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Choreography SC.8

From Simó (2001)

Choreography SC.8 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 5.1348 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 30764), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0757 of each other at a top speed of 4.17, line up 12 times a period, and the computed loop closes to 5.2×10⁻³⁰.

Measured over one period

Period: 5.134832286
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.98756
Closest approach: 0.07570
Top speed: 4.175
Path length: 25.276
Alignments per period: 12
Stability: unstable (|λ|max 3.1×10⁹)
Loop closure: 5.2×10⁻³⁰

Neighbours on the map

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