Rapid Evaluation of Low-Thrust Transfers from Elliptical Orbits to Geostationary Orbit

Abstract

Low-thrust orbit transfers to geostationary equatorial orbit (GEO) will likely use a combination of chemical and electrical propulsion stages to strike a balance between transit time, minimal power degradation, and delivered payload mass. Therefore, mission designers need a method for rapidly evaluating low-thrust transfers to GEO. Relying on full trajectory optimization programs for preliminary studies is not a desirable option due to the time associated with optimizing multiple trajectories. This paper develops an algorithm that rapidly determines the for a low-thrust transfer from an arbitrary elliptical orbit to GEO. Transfer time to GEO is accurately computed by incorporating thrust interruption (due to Earth-shadow effects) and power degradation (due to passage through the Van Allen radiation belts). The method employs curve fits of optimal transfers and simple polynomial expressions for the orbital element histories. Hence, the technique is fast and does not require numerical integration of the powered equations of motion or a numerical search. The method is demonstrated by presenting several transfers to GEO and comparing the performance metrics with the associated optimal transfers.