Partial averaging near a resonance in planetary dynamics

An analytical treatment of the evolutionary dynamics of a three-body planetary system subject to dynamical friction with an interplanetary medium is presented. The analysis presented here is in connection with the results of numerical integrations of such systems recently published by Haghighipour. Using the method of partial averaging near a resonance, the dynamics of a restricted, circular, planar three-body system, with the inner body more massive, is studied and the time variation of quantities such as the orbital angular momentum and the eccentricity of the outer planet, which were previously obtained from numerical integrations, is analytically verified.