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Choreography SC.209

From Simó (2001)

Choreography SC.209 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 14.934 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 12774), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0168 of each other at a top speed of 8.64, line up 66 times a period, and the computed loop closes to 3.7×10⁻²⁶.

Measured over one period

Period: 14.93431690
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.96245
Closest approach: 0.01682
Top speed: 8.641
Path length: 67.688
Alignments per period: 66
Stability: unstable (|λ|max 1.3×10¹⁹)
Loop closure: 3.7×10⁻²⁶

Neighbours on the map

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