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Choreography SC.203

From Simó (2001)

Choreography SC.203 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 14.834 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 1.9414e+25), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0562 of each other at a top speed of 4.8, line up 54 times a period, and the computed loop closes to 1.5×10⁻²⁴.

Measured over one period

Period: 14.83384750
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0825
Closest approach: 0.05617
Top speed: 4.804
Path length: 72.342
Alignments per period: 54
Topology: aaaaaabAbAbAbAbAbABBBBBB (free-group class, read from the drawing)
Stability: unstable (|λ|max 1.9×10²⁵)
Loop closure: 1.5×10⁻²⁴

Neighbours on the map

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