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Choreography SC.37

From Simó (2001)

Choreography SC.37 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 6.8237 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 30151), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0724 of each other at a top speed of 4.14, line up 24 times a period, and the computed loop closes to 5.9×10⁻²⁸.

Measured over one period

Period: 6.823739204
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0763
Closest approach: 0.07241
Top speed: 4.145
Path length: 32.740
Alignments per period: 24
Topology: (abAB)² (free-group class, read from the drawing)
Stability: unstable (|λ|max 3.0×10¹⁴)
Loop closure: 5.9×10⁻²⁸

Neighbours on the map

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