Would jumping up and landing on an orbital space station whose rotation provided an acceleration of 1g feel exactly like doing the same on Earth?
Consider a non-spinning Earth, with me standing on a spot on its surface marked ‘X’. When I jump, I experience an attractive gravitational force of 1g throughout my jump. On the way down, my inner ear tells me I am more nearly weightless. I hit the X and my leg muscles decelerate my downward motion to a stop.
In a spinning Earth, the exact same happens. Even though I’m revolving at 1000 mph, or around the sun at 66000 mph, in mid air there is nothing to stop me continuing at this speed in this direction, and so I land on the ‘X’ having not effectively been able to tell the difference.
Now consider that I’m walking around on the wall of a giant Tornado ride (in UK fairground they’re called something different I think - Jack of Hearts?) in space, feeling an acceleration of 1g, until I stand on an X painted on the wall/floor. This time when I jump, I don’t experience an attractive gravitational force throughout my jump. (My inner ear will, I think, still provide a ‘weightless’ feeling once my leg muscles have jumped and thus counteracted the centrifugal force I feel as gravity). At the height of my jump, I am now effectively floating in space.
With a pencil and paper, I’ve managed to convince myself that I do still land on the ‘X’. By jumping, I cease to travel in a circle and (by Newton;s first law) start to travel in a straight line independent of the space station. The wall/floor then curves around to meet me.
Would my meeting back with the X on the wall/floor feel exactly like landing on a stationary ‘X’ on Earth?