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?
A lot of it depends how big the station is - for something the size of Larry Niven’s Ringworld, the sensation would probably be indistinguishable from gravity, for normal human movement. For something much, much smaller (and therefore rotating much faster) - i.e. something that is within our current capability to construct, coriolis forces would be quite noticeable.
Try it on a children’s playground roundabout - set it spinning and try to kick the central post - your leg appears to veer wildly off to one side, because you’re applying a vector force in a rotating reference frame.
No, it wouldn’t feel like it. Imagine you jump straight across, landing exactly opposite of where you started in “absolute” terms. You have no “sideways” component to your jump. So whether the X is there when you finish is just a coincidence based on the speed of rotation. And your jump would not feel like a normal jump, since all you’ve done is jump straight up.
Concur with Magnetout’s point about size. Imagine you take a jump from Earth in your new super gee whiz I am the Hulk boots. You jump straight up 20,000 miles and come back down again. Do you land in the same place. I’m thinking not.
Jumping straight across is also very difficult to do, because you’d be applying a vector force in the direction of the opposite side, but you’re already in motion with respect to the opposite side, so you don’t actually go straight across.
This is what I mean - you push off in the direction of the blue arrow, but because you’re already in motion in the direction of the green arrow, the two vectors combine and you travel in the direction of the orange arrow - not only do you fail to pass through the centre of the rotating ring, but your path of travel, relative to the ‘ground’ (even if it should happen to rotate so that you end up back on your ‘X’) isn’t parabolic.
