Can you please
use the term 'nude-eye' instead of naked-eye. It is so much more tasteful...
Stargazers at the US's University of Rochester have announced that Mizar in the asterism of the Plough (the Big Dipper to our US cousins) is actually a six-star system. Mizar was scientifically confirmed as the first known binary star system back in 1617, by Benedetto Castelli and Galileo, who demonstrated that Mizar was …
Isaac Asimov also depicted a six-star system, in his short story "Nightfall". Which incidentally was one of the best sci-fi pieces I've ever read.
As to any computer being able to figure out the orbits of six stars - google "three body problem". We can't figure out the orbits of 3 stars, let alone 6!
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No of course it wont be.. they'll be (to use an NHSism) circling the plug hole..
Point is that on a Human Scale of things they probably wont have made one orbit since they were named.
Stable is relative to your timescale. and on an astronomical scale pretty much Nothing is Stable.
Well, by the sound of things its not six stars all in a bunch. You've got three pairs of stars, each revolving round a common centre of gravity. Then two of the pairs are revolving round a common centre of gravity, and that cog is revolving round a common cog with the other pair. How stable it is will depend on how far apart each individual pair is... Presumably they are all pretty well spaced...