Optimum low thrust transfer to geosynchronous orbit

The low thrust transfer for geosynchronous mission has been studied by many investigators from the viewpoint of optimization in case of continuous thrust. This paper discusses the possibility of fuel saving to attain a geosynchronous orbit by introducing coast phases during each revolution. In advance of optimizing the whole transfer mission, optimization during a single revolution is treated, and it is shown that the entrance and the exit of optimal coasting arcs are expressed by a sixth order equation, which, in case of coplanar transfer, degenerates into a cubic equation, with respect to the cosine of true longitude. Then an optimum transfer to a geosynchronous orbit, including coast phases in each revolution, is simulated. Computational results for typical initial conditions are shown to be compared with those for all-propulsion cases.