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Choreography SC.149

From Simó (2001)

Choreography SC.149 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 13.087 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 15335), so a small nudge makes it unravel over a few periods. The bodies pass within 0.065 of each other at a top speed of 4.26, line up 102 times a period, and the computed loop closes to 2.7×10⁻²⁸.

Measured over one period

Period: 13.08744166
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0270
Closest approach: 0.06500
Top speed: 4.262
Path length: 59.917
Alignments per period: 102
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: unstable (|λ|max 1.5×10⁷)
Loop closure: 2.7×10⁻²⁸

Neighbours on the map

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