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Choreography SC.86

From Simó (2001)

Choreography SC.86 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 10.644 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 58023), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0935 of each other at a top speed of 3.33, line up 54 times a period, and the computed loop closes to 5.7×10⁻²⁹.

Measured over one period

Period: 10.64351078
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0794
Closest approach: 0.09350
Top speed: 3.331
Path length: 51.353
Alignments per period: 54
Topology: (aaaabAbAbAbABBBB)² (free-group class, read from the drawing)
Stability: unstable (|λ|max 5.8×10⁸)
Loop closure: 5.7×10⁻²⁹

Neighbours on the map

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