Near Time-Minimal Earth to L1 Transfers for Low-Thrust Spacecraft

What is it about?

A method for determining optimal trajectories for low-thrust spacecraft from low-Earth orbit to the L1 libration point is determined. This method separates the trajectory into two arcs and uses three steps to solve a minimum-time transfer with continuous thrust by (i) Averaging the necessary conditions for optimality and using numerical shooting to solving a minimum-time transfer from near-Earth orbit to the boundary of the region where averaging is applicable. (ii) Solving a minimum-time transfer without averaging using numerical shooting from this orbit to the Earth-Moon Lagrange point L1. These two steps yield two trajectories (in state and costate variables) that are minimum-time individually, but the concatenation of the two has a discontinuity in the state and costate space and carries no extremality property. (iii) A third combined problem is solved where the shooting equation is constructed to ensure the two extremal trajectories in steps (i) and (ii) join continuously in the state and costate, which restores the extremality of the transfer. The arcs join smoothly with no delta-V required to match the specific orbital energy. Since we consider the case where the low-thrust propulsion is continuous way, these time-minimizing transfers are also propellant- minimizing transfers

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