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Choreography SC.68

From Simó (2001)

Choreography SC.68 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 9.7318 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 62307), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0476 of each other at a top speed of 5.07, line up 66 times a period, and the computed loop closes to 1.7×10⁻²⁹.

Measured over one period

Period: 9.731804205
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0293
Closest approach: 0.04758
Top speed: 5.068
Path length: 44.473
Alignments per period: 66
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: unstable (|λ|max 6.2×10⁵)
Loop closure: 1.7×10⁻²⁹

Neighbours on the map

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