Atlas454 of 3,942

I.A.51

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.51 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 109.47 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 0.000144 of each other at a top speed of 89.2, line up 162 times a period, and the computed loop closes to 2.5×10⁻¹⁷.

Measured over one period

Period: 109.4686390
Masses: 1 : 1 : 0.75
Energy: -1.38802
Angular momentum: 0
Closest approach: 1.4×10⁻⁴
Top speed: 89.21
Path length: 271.04
Alignments per period: 162
Topology: abaBAbabABabaBABabABAbabABabaBAbabABAbaBABabaBAbabABAbaBABabABAbabABabaBABabABAbaBABabaBAbabABAbaBAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 2.5×10⁻¹⁷

Neighbours on the map

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