To conclude, in the case of distance, you either use a suited form of the angular diameter formula (the atan() or tan() one, depending on context) mentioned by everybody here from the beginning, or, if you already know the current apparent size at a given camera distance, just multiply the distance with the ratio between the current and the desired size, like I did in the above fiddle. To center things, simply look at the center of the projection.
The centering part will however alter the projection bounds (except for spheres, which look the same from every angle), so the only simple choice is to repeat the center + fit process until you get the desired outcome.