Here is a new paper:
In his 1606 De Stella Nova, Johannes Kepler attempted to answer Tycho Brahe's argument that the Copernican heliocentric hypothesis required all the fixed stars to dwarf the Sun, something Brahe found to be a great drawback of that hypothesis. This paper includes a translation into English of Chapter 16 of De Stella Nova, in which Kepler discusses this argument, along with brief outlines of both Tycho's argument and Kepler's answer (which references snakes, mites, men, and divine power, among other things). ...Here is the star size objection. Under a Copernican heliocentric model, the stars must be very far away, much farther than any known distances. Furthermore, the optics of the day made the stars appear to have a noticeable diameter that would make them unimaginably huge if they were really so far away.
Answers such as these to Brahe’s star size objection to Copernicus would endure. In 1651 Giovanni Battista Riccioli in his Almagestum Novum analyzed one hundred and twenty six proand anti-Copernican arguments, concluding that the vast majority in either direction were indecisive. As he saw it, there were two decisive arguments, both in favor of the antiCopernicans: one was the absence of any detectable Coriolis Effect (as it would be called today);6 the other was Brahe’s star size objection.
The apparent diameters were later understood to be spurious artifacts of diffraction. The stars are not really so large.
Kepler's arguments are interesting, but do not resolve the matter. Nothing truly resolves the matter, because choosing a frame of reference is not a scientific question. You can say that a Sun-centered frame is closer to being inertial, or that the large size of the Sun compared to the Earth makes it more reasonable to think of the Earth as moving, but that's about all.