Atlas329 of 3,942

I.A.139

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.139 m₃ = 0.5 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 0.5 that return to their starting positions and velocities every 185.5 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 unstable (largest Floquet multiplier 341.1), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000213 of each other at a top speed of 79, line up 302 times a period, and the computed loop closes to 2.6×10⁻²³.

Measured over one period

Period: 185.5037128
Masses: 1 : 1 : 0.5
Energy: -1.14421
Angular momentum: 0
Closest approach: 2.1×10⁻⁴
Top speed: 79.01
Path length: 447.82
Alignments per period: 302
Topology: ababAbaBABaBAbabAbaBABaBABabAbabABabABabABabABabABabABabABabABabABabaBabABAbABAbaBabaBAbABAbaBababAbABABaBAbabAbaBABaBAbabAbabABaBABabABabABabABabABabABabABabABabABabABAbABabaBabaBAbABAbaBabaBAbABABaB (free-group class)
Stability: unstable (|λ|max 341.1)
Loop closure: 2.6×10⁻²³

Neighbours on the map

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