Atlas269 of 3,915

I.A.64

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.64 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 101.34 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 5.677), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000403 of each other at a top speed of 57.5, line up 158 times a period, and the computed loop closes to 8.1×10⁻¹⁸.

Measured over one period

Period: 101.3437101
Masses: 1 : 1 : 0.5
Energy: -1.10740
Angular momentum: 0
Closest approach: 4.0×10⁻⁴
Top speed: 57.50
Path length: 241.52
Alignments per period: 158
Stability: weakly unstable (|λ|max 5.677)
Loop closure: 8.1×10⁻¹⁸

Neighbours on the map

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