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Choreography SC.48

From Simó (2001)

Choreography SC.48 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 8.0548 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 11649), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0177 of each other at a top speed of 7.56, line up 48 times a period, and the computed loop closes to 2.9×10⁻²⁸.

Measured over one period

Period: 8.054805763
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.87191
Closest approach: 0.01769
Top speed: 7.562
Path length: 37.304
Alignments per period: 48
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: unstable (|λ|max 1.2×10¹³)
Loop closure: 2.9×10⁻²⁸

Neighbours on the map

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