Atlas270 of 3,942

I.A.45

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.45 m₃ = 0.5 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 0.5 that return to their starting positions and velocities every 78.657 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 1.564), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000294 of each other at a top speed of 67.3, line up 122 times a period, and the computed loop closes to 7.6×10⁻¹⁸.

Measured over one period

Period: 78.65713568
Masses: 1 : 1 : 0.5
Energy: -1.10097
Angular momentum: 0
Closest approach: 2.9×10⁻⁴
Top speed: 67.33
Path length: 185.83
Alignments per period: 122
Topology: abaBAbaBAbaBAbaBAbaBAbabABabABabABabABabABAbaBAbaBAbaBAbaBAbaBABabABabABabABabAB (free-group class)
Stability: weakly unstable (|λ|max 1.564)
Loop closure: 7.6×10⁻¹⁸

Neighbours on the map

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