Atlas3,831 of 3,942

Family NF.59

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

Family NF.59 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 65.447 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 3005), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00692 of each other at a top speed of 12, line up 68 times a period, and the computed loop closes to 2.4×10⁻²⁶.

Measured over one period

Period: 65.44687910
Masses: 1 : 1 : 1
Energy: -1.34726
Angular momentum: 0
Closest approach: 0.006923
Top speed: 12.03
Path length: 160.58
Alignments per period: 68
Topology: abaBAbabABabaBABabABAbabABabaBAbabABAbaBAB (free-group class)
Stability: unstable (|λ|max 3005)
Loop closure: 2.4×10⁻²⁶

Neighbours on the map

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