The Encke and Keeler Gaps as Chirikov–Wisdom Effects

We consider and explain the Encke and Keeler Gaps in the A ring of Saturn as Chirikov–Wisdom effects, namely, as due to accumulation and overlap of the first-order mean-motion resonances of the ring particles with satellites Pan and Daphnis. An analytical improvement of Wisdom’s formula for the radial width of the “planetary” (here, satellite’s) chaotic zone is provided. It accounts for specific properties of the system: large number of interacting resonances in the multiplet, and their large (similar to each other, by the order of magnitude) amplitudes. Using the improved theory, we show that the width of the Encke Gap is accurately predicted, while the theoretically estimated Keeler Gap width is two times greater than the actual one. The disparity in the latter case is tentatively explained by the relatively small mass of Daphnis (two orders of magnitude less than that of Pan); when mass is so small, one has to take into account the central regular (horseshoe-orbit) part of the Gap.