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Choreography SC.123

From Simó (2001)

Choreography SC.123 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 12.51 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 9.7309e+22), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0218 of each other at a top speed of 7.51, line up 54 times a period, and the computed loop closes to 7.7×10⁻²⁵.

Measured over one period

Period: 12.50984182
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0444
Closest approach: 0.02180
Top speed: 7.513
Path length: 57.944
Alignments per period: 54
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: unstable (|λ|max 9.7×10²²)
Loop closure: 7.7×10⁻²⁵

Neighbours on the map

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