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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Cabral, H. E.: 1988, The Masses in an Isosceles Solution of the Three-Body Problem,Celest.Mech. 41, 175–177.
Diacu, F. N.: 1987, Some regularization in the N.Body problem,Astron. Nachr. 308, 163–168.
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.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Nicolae Diacu, F. The masses in a symmetric solution of the four body problem. Celestial Mech Dyn Astr 46, 27–30 (1989). https://doi.org/10.1007/BF02426709
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02426709