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We have two observers, one in a "stationary" frame outside the Earth. This observer is looking down on Earth at another observer sitting at rest with respect to the surface of the Earth, but obviously, rotating with the Earth and with respect to the outside observer. The outside observer can calculate the mass of the Earth and the velocity of the earth observer due to the Earth's rotation and calculate what the Earth observer would determine to be the net force acting on them: gravitational force minus centrifugal force.

Then, the Earth observer begins to move, at constant velocity, equal and opposite the rotation of the Earth, such that both observers are now at rest with respect to each other. The outside observer determines that the Earth observer would have noticed an increase in force toward the center of the Earth, due to the fact that there is no more centrifugal force, but it seems as though the Earth observer should feel themselves getting lighter, due to a centrifugal force from his new rotation around the spherical Earth.

Who is right? It seems like the outside observer should be right, and that the net force on the Earth observer should increase, leading to the Earth observer to conclude there is another "fictitious" force at work pulling him in to the center of the Earth as he starts to rotate opposite the spin of the Earth with respect to the Earth's surface. The strange thing is that this force would also be unexplainable to a third observer at rest in the Earth's rotating frame, watching the Earth observer racing around the planet.

I think I kinda understand this situation, but can someone maybe help me make heads and tails of it? Thanks!