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Choreography SC.324

From Simó (2001)

Choreography SC.324 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 16.582 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 22921), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0269 of each other at a top speed of 6.8, line up 78 times a period, and the computed loop closes to 4.0×10⁻²⁸.

Measured over one period

Period: 16.58174370
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0917
Closest approach: 0.02690
Top speed: 6.801
Path length: 77.133
Alignments per period: 78
Stability: unstable (|λ|max 2.3×10¹⁵)
Loop closure: 4.0×10⁻²⁸

Neighbours on the map

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