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Choreography SC.185

From Simó (2001)

Choreography SC.185 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 13.994 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 38837), so a small nudge makes it unravel over a few periods. The bodies pass within 0.116 of each other at a top speed of 3.29, line up 54 times a period, and the computed loop closes to 2.3×10⁻²⁹.

Measured over one period

Period: 13.99447440
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.1378
Closest approach: 0.1162
Top speed: 3.290
Path length: 69.318
Alignments per period: 54
Topology: aaaaaaaabAbAbAbAbAbAbAbABBBBBBBB (free-group class, read from the drawing)
Stability: unstable (|λ|max 3.9×10⁶)
Loop closure: 2.3×10⁻²⁹

Neighbours on the map

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