Halo orbit Information & Halo orbit Links at HealthHaven.com

A halo orbit is a periodic, three-dimensional orbit near the L₁, L₂, or L₃ Lagrange points in the three-body problem of orbital mechanics. A spacecraft in a halo orbit does not technically orbit the Lagrange point itself (which is just an equilibrium point with no mass), but travels in a closed, repeating path near the Lagrange point. Halo orbits are the result of a complicated interaction between the gravitational pull of the two planetary bodies and the centripetal acceleration on a spacecraft. Halo orbits exist in many three-body systems, such as the Sun-Earth system and the Earth-Moon system. Continuous "families" of both Northern and Southern halo orbits exist at each Lagrange point. Because halo orbits tend to be unstable, stationkeeping is required to keep a satellite on the orbit.

Halo orbit from above in a frame rotating with the two primary bodies. The blue sphere is the Earth, the gray sphere is the Moon, and the two red spheres are the Lagrange points L₁ and L₂. The spacecraft is orbiting near the L₂ point.

[edit] Definition and history

Robert Farquhar first used the name "halo" for these orbits in his 1968 Ph.D. thesis.^[1] Farquhar advocated using spacecraft in a halo orbit on the far side of 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 a halo orbit would be in continuous view of both the Earth and the far side of the Moon. In the end, neither a communication link satellite nor an Apollo co-mission positioned at L₂ for a far side Apollo lunar landing ever took flight.

The first mission to use a halo orbit was ISEE-3, 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 SOHO, a joint ESA and NASA mission to study the sun, which arrived at Sun-Earth L₁ in 1996. It used an orbit similar to ISEE-3.^[2] Although several other missions since then have traveled to Lagrange points, they typically have used non-periodic orbits (also called Lissajous orbits) that are slightly different than halo orbits.^{[citation needed]}

Farquhar used analytical expressions to represent halo orbits, but Kathleen Howell showed that more precise trajectories could be computed numerically.^[3] The most recent mission to use a halo orbit was Genesis, launched in 2001, which also pioneered the use of Dynamical systems theory to find low-energy trajectories to and from the halo orbit.

[edit] See also

Lissajous orbit, another Lagrangian point orbit.

[edit] References

^ Farquhar, R. W.: "The Control and Use of Libration-Point Satellites", Ph.D. Dissertation, Dept. of Aeronautics and Astronautics, Stanford University, Stanford, CA, 1968
^ Dunham, D.W. and Farquhar, R. W.:"Libration-Point Missions 1978-2000," Libration Point Orbits and Applications, Parador d'Aiguablava, Girona, Spain, June 2002
^ Howell, K. C.: "Three-Dimensional, Periodic, 'Halo' Orbits", Celestial Mechanics, Volume 32, Number 53, 1984

[0] Farquhar, R. W.: "The Control and Use of Libration-Point Satellites", Ph.D. Dissertation, Dept. of Aeronautics and Astronautics, Stanford University, Stanford, CA, 1968

[1] Dunham, D.W. and Farquhar, R. W.:"Libration-Point Missions 1978-2000," Libration Point Orbits and Applications, Parador d'Aiguablava, Girona, Spain, June 2002

[2] Howell, K. C.: "Three-Dimensional, Periodic, 'Halo' Orbits", Celestial Mechanics, Volume 32, Number 53, 1984

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