Motion is relative. If the Sun is the frame of reference, then the Earth is moving and the Sun isn't. If the Earth is the frame of reference, then the Sun is moving and the Earth isn't.

If you claim the Earth is absolutely stationary then you have to say which is the absolute frame of reference and why. To me it just looks like any choice would be arbitrary.

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The default position is that the Earth isn't moving. Every experiment ever conducted (as explained in this clip) verifies this position.

Therefore, if you wish to claim the opposite, then you have to provide evidence for this claim. Theoretical physics just doesn't cut it at this point. There is no experiment that can be done to demonstrate this - and we all know they have tried for centuries. So the only way you can argue your position is through theories.