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Choreography SC.267

From Simó (2001)

Choreography SC.267 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 16.134 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 4875), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0331 of each other at a top speed of 5.93, line up 90 times a period, and the computed loop closes to 5.3×10⁻²⁵.

Measured over one period

Period: 16.13411108
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0706
Closest approach: 0.03308
Top speed: 5.931
Path length: 72.745
Alignments per period: 90
Stability: unstable (|λ|max 4.9×10²⁰)
Loop closure: 5.3×10⁻²⁵

Neighbours on the map

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