Locally Optimal Trajectories from Low Lunar Orbit to Near Rectilinear Halo Orbits

Near rectilinear halo orbits have been proposed for NASA's Gateway concept, and they offer several desirable properties such as relatively easy access to/from earth, relatively easy access to/from low lunar orbit, visibility of the lunar surface, and low propulsive maintenance requirements. We consider a representative orbit for the Gateway with lunar periapse above the north pole with altitude of 4557 km and period of about 7 days. Abort scenarios from low lunar orbit to the Gateway are considered. We first pose the transfer problem as a minimum delta-v optimization problem in a two body field. We then develop a numerical continuation to generate locally optimally impulsive transfers in a three body field. Using MATLAB, solution times are on the order of minutes on a standard desktop computer. Based on this process, we study the relationship between Gateway position, time of flight, delta-v required, and lunar orbit inclination. Results suggest that it is best to target the Gateway when it is about 30% into the NRHO, which allows for a transfer time of less than two days and delta-v of 697 m/s. Targeting points away from periapse are best and can be reached with maximum delta-v of 750 m/s. Based on this process, locally optimal flight times are significantly shorter when targeting points in the first-half (outbound) portion of the NRHO. Moreover, locally optimal low lunar orbit inclinations are nearly polar.