Atlas3,648 of 3,942

Choreography SC.12

From Simó (2001)

Choreography SC.12 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 5.2463 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 78625), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0958 of each other at a top speed of 3.72, line up 18 times a period, and the computed loop closes to 7.2×10⁻²⁹.

Measured over one period

Period: 5.246329241
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0868
Closest approach: 0.09584
Top speed: 3.724
Path length: 25.654
Alignments per period: 18
Topology: aabAbABB (free-group class, read from the drawing)
Stability: unstable (|λ|max 7.9×10¹⁰)
Loop closure: 7.2×10⁻²⁹

Neighbours on the map

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