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Choreography SC.5

From Simó (2001)

Choreography SC.5 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 4.5239 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 22444), so a small nudge makes it unravel over a few periods. The bodies pass within 0.107 of each other at a top speed of 3.57, line up 12 times a period, and the computed loop closes to 9.2×10⁻³⁰.

Measured over one period

Period: 4.523865884
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.99432
Closest approach: 0.1070
Top speed: 3.569
Path length: 22.233
Alignments per period: 12
Stability: unstable (|λ|max 2.2×10¹²)
Loop closure: 9.2×10⁻³⁰

Neighbours on the map

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