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Choreography SC.236

From Simó (2001)

Choreography SC.236 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 15.27 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 23772), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0252 of each other at a top speed of 6.85, line up 66 times a period, and the computed loop closes to 1.1×10⁻²⁵.

Measured over one period

Period: 15.27038645
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0817
Closest approach: 0.02520
Top speed: 6.849
Path length: 72.739
Alignments per period: 66
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: unstable (|λ|max 2.4×10¹⁵)
Loop closure: 1.1×10⁻²⁵

Neighbours on the map

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