Atlas14 of 3,942

Figure-8 V.17.A

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

Figure-8 V.17.A is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 80.323 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 1.454), so a small nudge makes it unravel over a few periods. The bodies pass within 0.333 of each other at a top speed of 1.89, line up 102 times a period, and the computed loop closes to 2.0×10⁻²⁸.

Measured over one period

Period: 80.32257601
Masses: 1 : 1 : 1
Energy: -1.56351
Angular momentum: 0
Closest approach: 0.3325
Top speed: 1.888
Path length: 227.75
Alignments per period: 102
Topology: (abAB)¹⁷ (free-group class)
Stability: weakly unstable (|λ|max 1.454)
Loop closure: 2.0×10⁻²⁸

Neighbours on the map

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