Atlas724 of 3,915

I.A.7

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.7 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 36.517 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 87.29), so a small nudge makes it unravel over a few periods. The bodies pass within 0.133 of each other at a top speed of 2.73, line up 34 times a period, and the computed loop closes to 2.1×10⁻²⁸.

Measured over one period

Period: 36.51672193
Masses: 1 : 1 : 0.75
Energy: -1.08882
Angular momentum: 0
Closest approach: 0.1331
Top speed: 2.734
Path length: 86.658
Alignments per period: 34
Stability: unstable (|λ|max 87.29)
Loop closure: 2.1×10⁻²⁸

Neighbours on the map

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