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Choreography SC.198

From Simó (2001)

Choreography SC.198 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 14.238 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 8.8749e+25), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0695 of each other at a top speed of 4.25, line up 48 times a period, and the computed loop closes to 1.3×10⁻¹⁰.

Measured over one period

Period: 14.23791257
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0812
Closest approach: 0.06947
Top speed: 4.251
Path length: 68.882
Alignments per period: 48
Topology: aaabAbAbABBB (free-group class, read from the drawing, shape period T/2)
Stability: unstable (|λ|max 8.9×10²⁵)
Loop closure: 1.3×10⁻¹⁰

Neighbours on the map

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