Optimal impulsive orbital transfer between coplanar-noncoaxial orbits, local and global solutions

Nowadays, orbital transfer has a significant role in any space mission, and it can be firmly said that there is no space mission that does not need to the orbital transfer. On the other hand, since the cost of each space mission is very important and the mass of fuel directly related to the cost, decreasing the fuel usage has always been an important issue. So the discussion of minimization of fuel consumption in orbital transfer has always been considered important. Hence, the problem of fuel optimization in orbital transfer has a long history and many scientists have worked on this problem and solved many special and simple cases. To solve the problems with more complex geometry, such as optimal impulsive orbital transfer among coplanar non co-axial orbits, numerical solution of nonlinear equations is required which is extracted from the optimization. Numerical solution of these equations is very sensitive to initial guess values and the convergence process is very slow. Also solving these equations lead only to a local minimum and there is no assurance for global minimum. In this paper, to extract the optimization equations, some explicit equations have been extracted so the process to reach all solutions will be possible. These equations are not provided in other articles. Our method is implemented on two numerical examples. Results have shown acceptable accuracy and high speed calculation of this method.