Is this ever specifically references in the show? How long does it take to get from the station to Earth or to the Klingon Homeworld? I get the impression that you can't simply beam to Bajor, you have to take a runabout/transport ship but that's the only real distance I can recall.
To Bajor, I think they said a couple of hours by shuttle or runabout. To Earth, I don't think they were ever specific. A few days to a week is my impression, remembering the Defiant going back and forth in Homefront/Paradise Lost, and Quark's Treasure in Little Green Men. Kassidy said her brother (cousin?) who played baseball for the Pike City Pioneers on the other side of Federation space was six weeks away at maximum warp, but I'm not sure if she meant maximum warp of her freighter or maximum warp of a starship.
Bajor was either 2 or 6 hours by impulse (and they never tried warp). Which would appear to indicate that it takes 2 hours to cover 1 AU, and the station is 2 AU from the star (so that the trip is thrice as long when the station and the planet are on the opposite sides of the star). Earth was indeed a few days away when there was great hurry, such as in "Paradise Lost". That was with the Defiant, though, and she was a notorious underperformer, needing jury-rigging to get on par with other Starfleet ships as per "The Sound of Her Voice". But in the episode ironically named after that very ship, Bashir seems to think that borrowing a runabout would allow him to get stuff from Vulcan within a week... Meaning back and forth. Cestus III being far away at maximum warp is ambiguous, yes, and made even more ambiguous by Kasidy's freighter actually being very, very fast - she covers multiple star systems in a few hours in "For the Cause". As for solid numbers, Jake Sisko claims that Bajor is 300 ly from Regulus, which in turn is 80 ly from Earth, meaning Earth->Bajor would be at least 220 ly. And while there are onscreen maps to suggest the Okudaic distance of 50 ly, they never actually show Earth, just Bajor and her neighbors... Timo Saloniemi
Sounds like TOS to me. But seriously though.... I think the idea was that it was quite a long while away. Really pretty far. And the writers started to realise that having them weeks away at high warp would be difficult for plot reasons, and just sorta never really made a big point. We saw Earth twice in the whole of DS9, they never really wanted to visit Earth a lot anyway. Long story short..... Bajor is on the edge of Federation space. Make of that what you will. 50ly, 100, 1000..... Whatever floats your boat.
It makes sense that it should be three week's travel. Bajor is supposed to be remote and different from the center of the Federation. They don't visit Earth a lot.
Maybe the original idea was for DS9 to be someplace distant, but ultimately it ended up being not that terribly far from Earth as the series unfolded. Still, DS9 could yet be considered "in the wilderness" if Federation expansion had stopped shy of the Bajor Sector at the time the series began (an irregularly-shaped Federation could expand in other directions away from Bajor). Perhaps many of the earlier conflicts the Federation had with the Klingons, Romulans, and the Cardassians was due to all four powers being in fairly close proximity with one another.
We know that Bajor not only rests at the edge of UFP space, it rests a bit beyond it, in space that used to be Cardassian only a short moment ago. Indeed, we have every reason to think that this space used to be deep inside the Cardassian Union, because we quickly learn Bajor is next-door neighbors to the Cardassian home system! Apparently, the UFP carved a giant hole in the side of the Union in that old war, and stopped just short of invading Bajor, leaving the neighborhood formally "neutral" (although we soon also learn that everybody there from Klaestron to Xepolite is still a Cardassian sympathizer, knowing which side their bread is buttered or at least which side their hides will eventually be skinned if they decide otherwise). Bajor should certainly count as "edge" and "frontier", but there's no plot need for it to be "distant", too... The same probably goes for Jouret in "Best of Both Worlds". It's at most a week from there to Earth in a heated chase scene, and probably less, but Jouret could border on, say, Romulan space and therefore be as far as the UFP can get in that particular direction. Timo Saloniemi
The distance between the Station and Bajor would change due to Bajor's orbit. As for the time taken to get to places like Earth. "Ahead plot spped" Now in a Runabout perhaps it might take a week or so to get to Earth but a ship might be able to shave a few days off.
What bothered me, because I've always been interested in astronomy, was that we don't get a firm sense of a solar system that Bajor and the station are in. A couplemoons were talked about. any other planets? There's a sun, but just one? I don't think they show or talk about the star Bajor orbits. DS9's position is confusing. It started out in close orbit around Bajor. A little risky to have that big station so close in, I'd think, but what do I know. So in Emissary they send the station a bit out from Bajor, so it can snag the wormhole for Bajor. It's far enough away so Bajor isn't visible as a disc, I guess, though they never show it from the station. But, still in Bajor's solar system presumably. As far as another planet would be? Objects in space don't hold fixed positions generally, they're usually orbiting something. The wormhole wouldn't be orbiting anything. Is it "fixed" in relation to Bajor, which is of special importance to the Prophets? Then it in effect orbits their sun too. And DS9. Or the Wormhole (and DS9) stays put while Bajor orbits, and Bajor is sometimes near, sometimes very far. Or if DS9 is far out of the orbital plane I guess the distance to Bajor could stay fairly regular. My point? If I have one, it's that I like to know where things are. I just don't know this solar system we're supposed to be spending so much time in.
This is a consistent problem. It's hard for me to envision the UFP as one country if it takes more than a few weeks to traverse it at speeds of widely available transportation. This means the UFP can't be much larger than 100 ly across. It is supposed to be bigger, so we end up with these convoluted explanations as to how the characters can get around so fast.
The people living in Star Trek probably wouldn't be all that interested in astronomy, though. It's not as if being interested in geography is a requirement for living on Earth, either. The station's supposed mission was the planet. Why be anywhere else? We never learned the exact logistics of the setup, but being within transporter range of the surface would help, not just with commuting, but with getting all that ore up to the refinery. The travel times tell such a beautifully consistent story that I'm tempted to think somebody put thought into it. If a runabout takes 2 hours between the station and Bajor at one time, and 6 hours at another, both being trips involving hurrying (and this particular star system is one of those rare no-warp zones, perhaps because of that bad weather we saw in a couple of eps, plus the Denorios belt), then it makes sense to assume that the ratio of orbital radii is 1:2, and the trip is either the difference between the radii (closest) or the difference plus the full inner diameter (farthest) or then something between those. And while the Bajoran year appears a bit shorter than the Earth one, we probably still are talking about five-ish light minutes from the star to the planet, and thus ten-ish to the station. We know the wormhole mouth tags along the Bajoran star system as that system moves across the galaxy and the galaxy moves across the universe, so yes, something fixes it there. And this isn't dependent on whether the mouth is open or closed, although an open mouth also exerts a gravitational pull, as in "Destiny" et al. So yes, classic orbiting is assumed. In that case, DS9 would have to utilize engines to hover above the local star. While longterm hovering is an established Trek capacity and a likely starship mode of operations, we don't hear total power loss having the consequence of "disrupting the orbit" of DS9 or "Aaah, we're falling into the sun!". So a freefall orbit is the likelier scenario. The fun thing is, it appears the Bajorans don't know or care, either. They're an ancient civilization, in the sense of having been ancient back when the very rocks that ultimately were used for making the pyramids were but a glimmer in God's eye. But they don't go out much. There's an Earthlike moon orbiting their home planet, and nobody lives there. Nobody has ever admitted to living there. And once the Occupation kicks a bit of spatial interest into the Bajorans, what do they do? They scuttle this moon for power. There's one additional inhabited world there, planet number eight, with colonies as per "Past Prologue". Did the Cardassians force the Bajorans to that place, too? Certainly space travel plays an important role in the home planet's recovery from the Occupation, but that's for traffic coming from other star systems or from that other quadrant altogether; there just doesn't appear to be anything interesting in the Bajoran system. Timo Saloniemi
One way to easily explain it is that the Federation isn't a perfect sphere and that Earth isn't geographically at its center. So some of the Federation's borders may only be a few dozen light-years away, while other borders could be thousands of light-years away. Take into account three dimensions, and the Federation borders could be physically closer still while still comprising thousands of light-years in total volume.
Also, we don't have to envision the UFP as one country. The British Empire held together nicely enough even when it took months for anything, be it armies or messages, to reach the more distant corners. Ancient landlocked empires used to be even worse off, back when horses were at a premium and roads were hallowed myths. Indeed, the UFP is pretty well off in that communications (at least within the established network) are instantaneous, even if starships are not. A threat of "If you don't fix that taxation thing by next Tuesday, we'll raze your planet in four and a half years or thereabouts" still carries a lot of weight, especially if accompanied with "And we'll freeze your assets on Wednesday". Timo Saloniemi
In the Roman Empire it took months to travel from what is now Syria to England. In the 19th century it took months to travel from Britain to New Zealand. We're spoiled with airplanes these days.