Atlas664 of 3,915

I.A.8

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.8 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 30.37 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 3.852), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00679 of each other at a top speed of 12.9, line up 38 times a period, and the computed loop closes to 1.2×10⁻²⁶.

Measured over one period

Period: 30.36994799
Masses: 1 : 1 : 0.75
Energy: -1.25577
Angular momentum: 0
Closest approach: 0.006794
Top speed: 12.94
Path length: 73.658
Alignments per period: 38
Stability: weakly unstable (|λ|max 3.852)
Loop closure: 1.2×10⁻²⁶

Neighbours on the map

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