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Choreography SC.106

From Simó (2001)

Choreography SC.106 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 11.581 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 15047), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0365 of each other at a top speed of 5.8, line up 54 times a period, and the computed loop closes to 1.5×10⁻²⁸.

Measured over one period

Period: 11.58076921
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0957
Closest approach: 0.03654
Top speed: 5.805
Path length: 54.251
Alignments per period: 54
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: unstable (|λ|max 1.5×10⁹)
Loop closure: 1.5×10⁻²⁸

Neighbours on the map

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