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Concept
Halo orbit
Summary
A halo orbit is a periodic, three-dimensional orbit near one of the L1, L2 or L3 Lagrange points in the three-body problem of orbital mechanics. Although a Lagrange point is just a point in empty space, its peculiar characteristic is that it can be orbited by a Lissajous orbit or by a halo orbit. These can be thought of as resulting from an interaction between the gravitational pull of the two planetary bodies and the Coriolis and centrifugal force on a spacecraft. Halo orbits exist in any three-body system, e.g., a Sun–Earth–orbiting satellite system or an Earth–Moon–orbiting satellite system. Continuous "families" of both northern and southern halo orbits exist at each Lagrange point. Because halo orbits tend to be unstable, station-keeping using thrusters may be required to keep a satellite on the orbit.
Most satellites in halo orbit serve scientific purposes, for example space telescopes.
Robert W. Farquhar first used the name "halo" in 1966 for orbits around L_2 which were made periodic using thrusters. Farquhar advocated using spacecraft in such an orbit beyond the Moon (Earth–Moon ) as a communications relay station for an Apollo mission to the far side of the Moon. A spacecraft in such an orbit would be in continuous view of both the Earth and the far side of the Moon, whereas a Lissajous orbit would sometimes make the spacecraft go behind the Moon. In the end, no relay satellite was launched for Apollo, since all landings were on the near side of the Moon.
In 1973 Farquhar and Ahmed Kamel found that when the in-plane amplitude of a Lissajous orbit was large enough there would be a corresponding out-of-plane amplitude that would have the same period, so the orbit ceased to be a Lissajous orbit and became approximately an ellipse. They used analytical expressions to represent these halo orbits; in 1984, Kathleen Howell showed that more precise trajectories could be computed numerically. Additionally, she found that for most values of the ratio between the masses of the two bodies (such as the Earth and the Moon) there was a range of stable orbits.
Official source
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