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Choreography SC.216

From Simó (2001)

Choreography SC.216 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 15.009 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 21331), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0512 of each other at a top speed of 5.01, line up 78 times a period, and the computed loop closes to 3.1×10⁻²⁷.

Measured over one period

Period: 15.00914820
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.1199
Closest approach: 0.05118
Top speed: 5.012
Path length: 71.259
Alignments per period: 78
Topology: aaaaaaaaaabAbAbAbAbAbAbAbAbAbABBBBBBBBBB (free-group class, read from the drawing)
Stability: unstable (|λ|max 2.1×10¹⁶)
Loop closure: 3.1×10⁻²⁷

Neighbours on the map

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