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Choreography SC.135

From Simó (2001)

Choreography SC.135 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 12.732 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 7.610499999999999e+22), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0721 of each other at a top speed of 4.35, line up 48 times a period, and the computed loop closes to 7.9×10⁻²⁷.

Measured over one period

Period: 12.73174089
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0841
Closest approach: 0.07213
Top speed: 4.350
Path length: 61.853
Alignments per period: 48
Topology: (aabAbABB)² (free-group class, read from the drawing)
Stability: unstable (|λ|max 7.6×10²²)
Loop closure: 7.9×10⁻²⁷

Neighbours on the map

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