Skip to main content

New central configurations for the planar 5-body problem

Abstract

In this paper we show the existence of three new families of planar central configurations for the 5-body problem with the following properties: three bodies are on the vertices of an equilateral triangle and the other two bodies are on a perpendicular bisector.

This is a preview of subscription content, access via your institution.

References

  • Boccaletti, D., Pucacco, G.: Theory of Orbits, vol. 1. Integrable systems and non-perturbative methods. Astronomy and Astrophysics Library. Springer-Verlag, Berlin (1996)

    Google Scholar 

  • Euler, L.: De moto rectilineo trium corporum se mutuo attahentium. Novi Comm. Acad. Sci. Imp. Petrop. 11, 144–151 (1767)

    Google Scholar 

  • Hagihara, Y.: Celestial Mechanics, vol 1. MIT Press, Massachusetts (1970)

    Google Scholar 

  • Hampton, M.: Stacked central configurations: new examples in the planar five-body problem. Nonlinearity 18, 2299–2304 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  • Hampton, M., Moeckel, R.: Finiteness of relative equilibria of the four-body problem. Invent. Math. 163, 289–312 (2006)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Hampton, M., Santoprete, M.: Seven-body central configurations. Celestial Mech. Dynam. Astronom. 99, 293–305 (2007)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • Lagrange, J.L.: Essai sur le problème de trois corps. Ouvres, vol 6. Gauthier-Villars, Paris (1873)

    Google Scholar 

  • Llibre, J.: On the number of central configurations in the n-body problem. Celestial Mech. Dynam. Astronom. 50, 89–96 (1991)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Moeckel, R.: On central configurations. Math. Z. 205, 499–517 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  • Moulton, F.R.: The straight line solutions of n bodies. Ann. Math. 12, 1–17 (1910)

    Article  MathSciNet  Google Scholar 

  • Newton, I.: Philosophi Naturalis Principia Mathematica. Royal Society, London (1687)

    Google Scholar 

  • Roberts, G.E.: A continuum of relative equilibria in the five-body problem. Physica D 127, 141–145 (1999)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • Saari, D.: On the role and properties of central configurations. Celestial Mech. 21, 9–20 (1980)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • Santos, A.A.: Dziobek’s configurations in restricted problems and bifurcation. Celestial Mech. Dynam. Astronom. 90, 213–238 (2004)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • Smale, S.: Topology and mechanics II: the planar n-body problem. Invent. Math. 11, 45–64 (1970)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • Smale, S.: Mathematical problems for the next century. Math. Intelligencer 20, 7–15 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  • Wintner, A.: The Analytical Foundations of Celestial Mechanics. Princeton University Press (1941)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jaume Llibre.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Llibre, J., Mello, L.F. New central configurations for the planar 5-body problem. Celestial Mech Dyn Astr 100, 141–149 (2008). https://doi.org/10.1007/s10569-007-9107-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10569-007-9107-4

Keywords

  • Planar central configurations
  • 5-Body problem