Atlas3,635 of 3,942

Choreography SC.166

From Simó (2001)

Choreography SC.166 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 13.875 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 96141), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0739 of each other at a top speed of 3.85, line up 78 times a period, and the computed loop closes to 1.2×10⁻²⁵.

Measured over one period

Period: 13.87498598
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0666
Closest approach: 0.07393
Top speed: 3.849
Path length: 65.210
Alignments per period: 78
Topology: aaaaaaaabAbAbAbAbAbAbAbABBBBBBBB (free-group class, read from the drawing)
Stability: unstable (|λ|max 9.6×10¹⁹)
Loop closure: 1.2×10⁻²⁵

Neighbours on the map

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