Atlas528 of 3,942

I.A.71

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.71 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 145.67 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 1.010), so a small nudge only makes it wobble. The bodies pass within 0.000709 of each other at a top speed of 40.2, line up 206 times a period, and the computed loop closes to 5.7×10⁻²⁵.

Measured over one period

Period: 145.6730252
Masses: 1 : 1 : 0.75
Energy: -1.35130
Angular momentum: 0
Closest approach: 7.1×10⁻⁴
Top speed: 40.17
Path length: 359.07
Alignments per period: 206
Topology: abaBAbabABabaBAbabABabaBAbabABabaBAbabABAbaBABabABAbabABabaBAbabABAbaBABabABAbaBABabABAbaBABabABAbaBABabaBAbabABabaBABabABAbaBAB (free-group class)
Stability: stable (|λ|max 1.010)
Loop closure: 5.7×10⁻²⁵

Neighbours on the map

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