Resonance effects due to the longitude dependence of the gravitational field of a rotating primary

Abstract

There will be long-period oscillations in the position of a satellite if its path is nearly repetitive relative to the rotating primary, and there is an infinite sequence of such resonances. The behaviour near resonance is governed by a pendulum equation and in the extreme case a satellite can be captured by the resonance and stable against small drag forces. Moreover the presence of “drag” forces, which include a change in the primary's rotation e.g. by tidal effects, gives a mechanism for permanent or semi-permanent capture, a positive real drag or its equivalent being the more favourable condition. If capture takes place, “drag” forces lead to secular changes in inclination; the sense depends on the sign of the drag, whether the resonance is above or below synchronous height, and on the inclination itself. The resonance effects are highly dependent on inclination, and all except the synchronous resonance become ineffective on the equatorial plane. This appears to give a partial explanation of the formation and structure of the rings of Saturn, and suggests that there could be similar but much less regular bands of dust around the Earth.