Atlas21 of 3,942

Figure-8 V.11.A

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

Figure-8 V.11.A is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 53.621 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 4.234), so a small nudge makes it unravel over a few periods. The bodies pass within 0.282 of each other at a top speed of 1.99, line up 66 times a period, and the computed loop closes to 2.0×10⁻²⁹.

Measured over one period

Period: 53.62058600
Masses: 1 : 1 : 1
Energy: -1.53111
Angular momentum: 0
Closest approach: 0.2818
Top speed: 1.988
Path length: 151.02
Alignments per period: 66
Topology: (abAB)¹¹ (free-group class)
Stability: weakly unstable (|λ|max 4.234)
Loop closure: 2.0×10⁻²⁹

Neighbours on the map

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