A 2ND-ORDER LAPLACE-LAGRANGE THEORY APPLIED TO THE URANIAN SATELLITE SYSTEM

Computer algebra is used to derive analytical expressions for the elem ents of a secular perturbation theory of the second order in the masse s. The linear part of this theory is incorporated into the standard La place-Lagrange solution which is then applied to the motion of the ura nian satellites. This enables the effects of mean motion near-resonanc es in this system to be modelled. The results are in very good agreeme nt with the filtered output of a numerical integration by Malhotra et al (1989). The additional complexities of studying the outer solar sys tem using a similar approach are discussed.