Atlas3,759 of 3,942

Family NF.79

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

Family NF.79 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 32.814 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 22.53), so a small nudge makes it unravel over a few periods. The bodies pass within 0.013 of each other at a top speed of 8.81, line up 84 times a period, and the computed loop closes to 3.4×10⁻²⁷.

Measured over one period

Period: 32.81422681
Masses: 1 : 1 : 1
Energy: -2.36126
Angular momentum: 0
Closest approach: 0.01304
Top speed: 8.814
Path length: 92.816
Alignments per period: 84
Topology: aabABABababABABabbaBAABabbaBABAbabaBABAbaabABBAb (free-group class)
Stability: unstable (|λ|max 22.53)
Loop closure: 3.4×10⁻²⁷

Neighbours on the map

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