Atlas339 of 3,942

I.A.83

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.83 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 157.86 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 0.0000256 of each other at a top speed of 211, line up 266 times a period, and the computed loop closes to 3.9×10⁻²¹.

Measured over one period

Period: 157.8578915
Masses: 1 : 1 : 0.75
Energy: -1.49109
Angular momentum: 0
Closest approach: 2.6×10⁻⁵
Top speed: 211.3
Path length: 384.27
Alignments per period: 266
Topology: abaBAbabABAbabABAbabABAbabABAbabABAbabABAbabABAbabABAbabABAbabABAbabABAbabABAbabABAbaBABabaBABabaBABabaBABabaBABabaBABabaBABabaBABabaBABabaBABabaBABabaBABabaBAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 3.9×10⁻²¹

Neighbours on the map

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