Atlas3,786 of 3,942

Family NF.69

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

Family NF.69 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 54.411 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 10343), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000201 of each other at a top speed of 223, line up 72 times a period, and the computed loop closes to 2.2×10⁻²².

Measured over one period

Period: 54.41105975
Masses: 1 : 1 : 1
Energy: -1.60279
Angular momentum: 0
Closest approach: 2.0×10⁻⁵
Top speed: 223.3
Path length: 141.91
Alignments per period: 72
Topology: aaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbbABabAB (free-group class)
Stability: unstable (|λ|max 10343)
Loop closure: 2.2×10⁻²²

Neighbours on the map

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