Atlas667 of 3,942

I.A.61

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.61 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 140.42 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 399.3), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000341 of each other at a top speed of 57.9, line up 178 times a period, and the computed loop closes to 4.9×10⁻¹⁷.

Measured over one period

Period: 140.4203856
Masses: 1 : 1 : 0.75
Energy: -1.26438
Angular momentum: 0
Closest approach: 3.4×10⁻⁴
Top speed: 57.90
Path length: 340.39
Alignments per period: 178
Topology: abaBAbabABabaBAbabABabABAbaBABabABAbaBAbabABabaBAbabABabABAbaBABabABAbaBABabABabaBAbabABabaBAbaBABabABAbaBABabAB (free-group class)
Stability: unstable (|λ|max 399.3)
Loop closure: 4.9×10⁻¹⁷

Neighbours on the map

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