Periodic orbits in the N-body plane problem

N equal masses are moving in the same plane under the action of the mutual gravitational attraction. If the initial conditions are chosen in the right way, some periodic solutions of a very special kind may be found: all particles move along the same orbit and the total angular momentum vanishes in the center-of-mass system. One can see some examples in this simulation.

To get information on an element, put over it the mouse pointer to see the corresponding tooltip.

Activities

Check that the first example (due to Chris Moore: see http://count.ucsc.edu/~rmont/Nbdy.html) is stable: stop the simulation, use the mouse to move one particle a bit and press Continue.
Check that the remaining examples (due to Carles Simó: see http://www.maia.ub.es/dsg/nbody.html and http://burtleburtle.net/bob/physics/index.html) are unstable: just wait long enough to see the particles out of the periodic orbit due to the errors in initial conditions and integration method.
To check dependence on the integration method, try one unstable example with different values for the tolerance (tol) and compare the values of time t at which the particles start leaving the common orbit.
More examples (even in three dimensions!) can be found in the aforementioned links.

This is an English translation of the Basque original for a course on mechanics, oscillations and waves.
It requires Java 1.5 or newer and was created by Juan M. Aguirregabiria with Easy Java Simulations (Ejs) by Francisco Esquembre. I thank Wolfgang Christian and Francisco Esquembre for their help.