Optimal bi-impulse orbital transfer between Coplanar and non-coplanar orbits

In this paper optimal bi-impulse orbital transfer between elliptical orbits has been considered. At First, an effective algorithm has been developed to find the global solution of the both coplanar and non-coplanar initial and final orbits. In this algorithm we have three independent parameters for the both cases. These parameters are angular position of the point on the initial orbit that the first impulse is applied, angular position of the point on the final orbit that the second impulse is applied and the semi-latus rectum of the transfer orbit. Other required parameters can be obtained from these three parameters. Second, this algorithm has been examined by several numerical examples which have already been solved in other literature with other algorithms such as Genetic algorithms (GA), Differential Evolutional algorithms (DE), and particle swarm optimization (PSO). This authentic algorithm obtains the global solution of any arbitrary elliptical orbits, rapid and meticulous. Furthermore, this algorithm has been employed to solve a wide range of numerical examples including coplanar and non-coplanar, co-axial and non co-axial, similar and different shape and/or energy initial and final orbits. The wide range of various numerical examples are solved to disentangle the roles of each orbital parameter such as eccentricity, energy, argument of periapsis, inclination, and right ascension of ascending nodes in the evaluation of the optimal transfer singly. Finally, for some of these orbital parameters such as argument of periapsis and inclination, we state a fitting function which shows the effect of them on the optimal required impulse individually. However, finding a fitting function for other parameters, such as energy and right ascension of ascending node, is more complicated.