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Choreography SC.299

From Simó (2001)

Choreography SC.299 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 16.356 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 2.3211e+24), so a small nudge makes it unravel over a few periods. The bodies pass within 0.072 of each other at a top speed of 4.14, line up 54 times a period, and the computed loop closes to 3.3×10⁻²⁵.

Measured over one period

Period: 16.35620793
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0640
Closest approach: 0.07198
Top speed: 4.145
Path length: 79.306
Alignments per period: 54
Stability: unstable (|λ|max 2.3×10²⁴)
Loop closure: 3.3×10⁻²⁵

Neighbours on the map

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