Atlas677 of 3,942

I.A.3

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.3 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 25.944 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 10.12), so a small nudge makes it unravel over a few periods. The bodies pass within 0.269 of each other at a top speed of 2.36, line up 14 times a period, and the computed loop closes to 7.5×10⁻²⁹.

Measured over one period

Period: 25.94419531
Masses: 1 : 1 : 0.5
Energy: -0.633926
Angular momentum: 0
Closest approach: 0.2686
Top speed: 2.356
Path length: 51.205
Alignments per period: 14
Topology: aaabAAAB (free-group class)
Stability: unstable (|λ|max 10.12)
Loop closure: 7.5×10⁻²⁹

Neighbours on the map

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