# Halo orbit

A **halo orbit** is a periodic, three-dimensional orbit near the L_{1}, L_{2} or L_{3} Lagrange points in the three-body problem of orbital mechanics. Although the Lagrange point is just a point in empty space, its peculiar characteristic is that it can be orbited. Halo orbits are the result of a complicated interaction between the gravitational pull of the two planetary bodies and the Coriolis and centrifugal accelerations on a spacecraft. Halo orbits exist in any three-body system, e.g. 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.

## Definition and history

Robert W. 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 L_{2}) 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 L_{2} for a far side Apollo lunar landing ever took flight.^{[2]}

Farquhar used analytical expressions to represent halo orbits, but Kathleen Howell showed that more precise trajectories could be computed numerically.^{[3]}

The first mission to use a halo orbit was ISEE-3, launched in 1978. It traveled to the Sun–Earth L_{1} point and remained there for several years. The next mission to use a halo orbit was Solar and Heliospheric Observatory (SOHO), a joint ESA and NASA mission to study the Sun, which arrived at Sun–Earth L_{1} 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^{[5]} non-periodic variations called Lissajous orbits than an actual halo orbit. For example, Genesis, launched in 2001, which also pioneered the use of dynamical systems theory to find low-energy transfers to and from its orbit.

## See also

- Interplanetary Transport Network
- Lissajous orbit, another Lagrangian-point orbit which generalizes halo orbits.
- Category:Spacecraft using halo orbits

## References

- ↑ Farquhar, R. W.: "The Control and Use of Libration-Point Satellites", Ph.D. Dissertation, Dept. of Aeronautics and Astronautics, Stanford University, Stanford, California, 1968
- ↑ Schmid, P. E. (June 1968). "Lunar Far-Side Communication Satellites" (PDF). NASA. Retrieved 2008-07-16.
- ↑ Howell, K. C.: "Three-Dimensional, Periodic, 'Halo' Orbits", Celestial Mechanics, Volume 32, Number 53, 1984
- ↑ Dunham, D.W. and Farquhar, R. W.: "Libration-Point Missions 1978-2000," Libration Point Orbits and Applications, Parador d'Aiguablava, Girona, Spain, June 2002
- ↑ "What is that fine line difference between the terms Lissajous orbit and Halo orbit around unstable Lagrange points? What exactly are in-plane and out-of-plane frequencies when depicting Lissajous curves in PCR3BP? - Quora".
*www.quora.com*. Retrieved 2015-05-31.

## External links

- CDS140B: Computation of Halo Orbit Archived September 16, 2006, at the Wayback Machine.
- SOHO - The Trip to the L1 Halo Orbit
- Low Energy Interplanetary Transfers Using Halo Orbit Hopping Method with STK/Astrogator
- Gaia's Lissajous Type Orbit — a Lissajous-type orbit,
*i.e.*, a near-circular ellipse or "halo"