The influence of various moonlets on the optical depth profile in planetary rings

Abstract Our probability concept for characterizing the long-term gravitational influence of one moonlet on planetary rings has been generalized to: 1. (i) eccentric orbits of a single moonlet, 2. (ii) n co-orbital moonlets of different masses. We have applied a special scaling property of the three-body problem, which permits the generalization of the results of the scattering process, once they are obtained for a certain satellite, to moonlets of arbitrary mass. In this way, further test particle calculations can be avoided. Our results for each of the two cases are as follows: 1. (i) A narrow confined ringlet divides a wide gap which has evolved around the orbit of the moon. The radial density profile of that ringlet contains information about the size as well as the semimajor axis a m and the eccentricity e m of the orbit of the embedded moonlet. 2. (ii) Here the innermost ringlet profile is strongly modified by the small coorbital satellites. However, unambiguous hints of the existence of all moonlets can be gathered from the ringlet profile, but only if the moonlets are really isolated (in size) from the bulk of the ring particles and if they differ enough in size from each other. Otherwise, the typical density features of comparable moonlets interfere in a way that makes it impossible to distinguish between them. Then, additional information is needed to identify the number of embedded satellites, such as azimuthal ringlet features.