Atlas3,810 of 3,942

Family NF.68

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

Family NF.68 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 57.104 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 401), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000942 of each other at a top speed of 32.6, line up 72 times a period, and the computed loop closes to 6.9×10⁻²⁵.

Measured over one period

Period: 57.10412760
Masses: 1 : 1 : 1
Energy: -1.55162
Angular momentum: 0
Closest approach: 9.4×10⁻⁴
Top speed: 32.64
Path length: 148.43
Alignments per period: 72
Topology: (aaBAbaBAbaBAbaBAbbABabAB)² (free-group class)
Stability: unstable (|λ|max 401.0)
Loop closure: 6.9×10⁻²⁵

Neighbours on the map

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