Fuel-Efficient Cross-Track Distance Establishment in Satellite Formations

Satellite formation establishment may consume considerable fuel if cross-track distance (CTD) is a mission requirement. This work proposes a strategy for significantly reducing the required fuel. Instead of direct out-of-plane maneuvers, it is suggested to use in-plane maneuvers, while using the nodal precession caused by the J₂ perturbation. The CTD dynamics are analyzed, and representative formation geometries are considered. Analytical expressions for the CTD and related establishment timing are derived for the case of impulsive thrust. For most cases, the expected CTD establishment duration is reasonable, and the fuel saving with the J₂-assisted CTD establishment strategy is considerable. For the case of J₂-assisted CTD establishment with continuous thrust, optimal control methods are used. The proposed strategy is proven to be optimal for two cases: limited and unlimited thrust magnitude. Finally, the cases of J₂-assisted CTD establishment with impulsive and with continuous thrust are compared. It is shown that continuous thrust is preferable in terms of fuel, for similar CTD establishment durations.