Transfer to a Halo Orbit/BLT Phase 1

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Stable Manifolds
The stable manifold of a halo orbit at the Sun-Earth L2 point (EL2) 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 Sun-Earth L1 halo orbit.
Getting a spacecraft to a halo orbit at the Earth-Moon Lagrange points, LL1 or LL2, is a little more complicated. The stable manifolds of Earth-Moon halo orbits do not approach the Earth in the Three-body Problem. However, stable manifolds of lunar halo orbits generated in the Sun-Earth-Moon four-body problem DO approach the Earth.
BLT Phase 1
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 Sun-Earth halo orbit. In this case the halo orbit is at EL2.

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