An Efficient Calculation Method for Two-Impulse Transfers to Libration Point

An efficient calculation method is proposed for the optimization of the two-impulse transfers to the librations in circular restricted three-body problem. With the invariant manifolds approximation based on a two-dimensional interpolation, the computation of the great number of manifold insertions is much more efficient. While the conic curve in a two-body problem used as an approximation of the transfer segment connecting the low Earth orbit and the stable manifold, the maneuvers can be deduced with the classical orbital elements, thus the iterative computation of the maneuvers is avoided in the optimization process. Then the primer vector of CRTBP is deduced to verify the optimality of the two-impulse transfer. At last, a numerical simulation of the two-impulse transfer from a low Earth orbit to a L₁ point halo orbit is presented, verifying the validity of the two-body impulse approximation and the manifold approximation, and demonstrating the efficiency of the method.