Optimal impulsive transfer between coplanar non-coaxial orbits

The orbital transfer has a significant role in any space mission. This transfers generally categorized in impulsive and continuous maneuvers. An important challenge is fuel consumption in the maneuver. This problem is considered as a required delta-V problem. Hence, minimization of delta-V means minimization of fuel consumption orbital transfer. In simple cases, the problem has closed form solution for example transfer between coplanar circular orbits or transfer between coplanar coaxial elliptical orbits. The conventional methods cannot solve complex cases of initial and target orbits. In this paper, the impulsive optimal transfer between two coplanar- noncoaxial elliptical orbits is considered. The numerical solution of optimality nonlinear equations is necessary to obtain the solutions of complex problems. According to the nonlinearity of equations, two issues arise, firstly numerical solution is sensitive to initial guess, secondly, the local minimum solutions only may be found. In this paper, some equations have been derived that using them behavior of required delta-V function can be investigate based on various values of independent variables and can be found the boundary of the global solution. In this way, one can be determined a reasonable and proper initial guess for the nonlinear solver. The proposed methodology is applied to an example and the results are provided. The results include the local and global solutions and they show a good ability of the proposed method.