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Choreography SC.74

From Simó (2001)

Choreography SC.74 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 10.05 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 18462), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0408 of each other at a top speed of 5.58, line up 42 times a period, and the computed loop closes to 7.9×10⁻²⁹.

Measured over one period

Period: 10.05013945
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0373
Closest approach: 0.04080
Top speed: 5.585
Path length: 46.315
Alignments per period: 42
Stability: unstable (|λ|max 1.8×10¹²)
Loop closure: 7.9×10⁻²⁹

Neighbours on the map

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