Atlas3,750 of 3,942

Family NF.42

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

Family NF.42 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 56.196 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 19.75), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000141 of each other at a top speed of 267, line up 60 times a period, and the computed loop closes to 5.6×10⁻²².

Measured over one period

Period: 56.19639452
Masses: 1 : 1 : 1
Energy: -1.35674
Angular momentum: 0
Closest approach: 1.4×10⁻⁵
Top speed: 266.5
Path length: 133.84
Alignments per period: 60
Topology: ababABabaBABAbabABababABAbabABabaBAB (free-group class)
Stability: unstable (|λ|max 19.75)
Loop closure: 5.6×10⁻²²

Neighbours on the map

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