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Choreography SC.63

From Simó (2001)

Choreography SC.63 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 9.2766 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 31911), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0762 of each other at a top speed of 4.35, line up 48 times a period, and the computed loop closes to 8.0×10⁻²⁹.

Measured over one period

Period: 9.276567179
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.90064
Closest approach: 0.07620
Top speed: 4.354
Path length: 43.830
Alignments per period: 48
Stability: unstable (|λ|max 3.2×10¹⁴)
Loop closure: 8.0×10⁻²⁹

Neighbours on the map

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