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Choreography SC.213

From Simó (2001)

Choreography SC.213 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 14.986 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 2.9267e+34), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0451 of each other at a top speed of 5.29, line up 48 times a period, and the computed loop closes to 1.8×10⁻⁶.

Measured over one period

Period: 14.98560650
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.99874
Closest approach: 0.04513
Top speed: 5.294
Path length: 72.865
Alignments per period: 48
Topology: (aabAbABB)² (free-group class, read from the drawing)
Stability: unstable (|λ|max 2.9×10³⁴)
Loop closure: 1.8×10⁻⁶

Neighbours on the map

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