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Choreography SC.71

From Simó (2001)

Choreography SC.71 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 9.9013 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 1881), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0762 of each other at a top speed of 4.17, line up 54 times a period, and the computed loop closes to 1.0×10⁻²⁵.

Measured over one period

Period: 9.901313295
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.99662
Closest approach: 0.07622
Top speed: 4.172
Path length: 46.866
Alignments per period: 54
Stability: unstable (|λ|max 1.9×10¹⁸)
Loop closure: 1.0×10⁻²⁵

Neighbours on the map

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