Atlas487 of 3,942

I.A.13

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.13 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 39.188 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 1.001), so a small nudge only makes it wobble. The bodies pass within 0.000815 of each other at a top speed of 37.5, line up 58 times a period, and the computed loop closes to 6.4×10⁻²⁵.

Measured over one period

Period: 39.18771545
Masses: 1 : 1 : 0.75
Energy: -1.39220
Angular momentum: 0
Closest approach: 8.1×10⁻⁴
Top speed: 37.45
Path length: 97.895
Alignments per period: 58
Topology: abaBAbabABabaBAbabABAbaBABabABAbaBAB (free-group class)
Stability: stable (|λ|max 1.001)
Loop closure: 6.4×10⁻²⁵

Neighbours on the map

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