Specifically, if you want to run Trek-style science, Atomic Robo has a subsystem that may serve well. In this system the GM does *not* have to determine beforehand how a piece of tech or science works. The GM presents the visible phenomenon (say, for example, an aggressive herd of giant ants), and the players get to figure out how/why the ants are giant, and what that means in terms of dealing with said phenomena. I don't have the rulebook at hand, and I'd want to double check a detail or two before outlining it. But it gets the whole issue of having coherent science off the GM's plate. The players manage all the pseudoscientific gobbledigook for you, and if you have the right kind of players, they have a lot of fun with it.
Atomic Robo also has a concept of something other than the characteres that can take a hit for the PCs. In AR, it is an organization - players can have the organization they work for take "consequences" for them. This is pretty easily be slipped to it being a ship. If negotation fails, and a fight breaks out, instead of someone getting killed in the fight, the ship can take a consequence "warp drive offline", which has repercussions for the story going forward, without it falling on individuals. Or, you can still have someone specific take the hit in a ship-combat, and have Ensign Monroe zapped and flying across the bridge when an EPS conduit blows out...