Atlas3,790 of 3,942

Family NF.58

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

Family NF.58 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 51.842 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 4417), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00808 of each other at a top speed of 11.2, line up 66 times a period, and the computed loop closes to 8.4×10⁻²⁵.

Measured over one period

Period: 51.84237064
Masses: 1 : 1 : 1
Energy: -1.56218
Angular momentum: 0
Closest approach: 0.008079
Top speed: 11.20
Path length: 134.64
Alignments per period: 66
Topology: aaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbbABabAB (free-group class)
Stability: unstable (|λ|max 4417)
Loop closure: 8.4×10⁻²⁵

Neighbours on the map

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