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Choreography SC.87

From Simó (2001)

Choreography SC.87 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 10.666 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 59278), so a small nudge makes it unravel over a few periods. The bodies pass within 0.153 of each other at a top speed of 3, line up 60 times a period, and the computed loop closes to 3.2×10⁻²⁹.

Measured over one period

Period: 10.66588365
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0953
Closest approach: 0.1535
Top speed: 3.003
Path length: 52.364
Alignments per period: 60
Stability: unstable (|λ|max 5.9×10⁹)
Loop closure: 3.2×10⁻²⁹

Neighbours on the map

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