Atlas16 of 3,942

Figure-8 V.7.A

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

Figure-8 V.7.A is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 32.849 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 4.040), so a small nudge makes it unravel over a few periods. The bodies pass within 0.309 of each other at a top speed of 1.96, line up 42 times a period, and the computed loop closes to 1.1×10⁻²⁹.

Measured over one period

Period: 32.84907099
Masses: 1 : 1 : 1
Energy: -1.57045
Angular momentum: 0
Closest approach: 0.3094
Top speed: 1.960
Path length: 93.186
Alignments per period: 42
Topology: (abAB)⁷ (free-group class)
Stability: weakly unstable (|λ|max 4.040)
Loop closure: 1.1×10⁻²⁹

Neighbours on the map

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