Atlas3,726 of 3,942

Family NF.45

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

Family NF.45 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 65.24 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 5092), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000172 of each other at a top speed of 76.3, line up 62 times a period, and the computed loop closes to 1.1×10⁻²².

Measured over one period

Period: 65.23987027
Masses: 1 : 1 : 1
Energy: -1.23340
Angular momentum: 0
Closest approach: 1.7×10⁻⁴
Top speed: 76.29
Path length: 136.20
Alignments per period: 62
Topology: ababABababABABabaBABAbabABAB (free-group class)
Stability: unstable (|λ|max 5092)
Loop closure: 1.1×10⁻²²

Neighbours on the map

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