Atlas416 of 3,942

I.A.73

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.73 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 133.85 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 0.0000697 of each other at a top speed of 128, line up 210 times a period, and the computed loop closes to 1.4×10⁻²³.

Measured over one period

Period: 133.8460649
Masses: 1 : 1 : 0.75
Energy: -1.43303
Angular momentum: 0
Closest approach: 7.0×10⁻⁵
Top speed: 128.0
Path length: 329.49
Alignments per period: 210
Topology: abaBAbabABAbabABabaBABabaBABabABAbabABAbabABabaBABabaBAbabABAbabABAbaBABabaBABabABAbabABAbabABabaBABabaBABabABAbabABAbaBABabaBAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 1.4×10⁻²³

Neighbours on the map

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