The Effect of Gravity Between Particles on the Shape and Resonant Structure of Planetary Rings

The resonance perturbation of planetary ring by distant satellite is considered. The gravity interaction between rings particles is taken into account. The gravitation interaction between particles in rings can change shape of non-circular rings, so it is differ from keplerian ellipse. The shift between simple mean motion resonances and parametric resonance zones is detected. This shift depends on ring properties.