Atlas696 of 3,942

I.A.12

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.12 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 54.585 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 32.64), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00605 of each other at a top speed of 14.8, line up 46 times a period, and the computed loop closes to 5.7×10⁻²⁶.

Measured over one period

Period: 54.58461321
Masses: 1 : 1 : 0.5
Energy: -0.833967
Angular momentum: 0
Closest approach: 0.006053
Top speed: 14.85
Path length: 126.26
Alignments per period: 46
Topology: aabAAbaaBAAbabAABaaBAAbaaBAB (free-group class)
Stability: unstable (|λ|max 32.64)
Loop closure: 5.7×10⁻²⁶

Neighbours on the map

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