Atlas371 of 3,942

I.A.50

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.50 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 99.331 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 0.0000706 of each other at a top speed of 127, line up 166 times a period, and the computed loop closes to 2.3×10⁻²³.

Measured over one period

Period: 99.33126920
Masses: 1 : 1 : 0.75
Energy: -1.48425
Angular momentum: 0
Closest approach: 7.1×10⁻⁵
Top speed: 127.2
Path length: 242.24
Alignments per period: 166
Topology: abaBAbabABAbabABAbabABAbabABAbabABAbabABAbabABAbabABAbaBABabaBABabaBABabaBABabaBABabaBABabaBABabaBAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 2.3×10⁻²³

Neighbours on the map

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