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The masses in a symmetric solution of the four body problem

  • Florin Nicolae Diacu
Article

Abstract

It is proved that if a non-collinear motion of the four body problem has a symmetry axis (or plane), then the center of mass lies on this axis (plane) and the symmetric masses are equal. We also remark that this result is true for the generalized attraction law given by the inverse (α+1)-power of the distance, with α > 0.

Keywords

Symmetry Axis Symmetric Solution Body Problem Generalize Attraction Symmetric Masse 
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References

  1. Cabral, H. E.: 1988, The Masses in an Isosceles Solution of the Three-Body Problem,Celest.Mech. 41, 175–177.MathSciNetADSGoogle Scholar
  2. Diacu, F. N.: 1987, Some regularization in the N.Body problem,Astron. Nachr. 308, 163–168.MATHMathSciNetADSGoogle Scholar
  3. Diacu, F. N.: 1989, On the Planar Syzygy Solutions of the 3-Body Problem (to appear inCelest. Mech.). Wintner, A.: 1941,The Analytical Foundations of Celestial Mechanics, Princeton Univ. Press.Google Scholar

Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • Florin Nicolae Diacu
    • 1
  1. 1.Institut für Angewandte MathematikUniversität HeidelbergHeidelberg 1F.R.G.

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