Atlas13 of 3,942

Figure-8 V.17.C

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

Figure-8 V.17.C is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 81.217 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 2.134), so a small nudge makes it unravel over a few periods. The bodies pass within 0.342 of each other at a top speed of 1.86, line up 102 times a period, and the computed loop closes to 1.2×10⁻²⁸.

Measured over one period

Period: 81.21673100
Masses: 1 : 1 : 1
Energy: -1.55201
Angular momentum: 0
Closest approach: 0.3422
Top speed: 1.865
Path length: 229.84
Alignments per period: 102
Topology: (abAB)¹⁷ (free-group class)
Stability: weakly unstable (|λ|max 2.134)
Loop closure: 1.2×10⁻²⁸

Neighbours on the map

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