Celestial Mechanics and Dynamical Astronomy

, Volume 104, Issue 4, pp 369–381 | Cite as

Central configurations of the five-body problem with equal masses

  • Tsung-Lin LeeEmail author
  • Manuele Santoprete
Original Article


In this paper we present a complete classification of the isolated central configurations of the five-body problem with equal masses. This is accomplished by using the polyhedral homotopy method to approximate all the isolated solutions of the Albouy-Chenciner equations. The existence of exact solutions, in a neighborhood of the approximated ones, is then verified using the Krawczyk method. Although the Albouy-Chenciner equations for the five-body problem are huge, it is possible to solve them in a reasonable amount of time.


Celestial mechanics n-Body problem Central configurations Polyedral homotopy continuation method 


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of MathematicsMichigan State UniversityEast LansingUSA
  2. 2.Department of MathematicsWilfrid Laurier UniversityWaterlooCanada

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