With the presence of the Alliyana Shipyards partially inside a captured asteroid in orbit of Sorenson, I assume that the Tau Ceti system has at least one asteroid belt that served as the source of that asteroid. The being said, are those asteroids mined like the asteroids in the Darvano system? Are they mined from the surface or hollowed out like Karuzara?
We have seen from that refueling "5th moon" of Tanna, that the Jung dig into and build out the surface of asteroids. I imagine that this is Jung policy as they appear to have done the same at Tau Ceti. That Asteroid has 2 shipyards on the surface of it.
I imagine that the Asteroids are dug into for some of the resources used in construction of a) the surface buildings and b) what ever else they build there like new ships or replacement parts. meaning that the buildings could have "basements" from which came the material of the upper floors were build with. It stands to reason that if you dig into an asteroid you are going to utilize the hollowed out spaces for something even if just for storage.
I think Asteroids are good ship yards come because they do they most of the needed resource on hand, so far we have seem them only over worlds either this is because they have used asteroid moons or they have maneuverer an asteroid into place. I think they do this because it makes it easier for housing work crews. an asteroid out in a belt is likely to be many hours away by sub light.
Now with jump drive it doesn't really matter.
How ever to answer your Question Teu Ceti has been in Jung Control for 40-50 years, and before that the Tau Cetians had really gotten back into space. Bearing in mind that were told that to mine an asteroid takes decades, I would say the Jung used a moon come asteroid which was already in place over one of the worlds (may be it was moved there pre-BDP) How the Asteroid is Mined I would say Depends on the Technology proficiency. the Jung and the PC seem to be at equal technically levels how ever the JUNG I see as being much more brute force where as the Corair have much more feness.
Example the Jung land on the Asteroid and just start digging, and pulling out the most valuable materials. the Cornairians work out how to use the entire asteroid, digging out from the centre so that it remains stable to be moved in to orbit where it can be broken down entirely.
Tau Ceti had not gotten back into space. The Jung had to link the planets.
I like the idea of the Asteroid being there for a thousand years. But I think that the Jung move asteroids as a matter of course, using multiple frigates to push asteroids into different orbits, a similar but more robust method than the corinarians one-use engines. The Jung are a people who have made space they're home (those of their fleet anyway) and with the multiple purpose craft they have (Battle platforms as mobile space docks / Frigate merging into space docks) I would not be surprised if they're lighter craft were also tasked with more then just combat orientated goals.
There could also be working vehicles hidden in Jung Battle platforms or just moved system to system to do these tasks where and when the Jung Plan needs them.
