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Choreography SC.53

From Simó (2001)

Choreography SC.53 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 8.703 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 1731), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0896 of each other at a top speed of 3.79, line up 42 times a period, and the computed loop closes to 2.3×10⁻²⁶.

Measured over one period

Period: 8.702960268
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0829
Closest approach: 0.08960
Top speed: 3.795
Path length: 42.017
Alignments per period: 42
Topology: aaaabAbAbAbABBBB (free-group class, read from the drawing)
Stability: unstable (|λ|max 1.7×10¹⁶)
Loop closure: 2.3×10⁻²⁶

Neighbours on the map

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