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Choreography SC.243

From Simó (2001)

Choreography SC.243 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 15.326 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 60676), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00367 of each other at a top speed of 16.6, line up 120 times a period, and the computed loop closes to 3.6×10⁻²⁷.

Measured over one period

Period: 15.32610775
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.69258
Closest approach: 0.003669
Top speed: 16.58
Path length: 65.768
Alignments per period: 120
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: unstable (|λ|max 6.1×10¹⁷)
Loop closure: 3.6×10⁻²⁷

Neighbours on the map

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