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Choreography SC.294

From Simó (2001)

Choreography SC.294 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 16.345 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 2.4492e+21), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0905 of each other at a top speed of 3.61, line up 54 times a period, and the computed loop closes to 2.0×10⁻²⁵.

Measured over one period

Period: 16.34498809
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0867
Closest approach: 0.09045
Top speed: 3.609
Path length: 80.376
Alignments per period: 54
Topology: aaaaaaaabAbAbAbAbAbAbAbABBBBBBBB (free-group class, read from the drawing)
Stability: unstable (|λ|max 2.4×10²¹)
Loop closure: 2.0×10⁻²⁵

Neighbours on the map

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