Recently Discovered Periodic Solutions of the Three-Body Problem

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The three-body problem seeks solutions for the orbits of three masses under the mutual influence of gravity. Periodic solutions are very hard to find [1]; one of these is shown in Figure 8. Recently 13 new solutions were found by a combination of numerical search and a topological method [2]. The solutions are presented in 2D and on a "shape sphere" using Jacobi three-body coordinates [3]. The red dots on the shape sphere are related to the three two-body collision points.

Contributed by: Enrique Zeleny (July 2013)
Open content licensed under CC BY-NC-SA


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References

[1] J. Cartwright, "Physicists Discover a Whopping 13 New Solutions to Three-Body Problem," Science, March 8, 2013. news.sciencemag.org/sciencenow/2013/03/physicists-discover-a-whopping.html.

[2] M. Šuvakov and V. Dmitrašinović, "Three Classes of Newtonian Three-Body Planar Periodic Orbits," Physical Review Letters 110(11), 114301, 2013. arxiv.org/abs/1303.0181.

[3] Institute of Physics, Belgrade. "Three-Body Gallery." (Jul 2, 2013) suki.ipb.ac.rs/3body.



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