How can one prove, based on observations of the starry sky, that the Earth rotates around its own axis and that the rotation

How can one prove, based on observations of the starry sky, that the Earth rotates around its own axis and that the rotation occurs from west to east?

If the Earth did not rotate, then the frame of reference associated with a point on its surface would be inertial (IFR). In IFR, free bodies, which can be considered stars, would remain motionless on the celestial sphere.
The daily rotation of the starry sky unambiguously indicates the rotation of the topocentric frame of reference, i.e., the rotation of the Earth. The daily movement of celestial bodies from east to west indicates the rotation of the earth from west to east.

Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.