Star Size Illusion

On the topic of the size of the stars, see this story which describes that some of the visible stars are truly huge:

The Popular Creation Story of Astronomy Is Wrong (Archive)

  “ Astronomers dating all the way back to Ptolemy during the second century had determined that the more prominent of those star dots measure somewhere in the range of one-tenth to one-twentieth the diameter that the round moon appears to be. In On the New Star, Kepler said bright stars measure one-tenth the moon’s diameter, Sirius a bit more.

...An astronomer who believed Copernicus, and believed math, simply had to believe that all the stars were huge. ”

Under a model with distant stars it would need to be of tremendous proportions, and was one of the early controversies in astronomy. The geocentric model's closer stars seemed more reasonable. Some Copernicans claimed the mystery of God and later ones postulated an 'optical illusion'.

Also see this Scientific American article about the history of Heliocentrism vs. Geocentrism starting on p.75:

The Case Against Copernicus — Scientific American

  “ Copernicus’s revolutionary theory that Earth travels around the sun upended more than a millennium’s worth of scientific and religious wisdom. Most scientists refused to accept this theory for many decades—even after Galileo made his epochal observations with his telescope. Their objections were not only theological. Observational evidence supported a competing cosmology—the “geoheliocentrism” of Tycho Brahe. Copernicus famously said that Earth revolves around the sun. But opposition to this revolutionary idea didn’t come just from the religious authorities. Evidence favored a different cosmology. ”