Atlas3,826 of 3,942

Family NF.108

From Hristov, Hristova, Puzynin, Puzynina, Sharipov & Tukhliev (2022)

Family NF.108 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 54.201 time units, published by Hristov, Hristova, Puzynin, Puzynina, Sharipov & Tukhliev (2022). Orbits from topological families that no earlier catalogue contained; all of them unstable. It is unstable (largest Floquet multiplier 466.9), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00118 of each other at a top speed of 29.1, line up 100 times a period, and the computed loop closes to 1.1×10⁻²⁵.

Measured over one period

Period: 54.20082265
Masses: 1 : 1 : 1
Energy: -1.95382
Angular momentum: 0
Closest approach: 0.001179
Top speed: 29.15
Path length: 154.66
Alignments per period: 100
Topology: ababABababABAbabABAbabABAbabABabaBABAbabABabaBABabaBABabaBAB (free-group class)
Stability: unstable (|λ|max 466.9)
Loop closure: 1.1×10⁻²⁵

Neighbours on the map

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