Resonances in Saturn's rings

The locations and strengths of the major resonances of Saturn's known moons with particles orbiting within Saturn's rings are calculated. The resonant effects of an outer satellite on Saturn's rings is analyzed by Fourier expanding the satellite's potential, and it is found that the forcing at an l:(m-1) resonance depends on the moon's eccentricity to the (l-m) power. As most of Saturn's inner moons are in very nearly circular orbits, only their strongest resonances, with l = m and l = m+1, are calculated. For Mimas, which has a somewhat larger eccentricity, resonances with l = m+2 are also computed. All of the resonances of these forms which are located between Saturn's cloud tops and 2.267 Saturn radii are tabulated, except some of those due to tiny 1980 S28.