If you accept the one, you accept that the wobble isn’t terrestrial, but is more of a swirl in the movement of the sun, the moon, the planets and all celestial bodies.
There are some beautiful old lithographs showing such movement from that perspective, planets “kissing” and such, the music they made with the harmonies formed. The planets known to the ancients represented musical notes.
Speaking of which.... all this talk about pre-Copernican attitudes about the center of the solar system must be understood from a comparison.
It is like the Victorian era. When they used to cover piano legs with skirts in the name of modesty.
The point was, it was a temporary thing. The ancients knew darn well what was the center of the solar system, and they knew 'before' Copernicus was even born the exact number of planets (including Pluto), and their 'maps' show the Sun as the center.
Most of the Earth centered conceptualism seems to have been borne from the early church, meant in a spiritual way, and then some 'lord' thought it would help his candidacy if he voted it into law.
Point is, it was not an 'original' belief of the past civilizations.