Trajectory design of formation flying constellation for space-based solar power

The concept of collecting solar power in space and transmitting it to the Earth using a microwave beam has appealed to the imagination of numerous researchers in the past. The Space Solar Power Initiative at Caltech is working towards turning this idea into reality, by developing the critical technologies necessary to make this an economically feasible solution. The proposed system comprises an array of ultralight, membrane-like deployable modules with high efficiency photovoltaics and microwave transmission antennas embedded in the structure. Each module is 60 m χ 60 m in size and in the final configuration, ~2500 of these modules form a 3 km χ 3 km array in a geosynchronous orbit. As the constellation orbits the Earth, the orientation and position of each module has to be changed so as to optimize the angle made by the photovoltaic surface with respect to the sun and by the antenna surface with respect to the receiving station on Earth. We derive the optimum orientation profile for the modules and find that modules with dual-sided RF transmission can provide 1.5 times more orbit-averaged power than modules with single-sided RF transmission. To carry out the corresponding orbital maneuvers, an optimization framework using the Hill-Clohessy-Wiltshire (HCW) equations is developed to achieve the dual goal of maximizing the power delivered, while minimizing the propellant required to carry out the desired orbital maneuvers. Results are presented for a constellation with modules in fixed relative positions and also for a constellation where the modules execute circularized periodic relative motion in the HCW frame. We show that the use of these periodic relative orbits reduces the propellant consumption from ~150 kg to ~50 kg. This drastic reduction makes the propellant mass a significantly smaller fraction of the module's dry mass (370 kg), thereby solving a major technical hurdle in the realization of space-based solar power.