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Choreography SC.125

From Simó (2001)

Choreography SC.125 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 12.517 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 60536), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0649 of each other at a top speed of 4.39, line up 54 times a period, and the computed loop closes to 2.3×10⁻²⁶.

Measured over one period

Period: 12.51748734
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0902
Closest approach: 0.06488
Top speed: 4.392
Path length: 59.944
Alignments per period: 54
Stability: unstable (|λ|max 6.1×10¹⁸)
Loop closure: 2.3×10⁻²⁶

Neighbours on the map

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