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Choreography SC.223

From Simó (2001)

Choreography SC.223 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 15.126 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 15607), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0227 of each other at a top speed of 7.22, line up 84 times a period, and the computed loop closes to 2.8×10⁻²⁴.

Measured over one period

Period: 15.12557685
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0563
Closest approach: 0.02266
Top speed: 7.220
Path length: 67.836
Alignments per period: 84
Stability: unstable (|λ|max 1.6×10¹⁵)
Loop closure: 2.8×10⁻²⁴

Neighbours on the map

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