Minimum-fuel electric orbit-raising of telecommunication satellites subject to time and radiation damage constraints

The capability of a Geostationary satellite to perform electric orbit-raising enables the development of all-electric satellites. Key challenges to the realization of electric deployment of satellites to the Geostationary orbit are the long transfer times, high power requirement of the electric thrusters and the solar array degradation experienced by the satellite during its transit through the Van Allen radiation belts. In this paper, we consider the problem of electric orbit-raising of a telecommunication satellite to the Geostationary orbit. We propose an optimization framework to minimize the fuel expenditure during the transfer subject to upper bounds on the transfer time and the displacement damage dose. Our developed framework considers the discretization of the satellite trajectory as well as the energy spectrum of protons encountered during the transfer, and utilizes analytic models of the geomagnetic field and associated radiation flux. Finally, we illustrate with numerical examples the fuel savings that can be achieved by comparing minimum-time and minimum-fuel solution.