Imagine trying to make sense of outside motions while being on a carousel yet this is exactly what celestial sphere proponents did by giving a North/South/East/West (RA/Dec) framework priority -

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

The foundation of astrophysics is based on a notion that the Sun about the Earth and the Earth about the Sun are equivalent in terms of observations however the Sun around the Earth is taken up by daily rotation whereas the Sun through the constellations is the closest to the Earth's orbital motion.

It is no wonder people over the last 20 years in this newsgroup haven't a clue how to deal with Huygen's geocentric/heliocentric equivalency that is related to the Equation of Time even though it is flawed -

"Here take notice, that the Sun or the Earth passes the 12 signs
or makes an entire revolution in the ecliptic in 365 days, 5 hours 49
min. or there about, and that those days, reckoned from noon to noon,
are of different lengths; as is known to all that are versed in
Astronomy. Now between the longest and the shortest of those days, a
day may be taken of such a length, as 365 such days, 5. hours &c. (the
same numbers as before) make up, or are equal to that revolution: And
this is called the Equal or Mean day, according to which the watches
are to be set; and therefore the hour or minute showed by the watches,
though they be perfectly just and equal, must needs differ almost
continually from those that are showed by the Sun, or are reckoned
according to its motion. But this difference is regular, and is
otherwise called the Equation of Time.." Huygens

While entertaining in its own way, most if not all of you imitate Newton who made things up as he went along but, unlike the nuisances here, he did it in a very careful way - more like the actions of a politicians filling in deficiencies and gaps while appearing to affirm astronomical or timekeeping principles, even flawed ones.

I have seen the ground where mathematicians can work productively and with great creativity and that is what is so dismaying, they would rather lean on old familiar junk like solar vs sidereal time than act to clean up a mess they created.