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Choreography SC.152

From Simó (2001)

Choreography SC.152 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 13.162 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 32933), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0464 of each other at a top speed of 5.15, line up 54 times a period, and the computed loop closes to 6.7×10⁻²⁹.

Measured over one period

Period: 13.16220112
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0970
Closest approach: 0.04641
Top speed: 5.146
Path length: 62.399
Alignments per period: 54
Topology: (aaaabAbAbAbABBBB)² (free-group class, read from the drawing)
Stability: unstable (|λ|max 3.3×10⁸)
Loop closure: 6.7×10⁻²⁹

Neighbours on the map

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