Higher Approximations of the Method of Averaging for the Equation of Plane Oscillations of a Satellite

We apply the averaging procedure to study the equation of oscillations of an almost symmetric satellite in a plane of its elliptic orbit with the eccentricity e close to 1 (the singular case). The right-hand side of the equation is a series in powers of a small parameter $\mu$. For the coefficients of the series at each power of $\mu$, the growth estimates as e \to 1 are obtained, and the Newton polygon in the plane of power exponents of the parameters m and (1-e) is drawn. The Newton polygon consists of two edges, finite and infinite. The finite edge defines the approximation, earlier found by the author. The infinite edge gives the region of validity for the averaging method in this case: | $\mu$ | « (1-e)^1/2.