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Choreography SC.307

From Simó (2001)

Choreography SC.307 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 16.443 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 96481), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0564 of each other at a top speed of 4.92, line up 120 times a period, and the computed loop closes to 4.7×10⁻²⁷.

Measured over one period

Period: 16.44292266
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.83613
Closest approach: 0.05641
Top speed: 4.922
Path length: 74.628
Alignments per period: 120
Stability: unstable (|λ|max 9.6×10¹⁷)
Loop closure: 4.7×10⁻²⁷

Neighbours on the map

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