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Choreography SC.115

From Simó (2001)

Choreography SC.115 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 11.977 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 4643), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0464 of each other at a top speed of 5.11, line up 90 times a period, and the computed loop closes to 7.8×10⁻²⁹.

Measured over one period

Period: 11.97719863
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0258
Closest approach: 0.04642
Top speed: 5.113
Path length: 53.954
Alignments per period: 90
Stability: unstable (|λ|max 4643)
Loop closure: 7.8×10⁻²⁹

Neighbours on the map

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