Say a spaceship is traveling though space in a uniform circular motion.
It's not orbiting any planet, it just flies in circles in an empty space.
The only force working on the spaceship would be the centripetal force caused by the ship's engine.
Thus, the work would be $0$, as the force would always be perpendicular to the ship's path.
But that sounds counterintuitive to me, it would seem that the spaceship must do some work, otherwise it would just float in a straight line.
Can anyone point out the error in my reasoning?