Atlas3,753 of 3,942

Family NF.64

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

Family NF.64 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 40.862 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 2612), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000199 of each other at a top speed of 71, line up 72 times a period, and the computed loop closes to 6.9×10⁻²⁵.

Measured over one period

Period: 40.86178377
Masses: 1 : 1 : 1
Energy: -1.90957
Angular momentum: 0
Closest approach: 2.0×10⁻⁴
Top speed: 70.99
Path length: 115.36
Alignments per period: 72
Topology: (ababABAbaBABabABAbaBAB)² (free-group class)
Stability: unstable (|λ|max 2612)
Loop closure: 6.9×10⁻²⁵

Neighbours on the map

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