Atlas27 of 3,942

Figure-8 V.8.A

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

Figure-8 V.8.A is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 80.249 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 2176), so a small nudge makes it unravel over a few periods. The bodies pass within 0.351 of each other at a top speed of 1.82, line up 48 times a period, and the computed loop closes to 6.1×10⁻²⁷.

Measured over one period

Period: 80.24867668
Masses: 1 : 1 : 1
Energy: -0.945799
Angular momentum: 0
Closest approach: 0.3513
Top speed: 1.816
Path length: 174.18
Alignments per period: 48
Topology: (abAB)⁸ (free-group class)
Stability: unstable (|λ|max 2176)
Loop closure: 6.1×10⁻²⁷

Neighbours on the map

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