Halo orbit

Short description: Periodic, three-dimensional orbit

For the hypothetical satellite employing a solar sail, see Statite.

Halo orbit

Polar view

Equatorial view

SOHO's trajectory, a halo orbit around the Sun-Earth L1 point
Earth * SOHO

Polar view of the Sun-Earth Lagrange points. Halo orbits orbit L1, L2, or L3 (orbits not shown in diagram). Part of a series on

Astrodynamics

Orbital mechanics

Orbital parameters

* Apsis
* Argument of periapsis
* Azimuth
* Eccentricity
* Inclination
* Mean anomaly
* Orbital nodes
* Semi-major axis
* True anomaly

Types of two-body orbits, by
eccentricity

* Circular orbit
* Elliptic orbit

Transfer orbit

* (Hohmann transfer orbit
* Bi-elliptic transfer orbit)

* Parabolic orbit
* Hyperbolic orbit
* Radial orbit
* Decaying orbit

Equations

* Dynamical friction
* Escape velocity
* Kepler's equation
* Kepler's laws of planetary motion
* Orbital period
* Orbital velocity
* Surface gravity
* Specific orbital energy
* Vis-viva equation

Celestial mechanics

Gravitational influences

* Barycenter
* Hill sphere
* Perturbations
* Sphere of influence

N-body orbits

Lagrangian points

* (Halo orbits)

* Lissajous orbits
* Lyapunov orbits

Engineering and efficiency

Preflight engineering

* Mass ratio
* Payload fraction
* Propellant mass fraction
* Tsiolkovsky rocket equation

Efficiency measures

* Gravity assist
* Oberth effect

* v
* t
* e

A halo orbit is a periodic, non-planar orbit associated with 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.

## Contents

* 1 Definition and history
* 2 See also
* 3 References
* 4 External links

## Definition and history

Robert W. Farquhar first used the name "halo" in 1966 for orbits around L2 which were 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,[3] so the orbit ceased to be a Lissajous orbit and became approximately an ellipse.[citation needed] 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.[4]

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.[5] Although several other missions since then have traveled to Lagrange points, they (eg. Gaia astrometric space observatory) typically have used the related non-periodic variations called Lissajous orbits rather than an actual halo orbit.

Although halo orbits were well known in the RTBP (Restricted Three Body Problem), it was difficult to obtain Halo orbits for the real Earth-Moon system. Translunar halo orbits were first computed in 1998 by M.A. Andreu, who introduced a new model for the motion of a spacecraft in the Earth-Moon-Sun system, which was called Quasi-Bicircular Problem (QBCP).[6]

In May 2018, Farquhar's original idea was finally realized when China placed the first communications relay satellite, Queqiao, into a halo orbit around the Earth-Moon L2 point.[7] 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.[8][9]

The James Webb Space Telescope entered a halo orbit around the Sun-Earth L2 point on 24 January 2022.[10] Euclid entered a similar orbit around this point in August 2023.

India's space agency ISRO launched Aditya-L1 to study the Sun from a halo orbit around the Sun-Earth L1 point.[11] On 6 January 2024, the spacecraft, India's first solar mission, successfully entered a halo orbit with a period of approximately 178 days, at a distance of approximately 1.5 million kilometers from Earth.[12]

## See also

* Interplanetary Transport Network - Low-energy trajectories in the Solar System
* Astronomy:Interplanetary spaceflight - Crewed or uncrewed travel between stars or planets
* Lissajous orbit - Quasi-periodic orbital trajectory, another Lagrangian-point orbit which generalizes halo orbits.
* Astronomy:Near-rectilinear halo orbit - Periodic, three-dimensional orbit
* Category:Spacecraft using halo orbits
* Astronomy:Libration point orbit - Quasiperiodic orbit around a Lagrange point

## References

1. ↑ Robert Farquhar (1966). "Station-Keeping in the Vicinity of Collinear Libration Points with an Application to a Lunar Communications Problem". AAS Science and Technology Series: Space Flight Mechanics Specialist Symposium 11: 519–535. , see Farquhar, R.W.: "The Control and Use of Libration-Point Satellites", Ph.D. Dissertation, Dept. of Aeronautics and Astronautics, Stanford University, Stanford, California, 1968, pp. 103, 107–108.
2. ↑ Schmid, P. E. (June 1, 1968). "Lunar far-side communication satellites". NASA, Goddard Space Flight Center. https://ntrs.nasa.gov/citations/19680015886.
3. ↑ Farquhar, R. W.; Kamel, A. A. (June 1973). "Quasi-Periodic Orbits about the Translunar Libration Point". Springer. https://adsabs.harvard.edu/full/1973CeMec...7..458F.
4. ↑ Howell, Kathleen C. (1984). "Three-Dimensional Periodic Halo Orbits". Celestial Mechanics 32 (1): 53–71. doi:10.1007/BF01358403. Bibcode: 1984CeMec..32...53H. http://adsabs.harvard.edu/full/1984CeMec..32...53H.
5. ↑ Dunham, D. W.; Farquhar, R. W. (2003). "Libration Point Missions, 1978–2002" (in en-us). Libration Point Orbits and Applications. pp. 45–73. doi:10.1142/9789812704849_0003. ISBN 978-981-238-363-1.
6. ↑ Andreu, M.A. (1998). The Quasi-bicircular problem. Ph. D. Thesis, Dept. Matemática Aplicada i Anàlisi, Universitat de Barcelona. Publicacions Universitat de Barcelona. ISBN 84-475-2319-5. http://www.maia.ub.es/dsg/1998/9801mangel_e.ps.gz.
7. ↑ Xu, Luyuan (2018-06-15). "How China's lunar relay satellite arrived in its final orbit" (in en). The Planetary Society. http://www.planetary.org/blogs/guest-blogs/2018/20180615-queqiao-orbit-explainer.html. "This is the first-ever lunar relay satellite at this location."
8. ↑ Jones, Andrew (December 5, 2018). "China to launch Chang'e-4 lunar far side landing mission on December 7". gbtimes.com. https://gbtimes.com/china-to-launch-change-4-lunar-far-side-landing-mission-on-december-7.
9. ↑ Jones, Andrew (2019-01-03). "Chang'e-4 returns first images from lunar farside following historic landing" (in en-US). https://spacenews.com/change-4-makes-historic-first-landing-on-the-far-side-of-the-moon/.
10. ↑ Roulette, Joey (24 January 2022). "After Million-Mile Journey, James Webb Telescope Reaches Destination – The telescope's safe arrival is a relief to scientists who plan to spend the next 10 or more years using it to study ancient galaxies.". The New York Times. https://www.nytimes.com/2022/01/24/science/james-webb-telescope-arrival.html.
11. ↑ "After Chandrayaan-3, ISRO getting ready for Sun mission ADITYA-L1. Key things to know" (in en). The Economic Times. 2023-07-24. https://economictimes.indiatimes.com/news/india/after-chandrayaan-3-isro-getting-ready-for-sun-mission-aditya-l1-key-things-to-know/articleshow/102074355.cms.
12. ↑ "Halo-Orbit Insertion of Aditya-L1 Successfully Accomplished". https://www.isro.gov.in/halo-orbit-insertion-adtya-l1.html.

## External links

* 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"

* v
* t
* e

Gravitational orbits

Types|

| General|

* Box
* Capture
* Circular
* Elliptical / Highly elliptical
* Escape
* Horseshoe
* Hyperbolic trajectory
* Inclined / Non-inclined
* Lagrangian point
* Osculating
* Parabolic trajectory
* Parking
* Prograde / Retrograde
* Synchronous
* semi
* sub
* Transfer orbit

|

Geocentric|

* Geosynchronous
* Geostationary
* Geostationary transfer
* Graveyard
* High Earth
* Low Earth
* Medium Earth
* Molniya
* Near-equatorial
* Orbit of the Moon
* Polar
* Sun-synchronous
* Tundra

About other points|

* Mars
* Areosynchronous
* Areostationary
* Lagrange points
* Distant retrograde
* Halo
* Lissajous
* Lunar
* Sun
* Heliocentric
* Earth's orbit
* Heliosynchronous

Parameters|

* Shape
* Size

* e Eccentricity
* a Semi-major axis
* b Semi-minor axis
* Q, q Apsides

|

Orientation|

* i Inclination
* Ω Longitude of the ascending node
* ω Argument of periapsis
* ϖ Longitude of the periapsis

Position|

* M Mean anomaly
* ν, θ, f True anomaly
* E Eccentric anomaly
* L Mean longitude
* l True longitude

Variation|

* T Orbital period
* n Mean motion
* v Orbital speed
* t0 Epoch

Maneuvers|

* Bi-elliptic transfer
* Collision avoidance (spacecraft)
* Delta-v
* Delta-v budget
* Gravity assist
* Gravity turn
* Hohmann transfer
* Inclination change
* Low energy transfer
* Oberth effect
* Phasing
* Rocket equation
* Rendezvous
* Transposition, docking, and extraction

Orbital mechanics|

* Celestial coordinate system
* Characteristic energy
* Escape velocity
* Ephemeris
* Equatorial coordinate system
* Ground track
* Hill sphere
* Interplanetary Transport Network
* Kepler's laws of planetary motion
* Lagrangian point
* n-body problem
* Orbit equation
* Orbital state vectors
* Perturbation
* Retrograde motion
* Specific orbital energy
* Specific relative angular momentum
* Two-line elements

* List of orbits

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