In this paper, a new analytical solution to optimal control problems in formation flying is presented, including the differential gravity effects to the second order. The perturbation approach and the calculus of variations are applied to the optimal control problems in order to obtain an approximate analytical solution. A nonlinear relative dynamics that includes quadratic terms in the differential gravitational accelerations is used. For the sake of validity, numerical simulations are performed for satellite reconfiguration cases in which the distance between the satellites is large. Finally, the improved accuracy of the new analytical solution ensuring reasonable fuel usage is confirmed.
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