Atlas3,734 of 3,942

Family NF.21

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

Family NF.21 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 39.207 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 2798), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000155 of each other at a top speed of 80.5, line up 44 times a period, and the computed loop closes to 2.7×10⁻²³.

Measured over one period

Period: 39.20675147
Masses: 1 : 1 : 1
Energy: -1.39607
Angular momentum: 0
Closest approach: 1.5×10⁻⁴
Top speed: 80.46
Path length: 92.948
Alignments per period: 44
Topology: ababABababABAbabABABabaBAB (free-group class)
Stability: unstable (|λ|max 2798)
Loop closure: 2.7×10⁻²³

Neighbours on the map

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