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Cooper Station is somewhat like a hollow cylinder. Buildings are attached on the surface.

Cooper Station

It has artificial gravity to hold on buildings and people. If, a person needs to fly in this spot

Imaginary Airplane Flying in the middle

Will the airplane experience two different gravitational field?

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Even though the effect of rotating can create a centrifugal force that is going to push you away from the center of rotation, towards the floor in this case, it does not mean that there is any gravitational field inside the cylinder. There isn't, this is only the effect of a non inertial reference frame, a rotating frame in this case. The apparent force comes from the object accompanying the rotation of the cylinder. For objects away from the center, if the object is rotating with the cylinder (same angular velocity as any point on the cylinder, as measured around the center), then it will experience a centrifugal force. At the center of the cylinder this centrifugal force is 0, so there would be no apparent gravity.

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The shape of the station seems to imply it uses centrifugal artificial gravity. Given role of new physics around gravitation in the film, and the role of the station‘s namesake Murphy Cooper plays in this physics, I would not bet on this, but since this website is about real physics and not scifi pseudo-physics, I will assume Cooper station relies on known laws of physics.

The centrifugal force at distance $r$ from the station centre is then $g=\left(\frac{2π}T\right)^2r$. When something is close to the axis, like your plane, $r≃0$ and the gravity is negligible. The station rotates around the plane, which does not feel any gravity.

Assuming the station has a 800 m radius (as computed in this scifi.sx answer) and a Earth gravity $g≃10\:\mathrm{m}⋅\mathrm{s}^{-2}$, it makes a turn every $$T=2π\sqrt{\frac{r}{g}}≃2π\sqrt{\frac{800}{10}}\:\mathrm{s}≃18π \:\mathrm{s}\simeq 54 \:\mathrm{s}. $$ With a turn every minute like this, one could feel the Coriolis force quite quickly. If one moves along the station axis, it will lead to an acceleration of $\frac{2\pi}{T}v$ for someone moving at speed $v$. An athlete running at $v=9\:\mathrm{m}⋅\mathrm{s}^{-1}$ will feel a lateral acceleration of $10\%$ of the gravity. For anything moving faster than $90\:\mathrm{m}⋅\mathrm{s}^{-1}= 324\mathrm{m}/\mathrm{h}=202\:\mathrm{mph} $, like a plane, the Coriolis force will be stronger than gravity, and it will imply strange trajectories.

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    $\begingroup$ Indeed. Playing baseball in those conditions (as happens in the movie) should be one heck of a game. $\endgroup$ – Emilio Pisanty Oct 10 '18 at 16:48
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In side a cylinder, the centrifugal force will depend on radius(in particular radius squared), and so at the center, there will be no centrifugal force to push an object away from center. But, at any point except the midpoint of cylinder length wise, there will be a gravitational pull because the length of cylinder infront and behind is different meaning different amount of mass and thus different gravitational pull. So, there will only be one gravitational force experienced by the spacecraft.

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