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Choreography SC.269

From Simó (2001)

Choreography SC.269 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 16.162 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 4859), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0585 of each other at a top speed of 4.71, line up 66 times a period, and the computed loop closes to 1.9×10⁻²⁴.

Measured over one period

Period: 16.16155558
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0879
Closest approach: 0.05848
Top speed: 4.708
Path length: 78.368
Alignments per period: 66
Stability: unstable (|λ|max 4.9×10²⁰)
Loop closure: 1.9×10⁻²⁴

Neighbours on the map

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