Mitigation of Differential Perturbations in Formation Flying Satellite Clusters

Aperture synthesis using distributed satellite systems opens up new possibilities for space-based surveillance of Earth. However, it brings with it new challenges for maintaining the geometry of the array in the presence of gravitational tidal forces and environmental pertubations. Balancing the aperture synthesis need to place the individual satellites in specific relative positions, with the desire to minimize the propellant consumed to do so, leads to the need for creative techniques which exploit the natural orbital motion of the satellites to maintain the geometry of the array. As a result, a new area of orbital mechanics has emerged which deals specifically with the formation flying of satellite clusters for aperture synthesis. This paper presents a candidate orbital formation for such an aperture. A key factor is the amount of propellant required to simply station-keep, or maintain the formation against the perturbative forces encountered in orbit: passive formation flying. This represents the baseline requirement for the propulsion system, before active cluster maneuvering is even considered. This paper quantifies these perturbative effects, first through dimensional analysis to derive the various scaling laws needed to conduct design trades, and then through a rigorous analysis of a specific formation flying mission: the Air Force space-based radar system (TechSat21). Values of lifetime ΔV and propulsive specific impulse, as well as peak thrust, are calculated for TechSat21 and compared to the levels needed for active cluster formation flying. For passive formation flying of TechSat21, 0.5 cm/sec/orbit of ΔV is required to counteract secular terms arising from environmental perturbations such as differential J2. Periodic variations in relative motion have an amplitude of about 0.12% of the array’s diameter, or 60 cm for a 500 m array, if left unchecked. For a required seven year life, with less than 7% propellant fraction, the needs of active formation flying are prohibitively large, and it is shown that an additional 500 seconds of specific impulse are needed for each 1 cm/sec/orbit of ΔV added.