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Choreography SC.234

From Simó (2001)

Choreography SC.234 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 15.269 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 68016), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0897 of each other at a top speed of 3.9, line up 66 times a period, and the computed loop closes to 3.9×10⁻²⁸.

Measured over one period

Period: 15.26880338
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.1162
Closest approach: 0.08967
Top speed: 3.901
Path length: 74.901
Alignments per period: 66
Topology: aaaaaaaaaabAbAbAbAbAbAbAbAbAbABBBBBBBBBB (free-group class, read from the drawing)
Stability: unstable (|λ|max 6.8×10¹¹)
Loop closure: 3.9×10⁻²⁸

Neighbours on the map

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