Atlas498 of 3,942

I.A.41

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.41 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 89.483 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 unstable (largest Floquet multiplier 14.96), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00063 of each other at a top speed of 42.6, line up 142 times a period, and the computed loop closes to 2.7×10⁻²⁵.

Measured over one period

Period: 89.48314720
Masses: 1 : 1 : 0.75
Energy: -1.45721
Angular momentum: 0
Closest approach: 6.3×10⁻⁴
Top speed: 42.59
Path length: 228.16
Alignments per period: 142
Topology: abaBAbabABabaBAbabABAbaBABabaBAbabABabaBAbabABAbaBABabABAbaBABabaBAbabABAbaBABabABAbaBAB (free-group class)
Stability: unstable (|λ|max 14.96)
Loop closure: 2.7×10⁻²⁵

Neighbours on the map

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