I was wondering why Tycho Brahe and Johannes Kepler weren’t prosecuted by the Catholic Church like many other astronomers of their time. I tried searching this question up on google to find no helpful articles. Does anyone know?
Because it was never about their astronomical discoveries - it was because Giordano Bruno was an outright heretic (and if you ask me, the most overrated heretic ever, not to mention that his astronomical discoveries amount to exactly zero), and Galileo was being a giant interfering dick at exactly the wrong time. More can always be said from anyone with the knowledge, but for the meantime, here's some previous posts on the matter. Admittedly, they're all about why Bruno and Galileo ran afoul of the Church, but they should serve to show why them, and not why the others.
Aside: I'd just like to reiterate, Bruno got excommunicated by the Roman Catholic and Lutheran and Calvinist churches. Think about that.
Separate from the specifics about Galileo and Bruno's respective persecutions (neither of which were "typical" sorts of things in any event), whether the Catholic Church could prosecute one in the early modern period depended heavily on where one lived. Kepler and Brahe spent their time in largely Protestant lands (Denmark, Germany, etc.) where the Inquisition had no power or jurisdiction. So they were unmolested by them. That doesn't mean they didn't have their own considerations to worry about (Kepler's mother was accused of witchcraft, for example), but it wasn't the same situation as someone in Florence (Galileo) or Venice (Bruno). Even in other Catholic nations, the Inquisition was generally not as imposing a force as it was in Spain and Italy.
I hope the collection of previous answers provided to you by u/DanKensington and u/restricteddata answer (with my own addition in reply to the latter) have clarified at least some of your doubts (of course, you need to read some books because the "Reformation of the Heavens" in sixteenth and seventeenth century is a darn complex matter, especially if you don't have enough knowledge of history of astronomy/celestial mechanics/physics/science in general of the period from Ancient Greece up to 1500). However I'd like to explain why Copernicus himself wasn't prosecuted (after all, heliocentrism started with him). The reason often given to this question, especially by those who still stick to the Draper-White theory just to bolster up their antitheism, is that Copernicus delayed the publication of his magnus opus out of fear for the Inquisition, and he avoided the stake only because he died the same year when De revolutionibus finally came out (1543). It was put on the Index only in 1616 thanks to the infamous preface by Andreas Osiander, stating that the astronomical model described in the book had to be intended just as a mathematical device, not a representation of the physical reality. This is a complete myth. Copernicus wasn't scared by the Inquisition and he wouldn't have faced any consequences if his heliocentric theories had circulated while he was still alive. In fact, they did. Even in the Papal Curia.
A little bit of context. In the fifteenth century, astronomers had grown dissatisfied with the traditional Ptolemaic system. It was way too clunky and convoluted and awkwardly complicated; it went against the common the principles of economy and elegance. Why the heck did the Creator make such a messy universe? So astronomers began coming up with new and better models to explain the sky. One of those was the Polish (actually, Prussian) Nicolaj Kopernik. I don't want to write biographical information about him unnecessary to the purpose of this comment. It's important to note that the hesitation of Copernicus on publishing his theory (on which had began to work already in 1503) wasn't caused by the fear of religious persecution. It had mostly to do with a grounded concern for the reception by physicists (and this was a big problem at the time, being physics on a higher step in the hierarchy of sciences). Actually, his theory lacked on the physics side, and also on "logic". It posed also astronomical problems, like the star size problem. In the decades after Copernicus' death, Copernicans said that this problem was non-existent appealing to the power of the Creator (as in a famous letter by Christoph Rothmann to Brahe).
In any case, that Copernicus held that the Earth is in motion around the Sun, and that he did consider this hypothesis to describe the actual physical reality, was known to a relatively large number of scholars and intellectuals in Europe. Firstly, the Commentariolus (1514), containing the first exposition of his theory, circulated for decades and a lot of members of the clergy read it, including one of Copernicus' closest friends, Bishop Tiedemann Giese, a valent scholar himself. Another one that knew of the Commentariolus was Johann Albrecht Widmanstadtten, German theologian and humanist secretary to Pope Clement VII. He asked Widmanstatten to give a series of lectures about Copernicanism to him and fellow cardinals, and this happened in 1533. The Pope was really pleased by this and awarded his secretary a valuable manuscript. I repeat that Widmanstatten said to him that Copernicus meant what he said, the theory was explained as a description of physical reality, not a calculation device. So, we should imagine the Pope unleashing his inquisitors to interrogate Copernicus, no? It didn't happen, at all. As I said, the Pope was interested in the theory (but didn't "approved" it, as written in the Wikipedia page at te moment I'm writing, nor disproved). Clement died the following year, but that year would have been enough for the Church to start investigation on Copernicus. Widmanstatten then was also a secretary to Clement's successor, Paul III, and then to Archbishop of Padua, cardinal and diplomat Nikolaus von Schoenberg. From his secretary, Schoenberg learned about the Copernican theory, and became really interested in it. He even sent a famous letter in 1536 to the Polish astronomer, urging him to publish his work. So, that the Church was totally unaware of Copernican theory, obviously a pillar of the myth about Copernicus, is nonsense. 10 years passed between 1533 and 1543, even if the Commentariolus was already known to members of the Church even before 1533. Copernicus still hesitated for the reason I provided before. It was Georg Joachim Rheticus that finally convinced him to publish everything. Before this, Rheticus published in 1540-41 the "Narratio Prima", an abstract of the theory, dedicated to Johann Schoner, a German catholic priest and highly praised polymath. It was maybe a way to see the reaction of a catholic. The Narratio was really appreciated by scholars of every religious confession. So, Rheticus and Copernicus decided at last to publish the complete work. The first entrusted the Lutheran theologian and amateur mathematician Andreas Osiander with the task. Osiander sent an interesting letter to Rheticus and Copernicus from Wittenberg, dated 20 April, 1541. It seems that Osiander actually thought something was needed to blunt the reaction of the peripatetics. The replies from the recipients of the letters, unfortunately, have been lost. Osiander had already sent a letter to Copernicus in 1540, but, again, the reply has been lost. As we don't know much about the correspondence, it's difficult to judge Osiander. But the addition of the infamous preface was not authorized by anyone and Giese was enraged when he discovered what Osiander had done (in good faith or bad faith? Scholars are divided on this point). So we cannot know if the religious reactions to the De revolutionibus would have been stronger without the preface (in our timeline, they were negligible). However, anyone who bothered to actually read the book (even only the first ten pages), would've realised that Copernicus' theory wasn't supposed to be a mere calculation device, but a real description of the universe. And astronomers and mathematicians realised that. But in the period 1543-1600, just 9 to 11 astronomers in Europe (out of hundreds) became advocates of the new theory. I won't venture into this period as this comment is already long enough. As for Bruno, he was executed for reasons that had nothing to do with science. In fact, he himself scorned mathematics and empiricism, preferring instead mystical and metaphysical speculations. While scholars are divided on the weight that his cosmological views had in the process (downplayed by Frances Yates and more recently by Hilary Gatti, and on the other hand emphasized by A. Martinez and others), we can rule out heliocentrism. In 1616, the Roman Inquisition had to examine and decide whether the heliocentric theory held by Galileo was heretical or not; as the Inquisition worked also on judiciary precedents, and Bellarmino was the same person that played a major role in Bruno's condemnation, it wouldn't have made sense to investigate again on the heretical status of heliocentrism. So, even if we don't have the final eight propositions that Giordano Bruno had to abjure (if someone says we have them, no we don't), we can rule out heliocentrism, whose teaching as a real representation of the universe was deemed heretical only in 1616, as I said. (Cont.)