I've only read the first chapter, but it seems to underplay the enourmous role the Ptolemaic System and Aristotelian thought had in early modern cosmology, and overplay the role of the Catholic church in preserving geocentrism.
Some historical points to make on the topic which may help as we're reading this. I'm not accusing the manga of this, but it's worth remembering as we read:
1. The medieval world thought that the center of the cosmos was corrupted with hell in the middle and the earth around it, whereas the heavens were where God dwelled. They did not think that the heavens revolved around the earth because it was special or perfect. Surrounding to isolate and stop the spread of evil would be closer to their view.
Part of the revulsion towards heliocentrism was because it included the heavenly sun in the earth's ignominy. They felt heliocentrism dragged the heavens down to the earth's level.
Modern writers are not often cognizant of this view and sometimes erroneously ascribe geocentrism to some kind of pro-earth chauvinism.
2. Initially the Catholic church was amenable to heliocentrism. Copernicus dedicated his work on heliocentrism to the current pope at the time.
3. Everyone, including Copernicus and Galileo, wrongly assumed spherical rather than the actual elongated orbits, and though the math didn't work well for either model under that assumption, it worked slightly better for the old geocentric model. Particularly for the movement of the moon which actually does orbit the earth, but also the stars which don't orbit either the earth or the sun.
4. The Catholic church only came down on the side of geocentrism after a series of actual scholarly debates between Galileo and Pope Urban VIII, who were former friends. Pope Leo had written a scholarly treatise and as part of the debate Galileo was supposed to refute it. Instead Galileo created an idiot strawman character called "Simpleton" to represent Pope Urban and parrot his claims which he then argued against. Urban was already worried about assassination and court intrigue so this went over about as well as expected. A trial was convened and Galileo was sentenced to house arrest. He was still allowed to go out as long as he didn't leave the city, and was buried in the Basilica of Santa Croce.
5. To my knowledge no scholar was ever tortured, let alone burned at the stake for advocating Copernican heliocentrism. Just as with modern scientific heretics they usually just lost their funding and their university positions.
6. This was only a problem in Catholic Europe. Protestant Europe embraced heliocentrism, although initially because the Catholics rejected it and screw those guys. Which is why Isaac Newton could freely publish "Philosophiæ Naturalis Principia Mathematica" just 50 years after Galileo's trial, which provided an explanation for Kepler's laws in terms of universal gravitation and what came to be known as Newton's laws of motion.