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Choreography SC.136

From Simó (2001)

Choreography SC.136 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 12.744 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 35442), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0708 of each other at a top speed of 4.25, line up 66 times a period, and the computed loop closes to 2.4×10⁻²⁶.

Measured over one period

Period: 12.74412464
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.1336
Closest approach: 0.07080
Top speed: 4.252
Path length: 61.144
Alignments per period: 66
Stability: unstable (|λ|max 3.5×10¹⁶)
Loop closure: 2.4×10⁻²⁶

Neighbours on the map

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