Optimal low-thrust transfers to lunar L1 halo orbit using variable specific impulse engine

Given the advantages of variable specific impulse (VSI) engine, it is very likely that in the future there will be deep space missions that use this thrust as propulsion system. In this study, a design technique for a fuel optimal Earth-to-Halo transfer using VSI is proposed. The calculus of variations approach and direct parameter optimization are combined to formulate the trajectory optimization problem. The classic stable manifold, developed in dynamical systems theory, is employed to further reduce fuel consumption. Adjoint control transformation (ACT) and analytical gradients are incorporated to improve performance of the algorithm. Four transfer examples - direct transfers from 500 km low Earth orbit (LEO) and 3,629 km medium Earth orbit (MEO) to lunar L1 halo orbit - and indirect transfers with lunar flybys, are presented.