Atlas455 of 3,942

I.A.45

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.45 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 98.638 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 0.000158 of each other at a top speed of 85.1, line up 150 times a period, and the computed loop closes to 6.3×10⁻²⁴.

Measured over one period

Period: 98.63760626
Masses: 1 : 1 : 0.75
Energy: -1.40846
Angular momentum: 0
Closest approach: 1.6×10⁻⁴
Top speed: 85.10
Path length: 243.50
Alignments per period: 150
Topology: abaBAbabABAbabABabaBABabABAbabABabaBABabaBAbabABAbaBABabaBABabABAbabABabaBABabABAbabABAbaBAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 6.3×10⁻²⁴

Neighbours on the map

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