Atlas3,636 of 3,942

Choreography SC.286

From Simó (2001)

Choreography SC.286 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 16.275 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 11418), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0261 of each other at a top speed of 6.55, line up 78 times a period, and the computed loop closes to 1.4×10⁻²⁷.

Measured over one period

Period: 16.27475083
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0312
Closest approach: 0.02612
Top speed: 6.552
Path length: 75.563
Alignments per period: 78
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: unstable (|λ|max 1.1×10¹⁷)
Loop closure: 1.4×10⁻²⁷

Neighbours on the map

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