Atlas3,588 of 3,942

Choreography SC.180

From Simó (2001)

Choreography SC.180 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 13.974 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 20536), so a small nudge makes it unravel over a few periods. The bodies pass within 0.104 of each other at a top speed of 3.52, line up 54 times a period, and the computed loop closes to 2.9×10⁻²⁶.

Measured over one period

Period: 13.97350359
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.1214
Closest approach: 0.1037
Top speed: 3.517
Path length: 68.976
Alignments per period: 54
Topology: aaaaaaaabAbAbAbAbAbAbAbABBBBBBBB (free-group class, read from the drawing)
Stability: unstable (|λ|max 2.1×10¹⁸)
Loop closure: 2.9×10⁻²⁶

Neighbours on the map

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