SEMIANALYTICAL THEORY OF THE MEAN ORBITAL MOTION

We have developed a semi-analytical theory based on the concept of fil tered elements permitting the exact separation between short period an d long period variations of the orbital motion. We have studied this c oncept and the one associated of mean orbital motion in a more compreh ensive way than has been done so far. The purpose of this paper is to show the complete description of the method of resolution, and to give a first application to main gravitational perturbations: a central po tential and a third body. The characteristics of the method concern th e use of an analytical filtering procedure based on Lie transforms, an d of a numerical integration of the orbit-averaged perturbations. Comp arisons with the classical numerical integration of the full motion eq uations is not directly possible. For this purpose, a specific procedu re has been developed which consists in applying a filtering to oscula ting elements. Finally, we present the result of tests in various dyna mical configurations. The accuracy of the theory is estimated to lie f rom few centimeters to few meters on time spans covering several revol utions of the node and of the perigee.