Celestial Mechanics and Dynamical Astronomy

, Volume 100, Issue 2, pp 141–149 | Cite as

New central configurations for the planar 5-body problem

  • Jaume LlibreEmail author
  • Luis Fernando Mello
Original Article


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.


Planar central configurations 5-Body problem 


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  1. 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
  2. Euler, L.: De moto rectilineo trium corporum se mutuo attahentium. Novi Comm. Acad. Sci. Imp. Petrop. 11, 144–151 (1767)Google Scholar
  3. Hagihara, Y.: Celestial Mechanics, vol 1. MIT Press, Massachusetts (1970)Google Scholar
  4. Hampton, M.: Stacked central configurations: new examples in the planar five-body problem. Nonlinearity 18, 2299–2304 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  5. Hampton, M., Moeckel, R.: Finiteness of relative equilibria of the four-body problem. Invent. Math. 163, 289–312 (2006)zbMATHCrossRefMathSciNetADSGoogle Scholar
  6. Hampton, M., Santoprete, M.: Seven-body central configurations. Celestial Mech. Dynam. Astronom. 99, 293–305 (2007)zbMATHCrossRefADSMathSciNetGoogle Scholar
  7. Lagrange, J.L.: Essai sur le problème de trois corps. Ouvres, vol 6. Gauthier-Villars, Paris (1873)Google Scholar
  8. Llibre, J.: On the number of central configurations in the n-body problem. Celestial Mech. Dynam. Astronom. 50, 89–96 (1991)CrossRefADSMathSciNetzbMATHGoogle Scholar
  9. Moeckel, R.: On central configurations. Math. Z. 205, 499–517 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  10. Moulton, F.R.: The straight line solutions of n bodies. Ann. Math. 12, 1–17 (1910)CrossRefMathSciNetGoogle Scholar
  11. Newton, I.: Philosophi Naturalis Principia Mathematica. Royal Society, London (1687)Google Scholar
  12. Roberts, G.E.: A continuum of relative equilibria in the five-body problem. Physica D 127, 141–145 (1999)zbMATHCrossRefADSMathSciNetGoogle Scholar
  13. Saari, D.: On the role and properties of central configurations. Celestial Mech. 21, 9–20 (1980)zbMATHCrossRefADSMathSciNetGoogle Scholar
  14. Santos, A.A.: Dziobek’s configurations in restricted problems and bifurcation. Celestial Mech. Dynam. Astronom. 90, 213–238 (2004)zbMATHCrossRefADSMathSciNetGoogle Scholar
  15. Smale, S.: Topology and mechanics II: the planar n-body problem. Invent. Math. 11, 45–64 (1970)zbMATHCrossRefADSMathSciNetGoogle Scholar
  16. Smale, S.: Mathematical problems for the next century. Math. Intelligencer 20, 7–15 (1998)zbMATHMathSciNetCrossRefGoogle Scholar
  17. Wintner, A.: The Analytical Foundations of Celestial Mechanics. Princeton University Press (1941)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterra, Barcelona, CataloniaSpain
  2. 2.Instituto de Ciências ExatasUniversidade Federal de ItajubáItajubaBrazil

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