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The masses in an isosceles solution of the three-body problem. (English) Zbl 0648.70005

A proof is given that the masses at the base of the triangle formed by the three particles of a three-body problem are necessarily equal. The proof uses only basic calculus.

MSC:

70F07 Three-body problems
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References:

[1] J. Chazy, ?Sur les solutions isosceles du Probl?me des Trois Corps?,Bull. Astronom. 1, 171?188. (1921).
[2] D. Saari, ?From rotations and inclinations to zero configurational velocity surfaces?,Celest. Mech. 33, 299?318, (1986). · Zbl 0549.70003 · doi:10.1007/BF01241046
[3] J. Wilczynski, ?Ricerche geometriche intorno al problema dei tre corpi?,Ann. di Mat. 21 17?31, (1913). · JFM 44.0824.02
[4] A. Wintner,The Analytical Foundations of Celestial Mechanics. Princeton Univ. Press, Princeton, N.J., 1947. · Zbl 0041.59006
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