Atlas3,740 of 3,942

Family NF.34

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

Family NF.34 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 20.915 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 16924), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0113 of each other at a top speed of 9.48, line up 56 times a period, and the computed loop closes to 2.1×10⁻²⁵.

Measured over one period

Period: 20.91473163
Masses: 1 : 1 : 1
Energy: -2.43045
Angular momentum: 0
Closest approach: 0.01132
Top speed: 9.480
Path length: 58.031
Alignments per period: 56
Topology: aabABABabbaBAABabbaBABAbaabABBAb (free-group class)
Stability: unstable (|λ|max 16924)
Loop closure: 2.1×10⁻²⁵

Neighbours on the map

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