Atlas460 of 3,942

I.A.89

From Li, Jing & Liao (2018)

I.A.89 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 115.44 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 1.075), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000234 of each other at a top speed of 65.4, line up 198 times a period, and the computed loop closes to 6.7×10⁻²⁵.

Measured over one period

Period: 115.4448018
Masses: 1 : 1 : 1
Energy: -1.83990
Angular momentum: 0
Closest approach: 2.3×10⁻⁴
Top speed: 65.36
Path length: 307.59
Alignments per period: 198
Topology: ababABAbabaBABababABAbabABABabaBABAbabABAbabaBABababABAbabABABabaBABAbabABABabaBABababABAbabaBABabaBABAbabABABabaBAB (free-group class)
Stability: weakly unstable (|λ|max 1.075)
Loop closure: 6.7×10⁻²⁵

Neighbours on the map

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