Atlas3,824 of 3,942

Family NF.75

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

Family NF.75 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 64.471 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 1936), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000079 of each other at a top speed of 113, line up 76 times a period, and the computed loop closes to 1.7×10⁻²³.

Measured over one period

Period: 64.47106037
Masses: 1 : 1 : 1
Energy: -1.48541
Angular momentum: 0
Closest approach: 7.9×10⁻⁵
Top speed: 112.5
Path length: 173.73
Alignments per period: 76
Topology: abaBAbaBAbabABabABabABabABabABabABabABabABabABabAB (free-group class)
Stability: unstable (|λ|max 1936)
Loop closure: 1.7×10⁻²³

Neighbours on the map

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