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Choreography SC.311

From Simó (2001)

Choreography SC.311 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 16.49 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 91184), so a small nudge makes it unravel over a few periods. The bodies pass within 0.071 of each other at a top speed of 4.24, line up 72 times a period, and the computed loop closes to 1.8×10⁻²⁸.

Measured over one period

Period: 16.49038744
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.1198
Closest approach: 0.07104
Top speed: 4.237
Path length: 80.070
Alignments per period: 72
Topology: aaaaaaaaaaaabAbAbAbAbAbAbAbAbAbAbAbABBBBBBBBBBBB (free-group class, read from the drawing)
Stability: unstable (|λ|max 9.1×10¹¹)
Loop closure: 1.8×10⁻²⁸

Neighbours on the map

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