Atlas671 of 3,942

I.A.52

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.52 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 139.21 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 17.07), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00122 of each other at a top speed of 30.5, line up 162 times a period, and the computed loop closes to 2.8×10⁻²⁵.

Measured over one period

Period: 139.2068093
Masses: 1 : 1 : 0.75
Energy: -1.20569
Angular momentum: 0
Closest approach: 0.001225
Top speed: 30.53
Path length: 336.03
Alignments per period: 162
Topology: abaBAbaBAbabABabABabaBAbaBAbabABabABabaBAbaBAbabABabABAbaBAbaBABabABabABAbaBAbaBABabABabABAbaBAbaBABabAB (free-group class)
Stability: unstable (|λ|max 17.07)
Loop closure: 2.8×10⁻²⁵

Neighbours on the map

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