Three Classes of Newtonian Three-Body Planar Periodic Orbits

Abstract

We present the results of a numerical search for periodic orbits of three equal masses moving in a plane under the influence of Newtonian gravity, with zero angular momentum. A topological method is used to classify periodic three-body orbits into families, which fall into four classes, with all three previously known families belonging to one class. The classes are defined by the orbits geometric and algebraic symmetries. In each class we present a few orbits initial conditions, 15 in all; 13 of these correspond to distinct orbits.

to be published in Phys. Rev. Lett.; 4 pages, 1 figure; for associated web gallery of solutions, see http://suki.ipb.ac.rs/3body

References in corpus (8)

• Gravitational waveforms for 2- and 3-body gravitating systems
• Choreographic solution to the general relativistic three-body problem
• New Orbits for the n-Body Problem
• Choreographic Three Bodies on the Lemniscate
• Binary--single-star scattering VII. Hard Binary Exchange Cross Sections for Arbitrary Mass Ratios: Numerical Results and Semi-Analytic Fits
• Periodic orbits for three particles with finite angular momentum
• Can N-body systems generate periodic gravitational waves?
• Approximate action-angle variables for the figure-eight and other periodic three-body orbits

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