Atlas3,517 of 3,942

Choreography SC.335

From Simó (2001)

Choreography SC.335 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 16.843 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 76949), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0578 of each other at a top speed of 4.62, line up 66 times a period, and the computed loop closes to 5.6×10⁻²⁸.

Measured over one period

Period: 16.84319927
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.1034
Closest approach: 0.05777
Top speed: 4.616
Path length: 81.944
Alignments per period: 66
Topology: (aaaaabAbAbAbAbABBBBB)² (free-group class, read from the drawing)
Stability: unstable (|λ|max 7.7×10¹⁶)
Loop closure: 5.6×10⁻²⁸

Neighbours on the map

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