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Choreography SC.249

From Simó (2001)

Choreography SC.249 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 15.429 time units, published by Simó (2001). Carles Simó’s catalogue of three-body choreographies with nonzero angular momentum, the curves that made choreographies famous. All unstable except the figure-eight. It is unstable (largest Floquet multiplier 29148), so a small nudge makes it unravel over a few periods. The bodies pass within 0.138 of each other at a top speed of 3.22, line up 108 times a period, and the computed loop closes to 1.7×10⁻²⁸.

Measured over one period

Period: 15.42858365
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0714
Closest approach: 0.1377
Top speed: 3.218
Path length: 74.913
Alignments per period: 108
Topology: aaaaaaaabAbAbAbAbAbAbAbABBBBBBBB (free-group class, read from the drawing, shape period T/2)
Stability: unstable (|λ|max 2.9×10¹²)
Loop closure: 1.7×10⁻²⁸

Neighbours on the map

All Simó’s choreographies, the families of periodic three-body orbits, or the atlas map.