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Choreography SC.321

From Simó (2001)

Choreography SC.321 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 16.571 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 87792), so a small nudge makes it unravel over a few periods. The bodies pass within 0.102 of each other at a top speed of 3.47, line up 114 times a period, and the computed loop closes to 6.1×10⁻²⁹.

Measured over one period

Period: 16.57124683
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0637
Closest approach: 0.1019
Top speed: 3.471
Path length: 79.308
Alignments per period: 114
Topology: (aaaaaaaaabAbAbAbAbAbAbAbAbABBBBBBBBB)² (free-group class, read from the drawing)
Stability: unstable (|λ|max 8.8×10¹¹)
Loop closure: 6.1×10⁻²⁹

Neighbours on the map

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