Atlas3,397 of 3,942

Choreography SC.303

From Simó (2001)

Choreography SC.303 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 16.413 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 16706), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0612 of each other at a top speed of 4.81, line up 78 times a period, and the computed loop closes to 3.2×10⁻²⁷.

Measured over one period

Period: 16.41276389
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0558
Closest approach: 0.06125
Top speed: 4.810
Path length: 78.198
Alignments per period: 78
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: unstable (|λ|max 1.7×10¹⁶)
Loop closure: 3.2×10⁻²⁷

Neighbours on the map

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