When something is in an orbit, gravity and acceleration kind of cancel each other - hence weightlessness. I think the equivalence principle says that such a frame is in fact an inertial frame so that SR applies.

 

But if you've two things rotating around each other wouldn't this present a similar situation as a giant circular spacestation with artificial gravity?

But if you've two things rotating around each other wouldn't this present a similar situation as a giant circular spacestation with artificial gravity?

 

No. If the outer perimeter of the Space station was moving slow enough to "orbit itself", just cancelling out it's weight, there would be no artificial gravity. It has to spin faster to do this.