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Choreography SC.56

From Simó (2001)

Choreography SC.56 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 8.8143 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 18916), so a small nudge makes it unravel over a few periods. The bodies pass within 0.04 of each other at a top speed of 5.37, line up 42 times a period, and the computed loop closes to 5.8×10⁻²⁸.

Measured over one period

Period: 8.814273696
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0636
Closest approach: 0.03999
Top speed: 5.367
Path length: 41.251
Alignments per period: 42
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: unstable (|λ|max 1.9×10¹³)
Loop closure: 5.8×10⁻²⁸

Neighbours on the map

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