Finite thrust orbital transfers

Abstract The finite thrust optimal transfer in the presence of the Earth׳s shadow and oblate planet perturbations is a problem of strong interest in modern telecommunication satellite design with plasmic propulsion. The Maximum Principle cannot be used in its standard form to deal with the Earth׳s shadow. In this paper, using a regularization of the Hamiltonian which expands the Maximum Principle application domain, we provide for the first time, the necessary conditions in a very general context for the finite thrust optimal transfer with limited power around an oblate planet. The costate in such problems is generally discontinuous. To obtain fast numerical solutions, the averaging of the Hamiltonian is introduced. Two classes of boundary conditions are analyzed and numerically solved: the minimum time and the minimum fuel at a fixed time. These two problems are the basic tools for designing the orbit raising of a satellite after the launcher injection into its separation orbit. Numerical solutions have been calculated for the more important applications of LEO to GEO/MEO missions and the results have been reported and discussed.