Atlas3,440 of 3,915

Choreography SC.246

From Simó (2001)

Choreography SC.246 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 15.343 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 20361), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0711 of each other at a top speed of 3.7, line up 72 times a period, and the computed loop closes to 5.8×10⁻²⁶.

Measured over one period

Period: 15.34281369
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0848
Closest approach: 0.07106
Top speed: 3.697
Path length: 74.573
Alignments per period: 72
Stability: unstable (|λ|max 2.0×10¹⁹)
Loop closure: 5.8×10⁻²⁶

Neighbours on the map

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