Atlas430 of 3,942

I.A.42

m₃ = 2

From Li, Jing & Liao (2018)

I.A.42 m₃ = 2 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 2 that return to their starting positions and velocities every 126.12 time units, published by Li, Jing & Liao (2018). Class I.A orbits found with Liao’s clean numerical simulation method, for a third body of varying mass. It is weakly unstable (largest Floquet multiplier 1.501), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000166 of each other at a top speed of 127, line up 334 times a period, and the computed loop closes to 3.9×10⁻²³.

Measured over one period

Period: 126.1180060
Masses: 1 : 1 : 2
Energy: -3.91317
Angular momentum: 0
Closest approach: 1.7×10⁻⁴
Top speed: 126.7
Path length: 398.91
Alignments per period: 334
Topology: ababababABABABAbababaBABABABabababaBABABABabababaBABABABabababaBABABABabababaBABABAbabababABABABABabababaBABABAbabababABABABAbabababABABABAbabababABABABAbabababABABABAbababaBABABAB (free-group class)
Stability: weakly unstable (|λ|max 1.501)
Loop closure: 3.9×10⁻²³

Neighbours on the map

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