How do astronomers know the earth rotates?
They have to use an RA (Right Ascension) drive on their telescopes to keep the stars still.
If you are really determined you could model the universe by saying the Earth does not rotate and everything else rotates around it. There are numerous complications to such an approach - the motions of the other planets for one, which do not follow simple paths in relation to a geocentric (i.e. Earth-centred) model.
It is far more reasonable to recognise the Earth as a planet like other planets, rotating on an axis (wobbling a bit) and following a roughly elliptical orbit around the much more massive Sun.
The rotation of the Earth can be detected by the Coriolis effect - an inertial force (a.k.a. fictitous force) observed in a rotating frame of reference. This causes long range projectiles in the northern hemisphere to land to the right of where they are aimed and to the left in the southern hemisphere.