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Choreography SC.345

From Simó (2001)

Choreography SC.345 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 17.298 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 65857999999999991808), so a small nudge makes it unravel over a few periods. The bodies pass within 0.017 of each other at a top speed of 8.37, line up 90 times a period, and the computed loop closes to 1.2×10⁻²⁴.

Measured over one period

Period: 17.29818337
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.99024
Closest approach: 0.01704
Top speed: 8.365
Path length: 77.640
Alignments per period: 90
Stability: unstable (|λ|max 6.6×10¹⁹)
Loop closure: 1.2×10⁻²⁴

Neighbours on the map

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