A direct optimization based tool to determine orbit-raising trajectories to GEO for all-electric telecommunication satellites

In this paper, we consider the development of an optimization solver that provides optimal low-thrust trajectories to the Geostationary Orbit, starting from an arbitrary orbit into which the satellite has been injected by an appropriate launch vehicle. Based on a direct optimization methodology, we formulate a minimum-time orbit-raising problem and use solvers like IPOPT and LOQO to solve the resulting non-linear programming problem. The tool allows for consideration of on-board energy storage system that helps the satellite to thrust in the Earth's shadow during an eclipse. Furthermore, the tool allows for the investigation of new scenarios from the point of view of reducing radiation damage incurred by the satellite during its transit through the Van Allen belt. For instance, we consider the case in which the satellite starting from an inclined orbit, delays any out-of-plane maneuvers until it crosses the inner Van Allen belt. The tool enables us to analyze electric orbit-raising scenarios for a variety of injection orbits and different technology alternatives (electric engines, on-board energy storage). We illustrate with numerical examples the usage of the developed tool for different orbit-raising examples. The development of this solver is a first-step towards an elaborate study of new mission scenarios for all-electric telecommunication satellites.