Atlas3,697 of 3,915

Choreography SC.339

From Simó (2001)

Choreography SC.339 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 17.18 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 51847), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0549 of each other at a top speed of 4.79, line up 114 times a period, and the computed loop closes to 3.6×10⁻²⁸.

Measured over one period

Period: 17.18044779
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0578
Closest approach: 0.05489
Top speed: 4.786
Path length: 78.800
Alignments per period: 114
Stability: unstable (|λ|max 5.2×10¹²)
Loop closure: 3.6×10⁻²⁸

Neighbours on the map

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