On the interaction between a spherical stellar system and a companion

An external satellite in a circular orbit close to the boundary of a spherical stellar system is considered. Assuming linear theory to be valid, and neglecting self-gravity an expression for the mean orbital decay rate is derived which is found to be computationally more convenient than that given by previous authors. Using this the orbital decay rate is evaluated for two models taking account of all effective resonances. The results indicate a strong but erratic tidal interaction. When self-gravity is included, a general upper limit is derived for a mean orbital decay rate over a frequency range, for perturbations associated with a particular spherical harmonic. This limit is approached to within a factor of 4 for one of the models. (author)