Atlas22 of 3,942

Figure-8 V.4.Aβ

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

Figure-8 V.4.Aβ is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 18.142 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 weakly unstable (largest Floquet multiplier 3.831), so a small nudge makes it unravel over a few periods. The bodies pass within 0.228 of each other at a top speed of 2.27, line up 24 times a period, and the computed loop closes to 5.1×10⁻³⁰.

Measured over one period

Period: 18.14210457
Masses: 1 : 1 : 1
Energy: -1.60557
Angular momentum: 0
Closest approach: 0.2281
Top speed: 2.265
Path length: 51.582
Alignments per period: 24
Topology: (abAB)⁴ (free-group class)
Stability: weakly unstable (|λ|max 3.831)
Loop closure: 5.1×10⁻³⁰

Neighbours on the map

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