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Choreography SC.40

From Simó (2001)

Choreography SC.40 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 7.4428 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 95308), so a small nudge makes it unravel over a few periods. The bodies pass within 0.103 of each other at a top speed of 3.6, line up 30 times a period, and the computed loop closes to 2.7×10⁻²⁷.

Measured over one period

Period: 7.442795522
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.96162
Closest approach: 0.1033
Top speed: 3.596
Path length: 35.602
Alignments per period: 30
Stability: unstable (|λ|max 9.5×10¹⁶)
Loop closure: 2.7×10⁻²⁷

Neighbours on the map

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