We have developed a semi-analytical theory of the mean orbital motion based on the concept of filtered elements.It has been defined on the basis of an exact separation between short period and long period variations (see[Metris and Exertier 1995]in Astron and Astrophys.,294).Schematically,the main characteristic of the theory consists in using first an analytical filtering procedure of the epuations of motion,and secondly a numerical integration of these transformed eauations.From the averaged expression of each force,a new tool has been constructed.It allows fine analyses of the dynamical behaviour of Earth orbiting satellites over long periods of time,typically of the order of several years.It is the purpose of this paper to show the valification steps,as well as its capacity to fast computation in easily interpretable mean orbital elements.
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