Optimization of Geostationary Orbit Transfers via Combined Chemical-Electric Propulsion

For geostationary orbit transfers, a long duration is required using electric propulsion and a large propellant mass is needed with chemical propulsion. Hybrid transfers can achieve a balance between the fuel consumption and transfer time. In this paper, a trajectory optimization method is proposed for time-fixed minimum-fuel orbital transfer with combined chemical-electric propulsion. The necessary conditions and transversality conditions related to impulsive burns are derived theoretically with Pontryagin's maximum principle. The long-duration geostationary orbit transfer is a many-revolution transfer, and is solved with the homotopic approach from the short-duration transfer problem. The variation in fuel consumption with transfer time is nearly linear, and the variation in the magnitude of impulsive burn is exponential. A simple model is presented for the estimation of fuel consumption and magnitude of impulsive burn with given transfer time, specific impulse of propulsion system and low-thrust magnitude.