Atlas723 of 3,942

I.A.1

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.1 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 5.9858 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 4.104), so a small nudge makes it unravel over a few periods. The bodies pass within 0.243 of each other at a top speed of 2.08, line up 6 times a period, and the computed loop closes to 3.4×10⁻²⁶.

Measured over one period

Period: 5.985818440
Masses: 1 : 1 : 0.75
Energy: -1.10929
Angular momentum: 0
Closest approach: 0.2429
Top speed: 2.081
Path length: 14.357
Alignments per period: 6
Topology: abAB (free-group class)
Stability: weakly unstable (|λ|max 4.104)
Loop closure: 3.4×10⁻²⁶

Neighbours on the map

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