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Choreography SC.333

From Simó (2001)

Choreography SC.333 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 16.819 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 5.9112e+27), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0461 of each other at a top speed of 5.43, line up 72 times a period, and the computed loop closes to 7.5×10⁻⁷.

Measured over one period

Period: 16.81870095
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0663
Closest approach: 0.04614
Top speed: 5.434
Path length: 80.390
Alignments per period: 72
Stability: unstable (|λ|max 5.9×10²⁷)
Loop closure: 7.5×10⁻⁷

Neighbours on the map

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