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Choreography SC.6

From Simó (2001)

Choreography SC.6 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 4.9853 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 17869), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0658 of each other at a top speed of 4.43, line up 18 times a period, and the computed loop closes to 7.5×10⁻³⁰.

Measured over one period

Period: 4.985287207
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0214
Closest approach: 0.06577
Top speed: 4.427
Path length: 24.210
Alignments per period: 18
Topology: aabAbABB (free-group class, read from the drawing)
Stability: unstable (|λ|max 1.8×10⁷)
Loop closure: 7.5×10⁻³⁰

Neighbours on the map

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