Atlas450 of 3,915

I.A.9

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.9 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 32.19 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 1.874), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00868 of each other at a top speed of 11.4, line up 46 times a period, and the computed loop closes to 6.1×10⁻²⁷.

Measured over one period

Period: 32.19017617
Masses: 1 : 1 : 0.75
Energy: -1.34544
Angular momentum: 0
Closest approach: 0.008675
Top speed: 11.41
Path length: 76.535
Alignments per period: 46
Stability: weakly unstable (|λ|max 1.874)
Loop closure: 6.1×10⁻²⁷

Neighbours on the map

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