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Choreography SC.46

From Simó (2001)

Choreography SC.46 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 7.535 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 19943), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0218 of each other at a top speed of 7.28, line up 30 times a period, and the computed loop closes to 5.3×10⁻²⁸.

Measured over one period

Period: 7.534966717
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0406
Closest approach: 0.02182
Top speed: 7.275
Path length: 34.866
Alignments per period: 30
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: unstable (|λ|max 2.0×10¹²)
Loop closure: 5.3×10⁻²⁸

Neighbours on the map

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