Atlas3,748 of 3,942

Family NF.35

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

Family NF.35 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 20.812 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 12862), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0134 of each other at a top speed of 8.77, line up 56 times a period, and the computed loop closes to 6.4×10⁻²⁶.

Measured over one period

Period: 20.81231258
Masses: 1 : 1 : 1
Energy: -2.43891
Angular momentum: 0
Closest approach: 0.01340
Top speed: 8.772
Path length: 60.303
Alignments per period: 56
Topology: aabABABabbaBAABabbaBABAbaabABBAb (free-group class)
Stability: unstable (|λ|max 12862)
Loop closure: 6.4×10⁻²⁶

Neighbours on the map

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