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Family NF.30

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

Family NF.30 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 64.029 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 4424), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000161 of each other at a top speed of 78.8, line up 52 times a period, and the computed loop closes to 5.4×10⁻²³.

Measured over one period

Period: 64.02864889
Masses: 1 : 1 : 1
Energy: -1.09809
Angular momentum: 0
Closest approach: 1.6×10⁻⁴
Top speed: 78.77
Path length: 125.67
Alignments per period: 52
Topology: aaabaBABAbabABABabaBABAbabbbAB (free-group class)
Stability: unstable (|λ|max 4424)
Loop closure: 5.4×10⁻²³

Neighbours on the map

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