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Choreography SC.176

From Simó (2001)

Choreography SC.176 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 13.961 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 1.9131e+24), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00402 of each other at a top speed of 16.8, line up 60 times a period, and the computed loop closes to 1.6×10⁻²⁴.

Measured over one period

Period: 13.96148517
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.90393
Closest approach: 0.004019
Top speed: 16.80
Path length: 61.716
Alignments per period: 60
Stability: unstable (|λ|max 1.9×10²⁴)
Loop closure: 1.6×10⁻²⁴

Neighbours on the map

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