OK, raise your hand if you knew that the in the 1600’s advocates of the heliocentric view appealed to God’s greatness to answer geocentric arguments. Yep. In fact, the “size of the star” issue was not fully resolved until the 1800s. The point is that the debate was not purely religion (geo) vs. science (helio). The geo advocates had scientific arguments that were not fully answered until the 1800s, and the helio advocates sometimes resorted to religious arguments. Anyone who has followed the standard history of the so-called war of religion against science would be surprised to learn there was nuance. John Hartnett writes:
The size of stars argument went as follows. Sizes of stars were first measured by eye, before the invention of the telescope. That is what Tycho Brahe spent much of his time doing. That gives a ‘magnitude’ for a star, catalogued as magnitudes 1 through 6, with 1 the largest and 6 the smallest. Of course, large meant bright and small meant dim. It was based on these ‘measured’ sizes of stars that Tycho Brahe developed an argument against Copernicus.
Then with the invention of the telescope, it was observed that the star sizes were at least 10 times smaller. But because the astronomers also observed solid disks for the planets out to Saturn (and even phases for Venus) it was then believed that the telescope gave the true sizes of the stars also. Based on telescopic measurements of the star sizes Riccioli formulated a version of the Brahe argument against the heliocentric system and in favour of the geocentric Tychonic system.
With the telescope astronomers looked for parallax of the distant stars but were not able to detect any parallax. In the geocentric universe the earth is immobile and hence no parallax would be expected. In the heliocentric universe, the earth orbits the sun once per year, and in so doing over a 6 month period moves from one side of its orbit to the other. Therefore based on trigonometry a foreground star should be seen to move against the more distant background stars between these two extrema. But of course the orbit is circular. Therefore if a star is close enough it should trace out a circle on the sky as seen from earth over the solar year.
Thus the argument followed that if a star was seen to have a certain size but it was too distant to exhibit any parallax then it must be massively large, at least as large as the orbit of the earth around the sun. It was argued that that must be the case otherwise no disk for the star could be observed. The only response the Copernican astronomers had to that was that God is a great God and He made such large stars for His own glory. Riccioli argued that it was not the geocentrists who appealed to authority but the heliocentrists, in their answer to the ‘size of stars’ argument. [more]