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Choreography SC.90

From Simó (2001)

Choreography SC.90 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 10.867 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 42888), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0707 of each other at a top speed of 4.07, line up 78 times a period, and the computed loop closes to 2.5×10⁻²⁸.

Measured over one period

Period: 10.86695695
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0357
Closest approach: 0.07071
Top speed: 4.073
Path length: 50.362
Alignments per period: 78
Stability: unstable (|λ|max 4.3×10⁶)
Loop closure: 2.5×10⁻²⁸

Neighbours on the map

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