Atlas20 of 3,915

Figure-8 V.12.A

From Šuvakov & Dmitrašinović (2013). Sequences of orbits from the Belgrade three-body gallery.

Figure-8 V.12.A is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 56.943 time units, published by Šuvakov & Dmitrašinović (2013). Three equal masses chase each other along a single figure-eight curve, the most famous choreography. It is unstable (largest Floquet multiplier 1009), so a small nudge makes it unravel over a few periods. The bodies pass within 0.21 of each other at a top speed of 2.29, line up 72 times a period, and the computed loop closes to 3.5×10⁻²⁸.

Measured over one period

Period: 56.94290690
Masses: 1 : 1 : 1
Energy: -1.55850
Angular momentum: 0
Closest approach: 0.2104
Top speed: 2.293
Path length: 160.40
Alignments per period: 72
Stability: unstable (|λ|max 1009)
Loop closure: 3.5×10⁻²⁸

Neighbours on the map

All Figure-8 orbits, the families of periodic three-body orbits, or the atlas map.