Regarding how Tycho Brahe noted the absurdity of the Copernican Theory   regarding the Bigness of Stars, while the Copernicans appealed to God to   answer that absurdity
  Tycho Brahe, the most prominent and accomplished astronomer of his era, made measurements of the apparent sizes of the Sun, Moon, stars, and planets. From these he showed that within a geocentric cosmos these bodies were of comparable sizes, with the Sun being the largest body and the Moon the smallest. He further showed that within a heliocentric cosmos, the stars had to be absurdly large - with the smallest star dwarfing even the Sun. (The results of Tycho's calculations are illustrated in this paper.) Various Copernicans responded to this issue of observation and geometry by appealing to the power of God: They argued that giant stars were not absurd because even such giant objects were nothing compared to an infinite God, and that in fact the Copernican stars pointed out the power of God to humankind. Tycho rejected this argument. 
Christopher M. Graney
physics.hist-ph physics.pop-ph