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Choreography SC.241

From Simó (2001)

Choreography SC.241 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 15.286 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 41064), so a small nudge makes it unravel over a few periods. The bodies pass within 0.058 of each other at a top speed of 4.86, line up 108 times a period, and the computed loop closes to 4.3×10⁻²⁸.

Measured over one period

Period: 15.28586634
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.84311
Closest approach: 0.05805
Top speed: 4.862
Path length: 69.700
Alignments per period: 108
Stability: unstable (|λ|max 4.1×10¹⁷)
Loop closure: 4.3×10⁻²⁸

Neighbours on the map

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