Atlas3,561 of 3,915

Choreography SC.257

From Simó (2001)

Choreography SC.257 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 15.555 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 19158), so a small nudge makes it unravel over a few periods. The bodies pass within 0.133 of each other at a top speed of 3.06, line up 60 times a period, and the computed loop closes to 1.4×10⁻²⁸.

Measured over one period

Period: 15.55479200
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.1309
Closest approach: 0.1334
Top speed: 3.062
Path length: 77.033
Alignments per period: 60
Stability: unstable (|λ|max 1.9×10¹⁵)
Loop closure: 1.4×10⁻²⁸

Neighbours on the map

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