Synopsis: New Orbits for Three Bodies

The surprisingly complex behavior of three gravitationally attracted bodies includes several previously unknown periodic orbits.
Synopsis figure
M. Šuvakov and V. Dmitrašinović, Phys. Rev. Lett. (2013)

Two objects responding to their mutual gravitational attraction adopt simple elliptical orbits for a wide range of initial conditions. But add one more object and things get complicated and generally defy simple mathematical description. One special case, in which the three bodies rotate as a fixed triangle, was identified by Lagrange two centuries ago. But it was not until the 1970s and the 1990s that researchers found two other families of periodic three-body motion.

Now, in Physical Review Letters, Milovan Šuvakov and Veljko Dmitrašinović of the Institute of Physics Belgrade, Serbia, have discovered 13 new families of periodic orbits for three equal masses moving under gravity in a plane. To classify these orbits, which were revealed by numerical simulations, Šuvakov and Dmitrašinović extended a previous analysis in which the evolving shape of the triangular arrangement is mathematically represented by a point on a sphere. The physical orbits correspond to closed paths on the sphere, which avoid so-called “collision” points that correspond to two bodies being in the same place. Using this topological classification scheme, the authors were able to distinguish various orbits by the number of times they wind clockwise and counterclockwise around the forbidden points. Of the 13 new families of periodic motion they found, three are related to previous solutions, but ten fall into three entirely new classes. (A gallery of the trajectories is on display here).

The complex motions are hard to visualize, and these orbits would only occur in nature for specific starting conditions. But these special solutions could help researchers better understand the surprisingly complex three-body problem. – Don Monroe


Features

More Features »

Announcements

More Announcements »

Subject Areas

GravitationMechanics

Previous Synopsis

Next Synopsis

Quantum Information

Big Shifts on an Atomic Scale

Read More »

Related Articles

Focus: Light Pushes and Pulls
Mechanics

Focus: Light Pushes and Pulls

Two forces coming from a light beam—one based on momentum transfer, the other on thermal effects—drive a tiny gold plate to move in opposite directions. Read More »

Synopsis: Plasma Mirror Mimics Evaporating Black Hole
Gravitation

Synopsis: Plasma Mirror Mimics Evaporating Black Hole

A proposal for using an accelerated plasma mirror to study the black hole information paradox elevates a thought experiment into a potential reality.   Read More »

Focus: Why Some Gels Shrink under Stress
Mechanics

Focus: Why Some Gels Shrink under Stress

The gel material that helps blood clot in a wound has anomalous material properties because of the interaction between the gel's fluid and its microscopic fiber network, according to experiments. Read More »

More Articles