That's assuming you take the stock Enterprise-in-orbit FX shots as a literal visual representation of reality. If that's the case, then the Enterprise's saucer must be at least a couple hundred miles across!
How so? We never see the ship disappear behind the planet or anything like that.
All we do see is the ship following an orbit that, if circular around the planet, might be interpreted as being extremely tight and thus establishing a planet the size of a small mountain at most. But then again, we have no evidence that the standard orbit of a starship would be circular, or even go around a planet. A tight figure-eight is a far likelier scenario, all things considered!
If anything, we should ignore all the views of the planet being visible on the bottom of the viewscreen, because those are equally inconsistent with scale considerations plus
they indicate unrealistically high speed around the planet. And we even have a proper in-universe reason for ignoring those views: they are synthetic and thus probably heavily manipulated, whereas the shots of the ship against the planet backdrop are authentic.
What canon (or non-canon, for that matter) source says the small dome over the shuttlebay entrance contains sensors?
None. But no such source indicates sensors under the other domes, either. It's just a simple case of looks like a duck, made all the more interesting because both this dome and the one under the saucer have the same sort of ducklings next to them, namely phaser emitters.
In canon terms only, all three domes could well be identified as honking big phaser turrets...