Atlas3,819 of 3,942

Family NF.84

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

Family NF.84 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 58.129 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 6698), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00202 of each other at a top speed of 22.3, line up 82 times a period, and the computed loop closes to 4.9×10⁻²⁵.

Measured over one period

Period: 58.12897751
Masses: 1 : 1 : 1
Energy: -1.64434
Angular momentum: 0
Closest approach: 0.002020
Top speed: 22.32
Path length: 155.07
Alignments per period: 82
Topology: ababABAbaBABabaBAbabABAbaBABababABAbaBABabABAbaBAB (free-group class)
Stability: unstable (|λ|max 6698)
Loop closure: 4.9×10⁻²⁵

Neighbours on the map

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