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Choreography SC.329

From Simó (2001)

Choreography SC.329 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 16.684 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 1.6885999999999998e+22), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0537 of each other at a top speed of 4.3, line up 84 times a period, and the computed loop closes to 4.5×10⁻²⁶.

Measured over one period

Period: 16.68376188
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0350
Closest approach: 0.05370
Top speed: 4.302
Path length: 80.160
Alignments per period: 84
Stability: unstable (|λ|max 1.7×10²²)
Loop closure: 4.5×10⁻²⁶

Neighbours on the map

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