference pattern axisymmetric density enhancements have been found at the resonance locations where the relative differential angular velocity m takes integer values m = +/- N. After a sufficiently long time are the only remaining structures in the wake region; the wakes are smeared out even in the kinematic model (phase mixing). This is of interest for the explanation of axisymmetric quasiperiodic features in the Cassini division of Saturn's rings, which might in fact be due to small satellites.
Hertzsch Jan-Martin
Scholl Hans
Spahn Frank
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