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Choreography SC.139

From Simó (2001)

Choreography SC.139 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 12.789 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 68071), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0268 of each other at a top speed of 6.73, line up 60 times a period, and the computed loop closes to 2.4×10⁻²⁵.

Measured over one period

Period: 12.78875160
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0564
Closest approach: 0.02678
Top speed: 6.726
Path length: 58.822
Alignments per period: 60
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: unstable (|λ|max 6.8×10¹⁴)
Loop closure: 2.4×10⁻²⁵

Neighbours on the map

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