Optimal three impulse orbital transfer between coplanar non co-axial orbits

The goal of this paper is to find the number of impulses, value of them and transfer orbit(s) parameters in the problem of optimal multi impulse orbital maneuver. Since there is no analytical solution for the problem, the number of impulses should be known before solving the problem. By comparison between the optimal solutions of the different numbers of impulses, the optimal solution and number of impulses will be known. At first, for solving the problem of optimal impulsive orbital maneuver, one optimization method based on the gradient is introduced and to avoid the local minimums, an algorithm is provided to reach the global solution. With comparing the global solution of transfer by various numbers of impulses for known initial and final orbits, the optimum number of impulses, optimal solution and parameters of transfer orbit(s) have been obtained. Finally, varying the initial and final orbits parameters, it is shown that the optimal number of impulses is depended on the scale of semi-latus rectum and eccentricity of initial and final orbits.