Atlas3,568 of 3,942

Choreography SC.330

From Simó (2001)

Choreography SC.330 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 16.702 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 4.052799999999999e+21), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0496 of each other at a top speed of 4.69, line up 84 times a period, and the computed loop closes to 2.1×10⁻²⁵.

Measured over one period

Period: 16.70153508
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0033
Closest approach: 0.04963
Top speed: 4.690
Path length: 78.910
Alignments per period: 84
Topology: (aaaaabAbAbAbAbABBBBB)² (free-group class, read from the drawing)
Stability: unstable (|λ|max 4.1×10²¹)
Loop closure: 2.1×10⁻²⁵

Neighbours on the map

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