From what I read in the rules, it looks like the only way to reveal celestial bodies is with galactic mapping.
Exactly. There are also 2 Progress cards that reveal 4 tiles.
Starships, for example, can't stop on an unrevealed tile and reveal it?
Absolutely NOT: we tested this rule and it totally ruined the game.
Planification is really important in Kepler-3042 and landing on planets (or mines) by random completely frustrates every strategy.
The game, simply, is incredibly less deep and interesting.