Qualitative Theory of Dynamical Systems

, Volume 8, Issue 2, pp 357–370 | Cite as

Finiteness in the Planar Restricted Four-Body Problem

  • Julianne L. Kulevich
  • Gareth E. Roberts
  • Christopher J. Smith


Using BKK theory, we show that the number of equilibria (central configurations) in the planar, circular, restricted four-body problem is finite for any choice of masses. Moreover, the number of such points is bounded above by 196.


Celestial mechanics Restricted four-body problem Central configurations BKK theory 

Mathematics Subject Classification (2000)

Primary 70F10 70F15 Secondary 37N05 14M25 


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Copyright information

© Birkhäuser/Springer Basel AG 2010

Authors and Affiliations

  • Julianne L. Kulevich
    • 1
  • Gareth E. Roberts
    • 1
  • Christopher J. Smith
    • 2
  1. 1.Department of Mathematics and Computer ScienceCollege of the Holy CrossWorcesterUSA
  2. 2.MilfordUSA

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