Rate of change in pixel coordinates during camera rotation (near vs far subjects)

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Lets say a camera is spinning around horizontally with its axis of rotation at the center of the camera lens. Do subjects farther away from the camera have a different rate of change in photo x coordinate than subjects closer to the camera when camera lens is rotating? Obviously this is true when translating the camera (when driving in a car the mountains in the distance go by slower than the stop sign). But after playing around a bit and doing some at-home experiments I couldnt find any evidence that suggests there is a difference when rotating...

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I don't know the answer for sure, but I will share my thoughts.

Let's pretend we are using a camera with an FOV (field of view) of 90 degrees or so. Let's start the position of the camera at some perpendicular distance away from two same sized objects that are aligned in a straight line. The camera is not yet included in that straight line.

As we translate the camera towards the two objects in order to make a straight line with them, the object that is further away will appear in the image before the closer object due to the triangular FOV. The further object will appear first but it's x-coordinate in the resulting image will shift slower than the closer object.

Now we stop the camera when it is in a straight line with the other two objects. The further object is behind the closer object, so it cannot be seen. I think no matter how we rotate the camera, we will not be able to see the further object behind the closer object. I also think changing the FOV will not help us here. This would mean that there is no difference in the rate of change of each object's x-coordinate. If there were, we would be able to see the further object behind the closer object. We would have created an x-ray vision camera!