World Library  
Flag as Inappropriate
Email this Article

Lissajous orbit

Article Id: WHEBN0010228498
Reproduction Date:

Title: Lissajous orbit  
Author: World Heritage Encyclopedia
Language: English
Subject: Lagrangian point, Halo orbit, Asteroid capture, Jules Antoine Lissajous, Lagrange point colonization
Collection: Orbits, Trigonometry
Publisher: World Heritage Encyclopedia
Publication
Date:
 

Lissajous orbit

Lissajous orbit around L2

In orbital mechanics, a Lissajous orbit, pronounced: , named after Jules Antoine Lissajous, is a quasi-periodic orbital trajectory that an object can follow around a Lagrangian point of a three-body system without requiring any propulsion. Lyapunov orbits around a libration point are curved paths that lie entirely in the plane of the two primary bodies. In contrast, Lissajous orbits include components in this plane and perpendicular to it, and follow a Lissajous curve. Halo orbits also include components perpendicular to the plane, but they are periodic, while Lissajous orbits are not.[1]

In practice, any orbit around Lagrangian points L1, L2, or L3 is dynamically unstable, meaning small departures from equilibrium grow exponentially over time.[2] As a result, spacecraft in libration point orbits must use their propulsion systems to perform orbital station-keeping. In the absence of other influences, orbits about Lagrangian points L4 and L5 are dynamically stable so long as the ratio of the masses of the two main objects is greater than about 25, meaning the natural dynamics (without the use of a spacecraft's propulsion system) keep the spacecraft in the vicinity of the Lagrangian point even when slightly perturbed from equilibrium.[3] These orbits can however be destabilized by other heavy nearby objects. It has been found for example that the L4 and L5 points in the Earth–Moon system would be stable for billions of years, even with perturbations from the sun, but because of smaller perturbations by the planets, orbits around these points can only last a few million years.[4]

Several missions have used Lissajous trajectories: ACE at Sun–Earth L1[5] and WMAP at Sun–Earth L2[6] and also the Genesis mission collecting solar particles at L1.[7] On 14 May 2009, the European Space Agency (ESA) launched into space the Herschel and Planck observatories, both of which use Lissajous orbits at Sun–Earth L2.[8] ESA's current Gaia mission also uses a Lissajous orbit at Sun–Earth L2.[9] In 2011, NASA transferred two of its THEMIS spacecraft from Earth orbit to Lunar orbit by way of Earth-Moon L1 and L2 Lissajous orbits.[10] China's lunar orbiter Chang'e 2 left lunar orbit on June 8, 2011 and flew to L2.[11]

In the science fiction novel Sunstorm by Arthur C. Clarke and Stephen Baxter, a huge shield is constructed in space to protect the Earth from a deadly solar storm. The shield is described to have been in a Lissajous orbit at L1. Similarly a group of wealthy and powerful people sheltered opposite the shield at L2 so as to be protected from the solar storm by the shield, Earth and Moon.

References

  1. ^ Koon, Wang Sang (2000). "International Conference on Differential Equations". Berlin: World Scientific. pp. 1167–1181. 
  2. ^ "ESA Science & Technology: Orbit/Navigation". European Space Agency. 14 June 2009. Retrieved 2009-06-12. 
  3. ^ Vallado, David A. (2007). Fundamentals of Astrodynamics and Applications (3 ed.). Space Technology Library (jointly with Microcosm Press).  
  4. ^ "Solar and planetary destabilization of the Earth–Moon triangular Lagrangian points" by Jack Lissauer and John Chambers, Icarus, vol. 195, issue 1, May 2008, pp. 16-27.
  5. ^ Advanced Composition Explorer (ACE) Mission Overview, CalTech, retrieved 2014-09-06.
  6. ^ WMAP Trajectory and Orbit, NASA, retrieved 2014-09-06.
  7. ^ Genesis: Lissajous Orbit Insertion, NASA, retrieved 2014-09-06.
  8. ^ "Herschel: Orbit/Navigation".  
  9. ^ "Gaia's Lissajous Type Orbit". ESA. Retrieved 2006-05-15. 
  10. ^ ARTEMIS: The First Mission to the Lunar Libration Orbits
  11. ^ http://scitech.people.com.cn/GB/14041406.html

External links

  • Koon, W. S.; M. W. Lo; J. E. Marsden; S. D. Ross (2006). Dynamical Systems, the Three-Body Problem, and Space Mission Design. 
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
 
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
 
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.
 



Copyright © World Library Foundation. All rights reserved. eBooks from World eBook Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.