Atlas348 of 3,942

I.A.47

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.47 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 109.37 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 weakly unstable (largest Floquet multiplier 1.787), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000256 of each other at a top speed of 66.8, line up 154 times a period, and the computed loop closes to 1.9×10⁻²⁵.

Measured over one period

Period: 109.3699499
Masses: 1 : 1 : 0.75
Energy: -1.31725
Angular momentum: 0
Closest approach: 2.6×10⁻⁴
Top speed: 66.81
Path length: 242.68
Alignments per period: 154
Topology: ababABababABAbaBABAbabABAbabABAbabABAbabaBAbabABABabABABabaBAbabaBABabaBABabaBABabaBABAbaBAB (free-group class)
Stability: weakly unstable (|λ|max 1.787)
Loop closure: 1.9×10⁻²⁵

Neighbours on the map

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