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Choreography SC.129

From Simó (2001)

Choreography SC.129 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 12.628 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 38536), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0263 of each other at a top speed of 6.56, line up 36 times a period, and the computed loop closes to 2.9×10⁻²⁶.

Measured over one period

Period: 12.62824843
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.99357
Closest approach: 0.02630
Top speed: 6.558
Path length: 60.291
Alignments per period: 36
Stability: unstable (|λ|max 3.9×10¹⁸)
Loop closure: 2.9×10⁻²⁶

Neighbours on the map

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