Halo Orbits

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Halo orbits are the simplest and most well-known orbits about the L1 and L2 Lagrange points. They exist in the Circular Restricted Three-body Problem (CRTBP).
The top-right figure above shows a halo orbit in the Earth-Moon rotating frame. In this frame, the Earth and Moon hold still and the spacecraft traces out a clear, periodic orbit. Halo orbits are large enough that the Moon never blocks communications between a halo orbiter and the Earth. The same halo orbit is plotted in the lower-right figure, but this time in the inertial frame. The next slide has animations showing the motion of a spacecraft in such an orbit.
Robert Farquhar named these orbits because of their unusual shape: when viewed from the Earth, these orbits make a "halo" about the Moon. Farquhar proposed using halo orbits to provide a communication relay for the far side of the Moon during the Apollo lunar missions. Although Earth-Moon halo orbits were never used for Apollo, many spacecraft have visited halo orbits or other libration point orbits at the Sun-Earth Lagrange points. ISEE-3 was the first spacecraft to use such an orbit. SOHO has had a very long and successful mission in orbit about the Sun-Earth L1 point (EL1). More recently, the Genesis mission used Sun-Earth halo orbits and low-energy transfers between halo orbits. These missions have proved that using halo orbits in mission design is not only feasible, but also very useful.
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