It's often stated that Tycho Brahe objected to Copernicus' heliocentric model on the basis that, if Earth were revolving around the Sun, stellar parallax would be observable, due to the changing position of the Earth.
In describing what model Copernicus and Brahe used for stellar parallax, most things I've seen give an explanation of the more common modern model, in which stars believed to be in the 'foreground' relative to Earth are observed against stars contended to be much further away (For the purposes of the formula, unmoving stars).
This couldn't be the the model meant by Copernicus and Brahe, however; Both believed the stars to be set upon an outer sphere (Although Brahe believed this sphere revolved around Earth and Copernicus believed it to be unmoving), and as such neither would have suggested the version of the stellar parallax model which sets stars contended to be in the 'foreground' against 'background' stars.
My question is, what was actually being contended by Brahe and by Copernicus, respectively? What form of stellar parallax model were they holding to with regards to this?