The development of secular part of perturbing function of mutual attraction of celestial bodies for uniform close orbits

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

a</sup> Keldysh Institute of Applied Mathematics, RAS
^b Lomonosov Moscow State University, Sternberg State Astronomical Institute
^c L’observatoire de Paris, Institut de Mecanique Celeste et de Calcul des Ephemerides

Abstract: The new development representation for secular part of perturbing function of mutual planet (satellite) attraction is proposed. Unlike from known representations the asymptotic of Gauss hypergeometric functions for arguments close to unit is used. Moreover the development proposed has united analytical form for external and internal variants of problem. The formula received is a partial sum of power row relative of eccentricities and sin of orbital inclinations with accuracy to forth power of these small parameters.

Keywords: mutual planet (satellite) attraction, secular perturbations, averaged perturbing function, close orbits.