Atlas676 of 3,942

I.A.9

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.9 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 35.278 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 2.696), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00413 of each other at a top speed of 18, line up 34 times a period, and the computed loop closes to 5.8×10⁻²⁶.

Measured over one period

Period: 35.27772220
Masses: 1 : 1 : 0.5
Energy: -0.839185
Angular momentum: 0
Closest approach: 0.004126
Top speed: 18.00
Path length: 75.636
Alignments per period: 34
Topology: aabABabABabAABabABabAB (free-group class)
Stability: weakly unstable (|λ|max 2.696)
Loop closure: 5.8×10⁻²⁶

Neighbours on the map

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