By using a Foucault pendulum or ring laser gyroscope?
Yes they can show that the earth is spinning. But if the earth is fixed and the sun is orbiting the earth in our thought experiment, how are they applicable?
The point I am trying to make is that the suns apparent position differs from its actual position whether the sun is rotating around the earth or the earth is spinning.
I am beginning to understand the gulf between creationists and scientists. I would never have guessed that such a simple concept would be so hard to explain.