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## Main Question or Discussion Point

Gravity in space is best simulated by rotation. If I were inside a rotating cylinder facing the direction of rotation (i.e. a window at my feet would show objects coming into view from the top of the window) and jumped straight into the air, would I land ahead of where I started or behind where I started?

I read that you should land behind where you started, which does not make sense to me. I think that you do drift as you jump due to Coriolis acceleration, but I never learned about that so I tried to work it all out in the inertial frame. The jumper and the space station start with a tangential velocity [tex]v_{t}[/tex]. The jumper then jumps and leaves the ground with radial velocity [tex]v_{r}[/tex], from his perspective. Now that he is in free fall he will travel in a straight path until he intersects the edge of the cylinder again. Meanwhile, the cylinder rotates beneath him. The jumper is following a straight path at a speed [tex]\sqrt{v^{2}_{t} + v^{2}_{r}}[/tex] and the starting point is moving along a curved path at a speed [tex]|v_{t}|[/tex]. The jumper will intersect the cylinder again before the starting point rotates to that point, because the jumper is moving on a shorter path at a greater speed. Thus, the jumper lands ahead of where he started after jumping straight up.

Did I make any mistakes there?

I read that you should land behind where you started, which does not make sense to me. I think that you do drift as you jump due to Coriolis acceleration, but I never learned about that so I tried to work it all out in the inertial frame. The jumper and the space station start with a tangential velocity [tex]v_{t}[/tex]. The jumper then jumps and leaves the ground with radial velocity [tex]v_{r}[/tex], from his perspective. Now that he is in free fall he will travel in a straight path until he intersects the edge of the cylinder again. Meanwhile, the cylinder rotates beneath him. The jumper is following a straight path at a speed [tex]\sqrt{v^{2}_{t} + v^{2}_{r}}[/tex] and the starting point is moving along a curved path at a speed [tex]|v_{t}|[/tex]. The jumper will intersect the cylinder again before the starting point rotates to that point, because the jumper is moving on a shorter path at a greater speed. Thus, the jumper lands ahead of where he started after jumping straight up.

Did I make any mistakes there?