Physics at Virginia

"The three-body problem: periodic solutions, topological classification"

Milovan Suvakov , Institute of Physics Belgrade
[Host: Marija Vucelja ]

The three-body problem dates back to the 1680s. Isaac Newton had
already shown that his 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 periodic two-body orbit is always an
ellipse (circle). For two centuries, scientists tried different tacks
to find similar solution for three-body problem, 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 that work only under particular conditions, were possible.
Only three families of such collisionless periodic orbits were known
until recently: 1) the Lagrange-Euler (1772); 2) the Broucke-Henon
(1975); and 3) Cris Moore's (1993) periodic orbit of three bodies
moving on a "figure-8" trajectory. Few years ago we reported the
discovery of 13 new families of periodic orbits. Meanwhile, hundreds
of new topologically different solutions have been reported by our and
other groups. We discuss the numerical methods used to find orbits and
to distinguish them from others. Additionally, we found that period T
of an orbit depends on its topology. This dependence is a simple
linear one, when expressed in terms of appropriate variables,
suggesting an exact mathematical law. This is the first known relation
between topological and kinematical properties of three-body systems.



Condensed Matter Seminar
Thursday, April 25, 2019
11:00 AM
Physics Building, Room 313
Note special time.
Note special room.

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