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Choreography SC.134

From Simó (2001)

Choreography SC.134 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 12.722 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 13215), so a small nudge makes it unravel over a few periods. The bodies pass within 0.054 of each other at a top speed of 4.24, line up 48 times a period, and the computed loop closes to 7.6×10⁻²⁷.

Measured over one period

Period: 12.72182946
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0590
Closest approach: 0.05403
Top speed: 4.241
Path length: 61.245
Alignments per period: 48
Topology: (aabAbABB)² (free-group class, read from the drawing)
Stability: unstable (|λ|max 1.3×10¹⁶)
Loop closure: 7.6×10⁻²⁷

Neighbours on the map

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