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Choreography SC.119

From Simó (2001)

Choreography SC.119 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 12.501 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 34445), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0648 of each other at a top speed of 4.08, line up 78 times a period, and the computed loop closes to 1.8×10⁻²⁸.

Measured over one period

Period: 12.50146814
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0756
Closest approach: 0.06482
Top speed: 4.085
Path length: 58.796
Alignments per period: 78
Stability: unstable (|λ|max 3.4×10¹²)
Loop closure: 1.8×10⁻²⁸

Neighbours on the map

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