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Choreography SC.108

From Simó (2001)

Choreography SC.108 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 11.782 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 99408), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00741 of each other at a top speed of 11.7, line up 84 times a period, and the computed loop closes to 1.9×10⁻²⁷.

Measured over one period

Period: 11.78222893
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.75590
Closest approach: 0.007415
Top speed: 11.68
Path length: 52.015
Alignments per period: 84
Stability: unstable (|λ|max 9.9×10¹⁵)
Loop closure: 1.9×10⁻²⁷

Neighbours on the map

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