Atlas712 of 3,915

I.A.4

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.4 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 30.216 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 47.39), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0951 of each other at a top speed of 3.5, line up 22 times a period, and the computed loop closes to 1.8×10⁻²⁸.

Measured over one period

Period: 30.21572800
Masses: 1 : 1 : 0.75
Energy: -0.916708
Angular momentum: 0
Closest approach: 0.09515
Top speed: 3.502
Path length: 67.723
Alignments per period: 22
Stability: unstable (|λ|max 47.39)
Loop closure: 1.8×10⁻²⁸

Neighbours on the map

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