Atlas734 of 3,942

I.A.29

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.29 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 93.405 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 260.8), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0062 of each other at a top speed of 13.6, line up 98 times a period, and the computed loop closes to 8.9×10⁻²⁶.

Measured over one period

Period: 93.40473799
Masses: 1 : 1 : 0.75
Energy: -1.13366
Angular momentum: 0
Closest approach: 0.006202
Top speed: 13.56
Path length: 221.99
Alignments per period: 98
Topology: abaBAbaBAbaBAbaBAbabABabABabABabABAbaBAbaBAbaBAbaBABabABabABabAB (free-group class)
Stability: unstable (|λ|max 260.8)
Loop closure: 8.9×10⁻²⁶

Neighbours on the map

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