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Choreography SC.91

From Simó (2001)

Choreography SC.91 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 11.119 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 8706300000000002), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0226 of each other at a top speed of 7.33, line up 42 times a period, and the computed loop closes to 6.9×10⁻²⁷.

Measured over one period

Period: 11.11878226
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0433
Closest approach: 0.02261
Top speed: 7.332
Path length: 52.761
Alignments per period: 42
Stability: unstable (|λ|max 8.7×10¹⁵)
Loop closure: 6.9×10⁻²⁷

Neighbours on the map

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