The general problem of regular motion of an axisymmetrical satellite in a central field

Abstract

In this paper, the stationary motions of an axisymmetrical satellite in a central field of attraction are investigated. Both the orbital, “translational”, and the self-rotational motions of the satellite are taken into consideration. In the decomposition of the Newtonian force function, all the harmonics up to the third order are taken into account. The exact solutions are deduced by Poincare's method of small parameters. The results show the existence of two solutions, which satisfy all the necessary and sufficient conditions. One of the solutions belongs to the group of stationary motions of a triaxial satellite obtained before by the author. The second solution, in which the axis of symmetry can keep an arbitrary constant inclination to the orbital plane, is a new and rather a more general solution. These solutions generalize the conical and hyperbolic precessions of the satellite, suggested by Sarichev [ Sci. Technol. J., Moscow, 1978] and the stationary solutions of the limited problem suggested by the author.