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Choreography SC.331

From Simó (2001)

Choreography SC.331 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 16.75 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 41599), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0722 of each other at a top speed of 4.39, line up 72 times a period, and the computed loop closes to 4.1×10⁻²⁶.

Measured over one period

Period: 16.75000976
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0854
Closest approach: 0.07216
Top speed: 4.395
Path length: 81.030
Alignments per period: 72
Topology: (aaaaabAbAbAbAbABBBBB)² (free-group class, read from the drawing)
Stability: unstable (|λ|max 4.2×10¹⁹)
Loop closure: 4.1×10⁻²⁶

Neighbours on the map

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