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 (3)

• Gravitational waveforms for 2- and 3-body gravitating systems
• Choreographic solution to the general relativistic three-body problem
• Can N-body systems generate periodic gravitational waves?

Cited by in corpus (6)

• The chaotic four-body problem in Newtonian gravity I: Identical point-particles
• Gravitational Waves from Periodic Three-Body Systems
• Periodic three-body orbits with vanishing angular momentum in the Jacobi-Poincare "strong" potential
• Periodic orbits of the two fixed centers problem with a variational gravitational field
• MPPhys - A many-particle simulation package for computational physics education
• Variational principle for bifurcation in Lagrangian mechanics