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Choreography SC.231

From Simó (2001)

Choreography SC.231 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 15.246 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 84209), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0284 of each other at a top speed of 6.57, line up 60 times a period, and the computed loop closes to 9.9×10⁻²⁵.

Measured over one period

Period: 15.24646825
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0734
Closest approach: 0.02842
Top speed: 6.571
Path length: 72.793
Alignments per period: 60
Stability: unstable (|λ|max 8.4×10¹⁸)
Loop closure: 9.9×10⁻²⁵

Neighbours on the map

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