In constructing a BLT, one does not need to create the stable and unstable manifolds of the SunEarth halo orbits. Instead, only the stable manifold of the lunar halo orbit is needed. From many locations along the desired lunar halo orbit, the orbit state is perturbed in the stable direction and the resulting trajectories are propagated backwards in time. These trajectories must be propagated using the combined gravitational effects of the Sun, Earth and Moon, and they form a map of the stable manifold of the lunar halo orbit. The trajectories on the stable manifold that encounter the Earth are identified and the optimum transfer can be selected from those that qualify.
