Proving the Earth's orbital motion.

The RA/Dec observers try their level best to equate circumpolar motion to daily rotation and that uses up the observation of the motion of the stars -

https://www.youtube.com/watch?v=BYy0EQBnqHI

The astronomers at the time of Copernicus were using the motion of the Sun through the constellations along with the motions of the other planets for prediction purposes but they never used a North/South motion of the Sun by inventing a celestial Equator -

"Moreover, we see the other five planets also retrograde at times, and
stationary at either end [of the regression]. And whereas the sun
always advances along its own direct path, they wander in various
ways, straying sometimes to the south and sometimes to the north; that
is why they are called "planets" [wanderers]. Copernicus


The most accurate question a student could ask is why some stars disappear as an evening appearance, remain out of sight and then return as a morning appearance insofar as this is proof of the Earth's orbital motion -

https://www.youtube.com/watch?v=eeQwYrfmvoQ

The simple act of removing the relationship of daily rotation to circumpolar motion and using the orbital motion of the Earth to account for the changing relationship between the fixed stars and the central Sun is paramount and seen in in actuality -

https://www.youtube.com/watch?v=MdFrE7hWj0A