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Choreography SC.337

From Simó (2001)

Choreography SC.337 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 16.869 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 12255), so a small nudge makes it unravel over a few periods. The bodies pass within 0.129 of each other at a top speed of 2.88, line up 72 times a period, and the computed loop closes to 7.0×10⁻²⁸.

Measured over one period

Period: 16.86917164
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.1278
Closest approach: 0.1291
Top speed: 2.883
Path length: 83.316
Alignments per period: 72
Stability: unstable (|λ|max 1.2×10¹²)
Loop closure: 7.0×10⁻²⁸

Neighbours on the map

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