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Choreography SC.112

From Simó (2001)

Choreography SC.112 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 11.87 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 14222), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0589 of each other at a top speed of 4.73, line up 48 times a period, and the computed loop closes to 8.5×10⁻²⁶.

Measured over one period

Period: 11.86974596
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0861
Closest approach: 0.05892
Top speed: 4.733
Path length: 56.671
Alignments per period: 48
Topology: (aaabAbAbABBB)² (free-group class, read from the drawing)
Stability: unstable (|λ|max 1.4×10¹⁸)
Loop closure: 8.5×10⁻²⁶

Neighbours on the map

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