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Choreography SC.285

From Simó (2001)

Choreography SC.285 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 16.269 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 75309), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0453 of each other at a top speed of 4.98, line up 90 times a period, and the computed loop closes to 1.6×10⁻²⁷.

Measured over one period

Period: 16.26889266
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0623
Closest approach: 0.04534
Top speed: 4.981
Path length: 77.278
Alignments per period: 90
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: unstable (|λ|max 7.5×10¹³)
Loop closure: 1.6×10⁻²⁷

Neighbours on the map

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