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Choreography SC.317

From Simó (2001)

Choreography SC.317 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 16.52 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 42109), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0283 of each other at a top speed of 6.49, line up 78 times a period, and the computed loop closes to 4.3×10⁻²⁵.

Measured over one period

Period: 16.52021756
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0883
Closest approach: 0.02825
Top speed: 6.489
Path length: 79.076
Alignments per period: 78
Stability: unstable (|λ|max 4.2×10¹⁷)
Loop closure: 4.3×10⁻²⁵

Neighbours on the map

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