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Choreography SC.287

From Simó (2001)

Choreography SC.287 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 16.281 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 25244), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0608 of each other at a top speed of 4.25, line up 90 times a period, and the computed loop closes to 6.0×10⁻²⁸.

Measured over one period

Period: 16.28090881
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0819
Closest approach: 0.06082
Top speed: 4.248
Path length: 77.929
Alignments per period: 90
Stability: unstable (|λ|max 2.5×10¹⁴)
Loop closure: 6.0×10⁻²⁸

Neighbours on the map

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