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Halo orbit

## Summary

Halo orbit
Polar view
Equatorial view
Animation of SOHO's trajectory
Earth ·    SOHO
Halo orbits orbit the L1, L2, or L3 Lagrangian points (orbits not shown in diagram).

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 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., the SunEarth–Orbiting Satellite system or the 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, stationkeeping may be required to keep a satellite on the orbit.

Most satellites in halo orbit serve scientific purposes, for example as space telescopes.

## Definition and history

Robert W. Farquhar first used the name "halo" in 1966 for orbits around L2 made periodic using thrusters.[1] Farquhar advocated using spacecraft in such an orbit beyond the moon (Earth–Moon L2) 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.[2]

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.[3]

The first mission to use a halo orbit was ISEE-3, a joint ESA and NASA spacecraft launched in 1978. It traveled to the Sun–Earth L1 point and remained there for several years. The next mission to use a halo orbit was Solar and Heliospheric Observatory (SOHO), also a joint ESA/NASA mission to study the Sun, which arrived at Sun–Earth L1 in 1996. It used an orbit similar to ISEE-3.[4] Although several other missions since then have traveled to Lagrange points, they typically have used the related non-periodic variations called Lissajous orbits rather than an actual halo orbit.

In May 2018, Farquhar's original idea was finally realized when China placed the first communications relay satellite into a halo orbit around the Earth-Moon L2 point.[5] On 3 January 2019, the Chang'e 4 spacecraft landed in the Von Kármán crater on the far side of the Moon, using the Queqiao relay satellite to communicate with the Earth.[6][7]

3. ^ Howell, Kathleen C. (1984). "Three-Dimensional Periodic Halo Orbits". Celestial Mechanics. Volume 32 (1): 53–71. `|volume=` has extra text (help)