in an alternate universe. Earth evolved the same, but the galaxy as we know it seems to be radically different (ie, smaller).
Skipping Travis' comment about how many galaxies he'd chased Blake through (either he knew the ship was bugged and was posing for a good sound bite, or 'galaxy' has an alternate meaning [either a political division (like states and counties) or else it's the name of a fast food restuarant chain]), the area seems pretty small.
1) Every solar system people enter by chance seems to have a habitable planet. Even if they only try to enter systems with a sun similiar to ours, that suggests a high number of habitable worlds within a short distance of Earth.
2) Since the dissident group in The Way Back felt the defection of one world would have impact and that it was a practical goal (even the most starry eyed idealists might have thought twice if it was one world vs thousands) but it was still possible to run into a new one each week, it seems safe to suppose the Federation had a few hundred planets. Sounds like a lot but, as this galaxy's supposed to have 100 billion stars in it, that means they could all be pretty close to home.
3) Take a look at Federation astrogation. In Deliverance, the small ship cuts through a solar system it has no reason to visit. There are a few other hints and references that ships move from one system to another even when that system isn't any part of their destination (the frequency with which they run into other ships while orbiting planets they didn't intend to land on until the fighting started, for example). This implies their astrogation is still pretty crude. They avoid plotting straight lines over great distances and instead seem to move to the nearest navigable point then on to the next. Add to this Cally's comments in Star One when they leave the galaxy, even if it's only a short distance. Whether or not Liberator or some Federation ships would be capable of navigating there, no one seems comfortable with the idea.
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