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Choreography SC.291

From Simó (2001)

Choreography SC.291 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 16.321 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 5.326299999999999e+33), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0184 of each other at a top speed of 7.9, line up 60 times a period, and the computed loop closes to 5.0×10⁻⁶.

Measured over one period

Period: 16.32101941
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0050
Closest approach: 0.01840
Top speed: 7.897
Path length: 77.857
Alignments per period: 60
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: unstable (|λ|max 5.3×10³³)
Loop closure: 5.0×10⁻⁶

Neighbours on the map

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