Atlas3,763 of 3,942

Family NF.81

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

Family NF.81 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 31.846 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 31833), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00594 of each other at a top speed of 13, line up 84 times a period, and the computed loop closes to 1.1×10⁻²⁵.

Measured over one period

Period: 31.84563556
Masses: 1 : 1 : 1
Energy: -2.41107
Angular momentum: 0
Closest approach: 0.005937
Top speed: 13.01
Path length: 89.181
Alignments per period: 84
Topology: aabABABababABABababABABababABABabbaBAABababABBAb (free-group class)
Stability: unstable (|λ|max 31833)
Loop closure: 1.1×10⁻²⁵

Neighbours on the map

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