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Choreography SC.109

From Simó (2001)

Choreography SC.109 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 11.816 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 2.3278e+23), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0128 of each other at a top speed of 9.65, line up 42 times a period, and the computed loop closes to 1.6×10⁻²⁴.

Measured over one period

Period: 11.81605398
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0350
Closest approach: 0.01282
Top speed: 9.648
Path length: 55.397
Alignments per period: 42
Stability: unstable (|λ|max 2.3×10²³)
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.