Atlas488 of 3,942

I.A.35

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.35 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 74.648 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 linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.000307 of each other at a top speed of 61, line up 110 times a period, and the computed loop closes to 1.4×10⁻²⁴.

Measured over one period

Period: 74.64803348
Masses: 1 : 1 : 0.75
Energy: -1.38516
Angular momentum: 0
Closest approach: 3.1×10⁻⁴
Top speed: 61.00
Path length: 185.03
Alignments per period: 110
Topology: abaBAbabABabaBABabABAbabABabaBAbabABAbaBABabABAbabABabaBABabABAbaBAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 1.4×10⁻²⁴

Neighbours on the map

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