One final thought. If the dome were truly a window, then it might appear black from the inside, as CLB described. Except that in the Trek universe (even TOS) this never happens - every time they look out of a window from a fully lit room, loads of stars are visible! Must be that futuristic Transparency they use...
Ummm... maybe I'm missing something, but I can't recall any times that we saw out of a WINDOW (as opposed to seeing a viewscreen) where we could see stars, from the character's perspective, in TOS.
The Enterprise's windows were only shown a couple of times. Everything else ever seen was on a viewscreen... and was almost certainly a computer-rendered image based upon sensor returns rather than a "direct view out the window."
Is there some "window shot" in TOS that I'm missing?