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Choreography SC.105

From Simó (2001)

Choreography SC.105 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 11.572 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 62509), so a small nudge makes it unravel over a few periods. The bodies pass within 0.067 of each other at a top speed of 4.55, line up 54 times a period, and the computed loop closes to 6.9×10⁻²⁹.

Measured over one period

Period: 11.57179595
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0839
Closest approach: 0.06701
Top speed: 4.552
Path length: 55.670
Alignments per period: 54
Stability: unstable (|λ|max 6.3×10¹³)
Loop closure: 6.9×10⁻²⁹

Neighbours on the map

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