Anime

That is a good point. If people are unfamiliar with the history of this time period, they might mistake this as being more accurate than it actually is. This is clearly a very fictionalized version of our world. Even the torture implement we see Nowak walking around with (the pear of anguish) most likely did not exist during this time period and was merely imagined hundreds of years later.

Anyway, you have given me an excuse to nerd out about some science history, so I will gladly take it...

The most famous prosecution of geocentrism by the church is likely Galileo. His use of the telescope and observations of both the four large moons of Jupiter (we still call them the Galilean Moons) as well as the phases of Venus were strongly supportive of a heliocentric solar system and could not be explained in a Ptolemaic system. However, Jesuit astronomers at the time were able to replicate his findings and did not dispute him. Instead, it caused most geocentric scholars of the time to support a variation on the heliocentric model that was earlier developed by Tycho Brahe (an outstanding astronomer btw), called the Tychonic System. This model had the Earth in the center of the solar system, and the Sun orbiting the Earth. However, all the rest of the planets orbited the Sun, just like in the heliocentric model:

In the absence of an understanding of the force of gravity (which Newton won't publish for another 100 years), this model actually works very well. It was basically the most accurate predictor of astronomical objects of its day. The heliocentric model wouldn't become more accurate until after Kepler's laws of planetary motion fully described the planet's orbits as ellipses instead of circles a couple decades later (like you mentioned). Kepler actually used the incredibly precise measurements made by Tycho Brahe to prove the accuracy of his model.

Anyway...back to Galileo. He was prosecuted twice. The first time he was basically just told to stop teaching about heliocentrism. He then proceeded to write a whole book about it in which he thinly veils calling the pope an idiot the whole way through. This is most likely what led to his second prosecution as church scholars of the time didn't look kindly on calling the infallible pope stupid. However, even after all that, he was only ever placed under house arrest until he eventually died.

One of the only natural philosophers of the time that I know of that was actually executed is Giordano Bruno. He publicly espoused heliocentrism, was eventually tried by the Inquisition, and then executed. However, heliocentrism is only one of many, many heretical things that he advocated. Some others would be pantheism (nature is God essentially) as well as reincarnation of the soul (directly contravening the church's doctrine of an afterlife). These beliefs were much more transgressive than his heliocentrism advocacy.