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Choreography SC.83

From Simó (2001)

Choreography SC.83 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 10.486 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 5.8759e+22), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0284 of each other at a top speed of 6.2, line up 36 times a period, and the computed loop closes to 1.6×10⁻²⁴.

Measured over one period

Period: 10.48617988
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.96366
Closest approach: 0.02843
Top speed: 6.196
Path length: 48.003
Alignments per period: 36
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: unstable (|λ|max 5.9×10²²)
Loop closure: 1.6×10⁻²⁴

Neighbours on the map

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