Shape up. Solutions to the three-body problem, such as the “figure eight” and “yarn,” can be viewed on an abstract shape-sphere (top) or in real space (bottom). Credit: Milovan Šuvakov and Veljko Dmitrašinovi?, Phys. Rev. Lett., (2013); Milovan Šuvakov and Veljko Dmitrašinovi? /University of Belgrade

 

Physicists Discover a Whopping 13 New Solutions to Three-Body Problem

by Jon Cartwright on 8 March 2013, 4:30 PM

It’s the sort of abstract puzzle that keeps a scientist awake at night: Can you predict how three objects will orbit each other in a repeating pattern? In the 300 years since this “three-body problem” was first recognized, just three families of solutions have been found. Now, two physicists have discovered 13 new families. It’s quite a feat in mathematical physics, and it could conceivably help astrophysicists understand new planetary systems.

The trove of new solutions has researchers jazzed. “I love these things,” says Robert Vanderbei a mathematician at Princeton University who was not involved in the work. He says he, in fact, spent all night thinking about the work.

The three-body problem dates back to the 1680s. Isaac Newton had already shown that his new law of gravity could always predict the orbit of two bodies held together by gravity—such as a star and a planet—with complete accuracy. The orbit is basically always an ellipse. However, Newton couldn’t come up with a similar solution for the case of three bodies orbiting one another. For 2 centuries, scientists tried different tacks until the German mathematician Heinrich Bruns pointed out that the search for a general solution for the three-body problem was futile, and that only specific solutions – one-offs that work under particular conditions—were possible. Generally, the motion of three bodies is now known to be nonrepeating.

Read more: Physicists Discover a Whopping 13 New Solutions to Three-Body Problem – ScienceNOW.

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