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Choreography SC.327

From Simó (2001)

Choreography SC.327 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 16.585 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 79105), so a small nudge makes it unravel over a few periods. The bodies pass within 0.135 of each other at a top speed of 3.25, line up 120 times a period, and the computed loop closes to 2.3×10⁻²⁸.

Measured over one period

Period: 16.58536075
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0672
Closest approach: 0.1354
Top speed: 3.252
Path length: 80.343
Alignments per period: 120
Stability: unstable (|λ|max 7.9×10¹²)
Loop closure: 2.3×10⁻²⁸

Neighbours on the map

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