Mathematics
Scientific paper
May 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978icar...34..240g&link_type=abstract
Icarus, vol. 34, May 1978, p. 240-253.
Mathematics
117
Celestial Mechanics, Gravitational Effects, Orbit Perturbation, Saturn Rings, Density Wave Model, Forced Vibration, Mathematical Models, Natural Satellites, Resonant Vibration, Paricles, Velocity, Cassini Division, Saturn, Rings, Mimas, Resonance, Satellites, Formation Of, Density Perturbations
Scientific paper
An explanation for the size and location of the Cassini division in Saturn's rings is proposed. The explanation is based on the collective response of the particles in the ring to the resonant forcing by Mimas. An upper limit is calculated for the width of the gap that could be opened at a resonance. In addition, an estimate is obtained regarding the damping of the density waves by viscous and nonlinear effects. A picture is presented of the development of a gap. The results are compared with the observed properties of the divisions in Saturn's rings. The exact position of the inner edge of the Cassini division is difficult to predict, because the 2:1 resonance lies very near several weaker resonances (4:2 and 6:3 with Mimas, 4:1 with Tethys). However, the edge should lie near 17 seconds, and this is consistent with ground based observations.
Goldreich Peter
Tremaine Scott D.
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