The problem, again, is one of energy. On the scale that we’re talking about, just the energy required in propelling the ship to any appreciable speed (even given a journey of a few thousand years) is going to be huge (and most of it, even with fission, dedicated to accelerating the fuel and propellent needed to accelerate and later decelerate). With even the highest imaginable specific impulse from any ion engine, you are going to need tens of thousands of pounds of propellent for every pound of actual payload, and the energy to accelerate it.
You’ll also need power to keep your miniature civilization alive; we’re used to thinking both in terms of energy being merely electricity and fuel, and as being an almost unlimited resource, with the energy from an ounce of enriched uranium equaling that from combusting a couple hundred tons of coal. However, in our miniature civilization inside the asteroid, we’re going to have to provide energy for everything; light to grow plants, energy for reprocessing waste and raw materials, et cetera. We get the vast amount of our energy current from the Sun, in the form of complex organic structures that make food, building materials (wood), organic fuels, the evaporation process that gives us fresh water, et cetera. Without the Sun, we have to replicate all of these processes, and without any outside help. (Picking up and scavenging supplies from space while in transit, especially when moving at even a small fraction of c, is so far beyond fantasy it’s not even worth consideration.)
If we’re going to assume that we’ve got time to kill and can spend a few eons preparing, then we don’t need to rely upon existing technology. In a thousand years, or perhaps even a couple hundred, we’ll most likely have controlled fusion as a mature technology. This alone might make such a journey possible (albeit just barely). Given a longer timeframe and we’re likely to have discovered even more advanced technologies that would fall into the realm of speculative science fiction today. And it’s almost certain that, given a spacefaring lifestyle, we won’t be dressing in spandex and giving orders to “fire at will” at bony-headed aliens whilst being tossed about the bridge. More than likely, we’ll modify ourselves to be more robust and tolerant of conditions in deep space so that radiation, freefall, and lack of vacuum aren’t immediately fatal hazards. As others have noted, whatever the future will be like, it’ll probably bear as much relation to our current expectations as the Jetsons does to life today.
Stranger
) has been shredded I’m unsure why you ask, but what the hell. No, it wouldn’t matter if some percentage of them went smash and go boom…for one thing the odds of actually hitting something have got to be, well, astronomical so to speak. For another, redundancy would be built into the system…i.e. we’d send out a lot more resupply ships than would actually be needed to get the job done.