R E is adjusted on the left side for the greater distance.
That is of course the same equation as the one used to demonstrate Newton's study of gravity. That can be interpreted as stating that in the astronaut's frame of reference, all bodies are subject to two forces, gravity and the centrifugal force, and the two are in perfect balance, adding up to zero. It makes no difference. The important thing to note here is that an astronaut inside that spacecraft is subject to the same gravity and therefore undergoes the same acceleration as the spacecraft itself. Viewing the astronaut's motion in the frame of the moving spacecraft, the astronaut is not pulled towards the floor of the cabin or in any other direction, and therefore has the impression that gravity has been eliminated.