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Choreography SC.173

From Simó (2001)

Choreography SC.173 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 13.943 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 62833999999999991808), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0515 of each other at a top speed of 4.92, line up 54 times a period, and the computed loop closes to 6.8×10⁻²⁵.

Measured over one period

Period: 13.94276878
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.1050
Closest approach: 0.05152
Top speed: 4.925
Path length: 67.639
Alignments per period: 54
Stability: unstable (|λ|max 6.3×10¹⁹)
Loop closure: 6.8×10⁻²⁵

Neighbours on the map

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