
The stable manifold of a halo orbit at the SunEarth L_{2} point (EL_{2}) is shown in different projections above and is the set of green trajectories. Some of the trajectories on the stable manifold pass close by the Earth on their way to the halo orbit, and these trajectories are colored blue. From Earth, it is possible to insert into a blue trajectory on the stable manifold and transfer to that halo orbit with a "free" insertion at the halo orbit. This type of trajectory was used to launch the Genesis spacecraft to a SunEarth L_{1} halo orbit.

Getting a spacecraft to a halo orbit at the EarthMoon Lagrange points, LL_{1} or LL_{2}, is a little more complicated. The stable manifolds of EarthMoon halo orbits do not approach the Earth in the Threebody Problem. However, stable manifolds of lunar halo orbits generated in the SunEarthMoon fourbody problem DO approach the Earth.


This slide shows how a Ballistic Lunar Transfer (BLT) can be found that takes a spacecraft from Earth to a lunar halo orbit. The first phase of the BLT (shown in blue) is to travel on a trajectory that is very close to the stable manifold (green) of a SunEarth halo orbit. In this case the halo orbit is at EL_{2}.
