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

Chenciner, Alain; Montgomery, Richard

Ann. Math. (2) 152, No. 3, 881-901 (2000).

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.

Reviewer: Sergei Georgievich Zhuravlev (Moskva)

MSC:

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

Keywords:

variational method; periodic orbit; eight-shaped curve; three equal masses in plane; zero angular momentum; symmetry; Euler configuration