Atlas443 of 3,942

I.A.90

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.90 m₃ = 0.75 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 0.75 that return to their starting positions and velocities every 128.2 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 linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.0000561 of each other at a top speed of 143, line up 290 times a period, and the computed loop closes to 1.7×10⁻²³.

Measured over one period

Period: 128.1965968
Masses: 1 : 1 : 0.75
Energy: -1.82499
Angular momentum: 0
Closest approach: 5.6×10⁻⁵
Top speed: 142.8
Path length: 339.74
Alignments per period: 290
Topology: ababAbabaBABabABABabABAbabABababABabaBABabABABabABAbabaBababABAbaBABAbaBABabaBAbabaBAbabABABaBABAbabABababABabaBABabABABabABAbabABababABabaBABAbABABabaBAbabaBAbabABAbaBABAbaBAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 1.7×10⁻²³

Neighbours on the map

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