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Choreography SC.289

From Simó (2001)

Choreography SC.289 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 16.296 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 1.5285e+24), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0453 of each other at a top speed of 4.89, line up 102 times a period, and the computed loop closes to 4.5×10⁻²⁵.

Measured over one period

Period: 16.29579246
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.95407
Closest approach: 0.04534
Top speed: 4.892
Path length: 75.373
Alignments per period: 102
Topology: aaaaaaaaaaaabAbAbAbAbAbAbAbAbAbAbAbABBBBBBBBBBBB (free-group class, read from the drawing)
Stability: unstable (|λ|max 1.5×10²⁴)
Loop closure: 4.5×10⁻²⁵

Neighbours on the map

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