Unated presentation for secular part of perturbing function of mutual attraction of planetary satellites

M. A. Vashkov’yak^a, S. N. Vashkov’yak^b, N. V. Emelyanov<sup>bc

a</sup> M.V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences
^b P. K. Sternberg Astronomical Institute, M. V. Lomonosov Moscow State University
^c Institut de Mé Canique Céleste et de Calcul des Éphemerides, Observatoire de Paris

Abstract: The special presentation for secular part of perturbing function of mutual satellite attraction is proposed. Unlike from known presentation it has united analytical form for any relation between semi-major axis of orbits of perturbed satellite and of perturbing one. The formula received is a partial sum of power row relative of small eccentricities and planet-equatorial inclinations of satellite orbits. This sum contains addendum up to fourth power inclusive relative small parameters above. The comparison of development proposed for secular part of perturbing function and known one is made.

Keywords: mutual satellite attraction, secular perturbations, averaged perturbing function.