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Choreography SC.2

From Simó (2001)

Choreography SC.2 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 1.5564 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 412), so a small nudge makes it unravel over a few periods. The bodies pass within 0.186 of each other at a top speed of 2.46, line up 6 times a period, and the computed loop closes to 1.1×10⁻³⁰.

Measured over one period

Period: 1.556414403
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.1239
Closest approach: 0.1865
Top speed: 2.457
Path length: 7.4898
Alignments per period: 6
Stability: unstable (|λ|max 4120)
Loop closure: 1.1×10⁻³⁰

Neighbours on the map

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