This article proposes a method to determine energy-optimal low-thrust trajectories for satellite formation manoeuvre in the presence of the J2 effect. This manoeuvre is cast as a non-linear optimization problem with a desired final satellite formation configuration subjecting to collision avoidance constraint. With this proposed approach, the deputy satellite is manoeuvred into a quasi-periodic desired final formation with respect to the chief satellite in the presence of the J2 effect. Resulting non-linear optimal control problem is converted into non-linear programming (NLP) problem by a direct transcription method called Legendre pseudospectral method. The NLP problem is then solved using a sparse non-linear optimization algorithm. Simulation results validate the proposed optimal trajectory design for formation manoeuvres in the presence of the J2 effect.
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