Atlas3,800 of 3,942

Family NF.13

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

Family NF.13 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 18.909 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 1771), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00738 of each other at a top speed of 12, line up 32 times a period, and the computed loop closes to 3.5×10⁻²⁶.

Measured over one period

Period: 18.90898054
Masses: 1 : 1 : 1
Energy: -1.83484
Angular momentum: 0
Closest approach: 0.007383
Top speed: 11.97
Path length: 50.888
Alignments per period: 32
Topology: aabABabAABabAbABabbAB (free-group class)
Stability: unstable (|λ|max 1771)
Loop closure: 3.5×10⁻²⁶

Neighbours on the map

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