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Choreography SC.58

From Simó (2001)

Choreography SC.58 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 8.8757 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 96243), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00447 of each other at a top speed of 15.7, line up 30 times a period, and the computed loop closes to 4.6×10⁻²⁴.

Measured over one period

Period: 8.875679031
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.99459
Closest approach: 0.004472
Top speed: 15.67
Path length: 41.111
Alignments per period: 30
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: unstable (|λ|max 9.6×10¹⁷)
Loop closure: 4.6×10⁻²⁴

Neighbours on the map

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