Atlas3,815 of 3,942

Family NF.38

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

Family NF.38 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 67.037 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 5436), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0355 of each other at a top speed of 5.41, line up 56 times a period, and the computed loop closes to 2.0×10⁻²⁷.

Measured over one period

Period: 67.03650614
Masses: 1 : 1 : 1
Energy: -1.15913
Angular momentum: 0
Closest approach: 0.03547
Top speed: 5.414
Path length: 149.94
Alignments per period: 56
Topology: ababABAbaBABabaBABabABAbabABAbaBAB (free-group class)
Stability: unstable (|λ|max 5436)
Loop closure: 2.0×10⁻²⁷

Neighbours on the map

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