Atlas3,730 of 3,942

Family NF.12

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

Family NF.12 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 18.713 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 306.1), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0135 of each other at a top speed of 8.99, line up 32 times a period, and the computed loop closes to 8.0×10⁻²⁵.

Measured over one period

Period: 18.71345759
Masses: 1 : 1 : 1
Energy: -1.84745
Angular momentum: 0
Closest approach: 0.01354
Top speed: 8.988
Path length: 50.938
Alignments per period: 32
Topology: aabABabAABabAbABabbAB (free-group class)
Stability: unstable (|λ|max 306.1)
Loop closure: 8.0×10⁻²⁵

Neighbours on the map

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