Atlas3,567 of 3,915

Choreography SC.247

From Simó (2001)

Choreography SC.247 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 15.411 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 39463), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0565 of each other at a top speed of 4.18, line up 72 times a period, and the computed loop closes to 2.3×10⁻²⁶.

Measured over one period

Period: 15.41119243
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0400
Closest approach: 0.05650
Top speed: 4.185
Path length: 74.006
Alignments per period: 72
Stability: unstable (|λ|max 3.9×10¹⁹)
Loop closure: 2.3×10⁻²⁶

Neighbours on the map

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