A remarkable periodic solution of the three-body problem in the case of equal masses. (English) Zbl 0987.70009

Using a variational method, the authors find a simple periodic orbit for Newtonian problem of three equal masses in a plane. The orbit has zero angular momentum, and possesses a very rich symmetry pattern. It is the most surprising feature that the three bodies chase each other around a fixed eight-shaped curve. Additionally, the orbit visits in turns every “Euler configuration” in which one of the bodies is located at the midpoint of the segment defined by the other two bodies.


70F07 Three-body problems
34C25 Periodic solutions to ordinary differential equations
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