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Choreography SC.21

From Simó (2001)

Choreography SC.21 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 5.9373 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 59272), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0529 of each other at a top speed of 4.85, line up 24 times a period, and the computed loop closes to 4.3×10⁻³⁰.

Measured over one period

Period: 5.937273428
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.1199
Closest approach: 0.05294
Top speed: 4.847
Path length: 28.442
Alignments per period: 24
Stability: unstable (|λ|max 5.9×10⁶)
Loop closure: 4.3×10⁻³⁰

Neighbours on the map

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