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Choreography SC.31

From Simó (2001)

Choreography SC.31 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 6.6643 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 45413), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0998 of each other at a top speed of 3.86, line up 24 times a period, and the computed loop closes to 3.6×10⁻²⁹.

Measured over one period

Period: 6.664336325
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.95063
Closest approach: 0.09985
Top speed: 3.860
Path length: 32.194
Alignments per period: 24
Stability: unstable (|λ|max 4.5×10¹⁰)
Loop closure: 3.6×10⁻²⁹

Neighbours on the map

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