Atlas3,405 of 3,915

Choreography SC.170

From Simó (2001)

Choreography SC.170 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 13.932 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 24699), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0748 of each other at a top speed of 4, line up 54 times a period, and the computed loop closes to 5.9×10⁻²⁸.

Measured over one period

Period: 13.93218435
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0560
Closest approach: 0.07479
Top speed: 3.999
Path length: 67.236
Alignments per period: 54
Stability: unstable (|λ|max 2.5×10¹⁵)
Loop closure: 5.9×10⁻²⁸

Neighbours on the map

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