Atlas3,802 of 3,942

Family NF.20

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

Family NF.20 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 50.449 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 759.5), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0129 of each other at a top speed of 8.79, line up 42 times a period, and the computed loop closes to 1.6×10⁻²⁷.

Measured over one period

Period: 50.44933923
Masses: 1 : 1 : 1
Energy: -1.16402
Angular momentum: 0
Closest approach: 0.01294
Top speed: 8.789
Path length: 114.37
Alignments per period: 42
Topology: abaBAbabABabaBAbabABAbaBAB (free-group class)
Stability: unstable (|λ|max 759.5)
Loop closure: 1.6×10⁻²⁷

Neighbours on the map

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