If there is no acceleration, then how are objects changing direction?
Also I should add, it is confusing thinking about 0g, because obviously bodies in a gravity well are experiencing a gravitational force. Really we're talking about 0 acceleration, where g is the acceleration due to gravity. In orbit this g acceleration is cancelled out by centripetal acceleration to produce 0 acceleration, or free fall.
If it were not for the force of gravity, an object in motion would move in the direction of its instantaneous velocity. It does not do that, it instead accelerates toward the center of the gravitational body.
>In orbit this g acceleration is cancelled out by centripetal acceleration to produce 0 acceleration, or free fall.
But again, they do not "cancel out," otherwise how is the instantaneous velocity constantly changing direction?
For example, it was very hard to replicate the moon's gravity when training pilots to land on the moon. How do you 'fake' a different gravity on Earth? It's pretty hard to do: https://www.youtube.com/watch?v=aw8kRZEvh_s
EDIT: to your question about centripetal force, either you experience acceleration or you don't. Since gravity is in equilibrium with centripetal force relative to movement around Earth you shouldn't get acceleration from this. However, you will get micro g's from rotation of the station itself, etc.