Minimum-fuel two-impulse transfer between coplanar noncoaxial elliptical orbits

Abstract

This paper investigates minimum-fuel two-impulse transfer between general coplanar noncoaxial elliptical orbits in a Newtonian gravitational field. First, without any restriction on the transfer time and boundary conditions, a necessary condition of optimality for the minimum-fuel solutions is derived via the primer vector analysis and thus, a simplified optimization model is presented. Then, a homotopic approach based algorithm is proposed to obtain the minimum-fuel solutions, which can start automatically from the analytical generalized Hohmann transfers. Finally, accuracy and efficiency of the algorithm are illustrated via different examples. Symmetric property of the minimum-fuel solutions is drawn. Special cases where the two-impulse solutions degenerate to one-impulse solutions are analyzed. Further discussions are given to explore the global optimality of the obtained minimum-fuel solutions.