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Choreography SC.45

From Simó (2001)

Choreography SC.45 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 7.4921 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 2393), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0481 of each other at a top speed of 5.09, line up 30 times a period, and the computed loop closes to 6.1×10⁻²⁸.

Measured over one period

Period: 7.492077228
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.1156
Closest approach: 0.04814
Top speed: 5.091
Path length: 35.871
Alignments per period: 30
Stability: unstable (|λ|max 2.4×10¹²)
Loop closure: 6.1×10⁻²⁸

Neighbours on the map

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