Analytical solution of the perturbed circular motion: an extended formulation for various perturbations

Abstract

An extended formulation of the solution is presented starting from the analytical theory of perturbed circular motions developed by Bois ( Celestial Mech. 58, 125–138, 1994) and from specific extended formulations of the perturbations. The field of applications of the theory is then increased. A treatment of several perturbations is presented such as an external potential, a non-gravitational force, both added to an extended central potential. The expanded solution permits to take into account immediately and simultaneously different periodic perturbations. It is then directly applicable to problems of various physical nature. In the present numerical applications devoted to artificial satellites with zero inclination, physical descriptions are given in each case. Over few orbits, the solutions are particularly accurate and the comparisons of the results with respect to a numerical integration are convincing. Moreover, the long period evolution over about a thousand orbits is illustrated stemming both from the solution and the numerical integration.