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Choreography SC.72

From Simó (2001)

Choreography SC.72 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 9.9019 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 55138), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0786 of each other at a top speed of 4.06, line up 54 times a period, and the computed loop closes to 4.4×10⁻²⁶.

Measured over one period

Period: 9.901907459
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0543
Closest approach: 0.07860
Top speed: 4.064
Path length: 47.236
Alignments per period: 54
Stability: unstable (|λ|max 5.5×10¹⁷)
Loop closure: 4.4×10⁻²⁶

Neighbours on the map

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