Atlas3,390 of 3,942

Choreography SC.227

From Simó (2001)

Choreography SC.227 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 15.191 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 35551), so a small nudge makes it unravel over a few periods. The bodies pass within 0.077 of each other at a top speed of 4.13, line up 66 times a period, and the computed loop closes to 2.8×10⁻²⁶.

Measured over one period

Period: 15.19105715
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0671
Closest approach: 0.07702
Top speed: 4.128
Path length: 72.962
Alignments per period: 66
Topology: aaaaaaaaaabAbAbAbAbAbAbAbAbAbABBBBBBBBBB (free-group class, read from the drawing)
Stability: unstable (|λ|max 3.6×10¹⁸)
Loop closure: 2.8×10⁻²⁶

Neighbours on the map

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