A new solution to the three-body problem. (English) Zbl 1047.70036

Montgomery, Richard

Notices Am. Math. Soc. 48, No. 5, 471-481 (2001).

Summary: Somewhere in the universe do three suns chase each other in a figure-eight pattern? This article explains a recent proof of the mathematical existence of such an orbit. It is found with the help of numerical methods by C. Moore in 1993 and rediscovered analytically by A. Chenciner and R. G. Montgomery [Ann. Math. (2) 152, No. 3, 881–901 (2000; Zbl 0987.70009)].

MSC:

70F07	Three-body problems
37J45	Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
34C45	Invariant manifolds for ordinary differential equations

Citations:

Zbl 0987.70009