You have what is considered to be a rather "pop" understanding of this which is considered quite wrong by historians of science. This is not really your fault, since this has been a popular way of talking about science since the 19th century, because it allows for an easy categorization of "heroes" and "villains," but it is wrong nonetheless.

"Scientific inquiry" is a very broad term. The study of astronomy for the purpose of calculating calendars and understanding orbits and the like was done for centuries. In Europe it was generally sponsored by the Church. This was both because they had general interests in these matters and because it involved perfecting the calendar which was important for determining feast days, agricultural cycles, and the like.

In the time from Copernicus through Galileo's life, it was generally considered (not just by the Church but by many educated people in Europe) that there was a distinct difference between philosophy and mathematics. What Copernicus did that was unusual for his time was not to inquire into how the planets moved but to imply that a mathematical model could overturn a philosophical model. From the perspective of early modern philosophy, the geocentric nature of the universe was ultimately a form of deductive reasoning (from both the Bible and the Greeks, who were seen as having a connection to knowledge deeper than what was currently available) which was seen as more reliable than scattered inductive reasoning. To put it another way that might make more sense, the philosophy of the day said that rock-hard-logic was more reliable than the random claims and observations of people you didn't necessarily trust to be reliable observers. So to say, "oh, hey, I've taken knowledge from this one domain, combined it with some observations, and now I want you to consider this a valid change to a major piece of philosophy" — this was an odd thing. Especially considering that Copernicus' model didn't actually work any better with the known observations (because, it turns out, a circular heliocentric model does not work, and an epicyclical Ptolemaic model, while not ideal, hypothetically has enough complexity in it that you can adapt it to a lot of observations loosely).

Between Copernicus and Galileo there was plenty of astronomical research and refinement of cosmological models, often by astronomers working inside the Church. The Jesuits in particular were very keen on this. They were not intellectual slouches in the least and were every bit as "scientific" as anyone else at the time. There were also those outside of the Church making observations and models. Brahe made exceedingly good observations for his day and developed an alternative heliocentric model (which is functionally equivalent to Copernicus' model); Kepler helped derive several important refinements though he also introduced a lot of other weirdness that today we tend to ignore when we focus on the parts that were judged "correct" by later scientists. (Kepler had a lot of nutty mystical astronomical beliefs as well.)

In different parts of Europe the political and economic context of "natural philosophy" (as it was called in England; the term "science" was not used) was very different. In England for example the Catholic Church obviously had less power post-Reformation. In Galileo's Italy, the politics of the Church were much more important. Galileo's own work is steeped in the patronage system of his time, and he pushed much further than others on the idea that mathematical models could influence philosophical worldviews. Of his new astronomical observations, which were all enabled by the invention of the telescope, only one caused the Church astronomers any serious contention: the phases of Venus, which clearly ruled out a Ptolemaic cosmology. The Jesuit astronomers recognized this was the case (after they had ruled out that it was a problem of interpretation or observation, since Galileo was not especially willing to share his work or his tools with them) and switched the official Church cosmology to the Tychonian system fairly soon afterwards.

Galileo had his own philosophical reasons for preferring the Copernican system to the Tychonian one — it was not based on any hard evidence (they were, at the time, indistinguishable from an observational standpoint). So his insistence in arguing for the Copernican system and even phrasing the debate as being between the Copernican and Ptolemaic systems, instead of the Copernican and Tychonian, was somewhat disingenuous, and his persistence in doing this at a time when the Church was under immense pressure to consolidate its remaining power is considered by scholars to be what really landed him in hot water, not the fact that he made observations and conclusions from them. From the Church's perspective, Galileo exceeded any mandate given him by his observations and was, in their mind, making a direct attack on the authority of the Church itself.

Newton was well-respected but remember he lived both later and in England. The English had their own religious issues but Copernicanism was not really part of that. (Newton was himself highly motivated by his own unusual religious beliefs which were a little beyond the pale for the English Church, so he kept them mostly secret. Along with his obsession with alchemy.) Once Newton became respected and powerful he used his position to persecute people who he thought were wrong, problematic, philosophically out-to-lunch as well. (He, of course, lacked the power of the Church, so that persecution took a more academic form.)

Anyway. There is much more that can be said — you are essentially asking, "what's up with early modern science?" which is an entire field of study. I hope the above just points to some of the complexity of the issues, the fact that you are talking about a span of several centuries (16th-18th centuries), a complex set of changing political/theological/economic/technologicalcircumstances. Most historians of science today would not support the assertion that the Church was actually hostile to scientific inquiry in general, they would not credit any individual with radically changing the situation, and they would instead say that if there was a "scientific revolution" that it is best characterized as slow and subtle change views towards the use of mathematics, inductive reasoning, and a change in the scope of what was considered to be philosophical/theological/natural questions, along with changing professional circumstances. (By Newton's time, the idea that you could be an independent "natural philosopher" was established, whereas it was not in Copernicus' time, and "science" itself didn't really professionalize fully until the 19th century.)

Historiographically, the reason that the science vs. religion way of talking about this (known as the "Conflict model" of the history of science) is so enduring is that it is part of the professionalization of science — it is a way for scientists to say, "hey, we are important, and we claim so-and-so as one of us, and also his/her achievements!" It makes good sociological sense but like many such approaches it is not very historically sound, as it makes sharp distinctions out of fuzzy boundaries, homogenizes what is heterogenous, and sometimes outright distorts things.

If you are interested, here is a short reading list of some of the "basic" books on this subject:

• Steven Shapin, The Scientific Revolution: "There was no such thing as the Scientific Revolution, and this is a book about it."

• Shapin and Schaffer, Leviathan and the Air-Pump: on the deductive/inductive question in post-Restoration England (aka Hobbes vs. Boyle)

• James Lattis, Between Copernicus and Galileo: on Jesuit astronomy in the 16th-17th centuries

• Mario Biagioli, Galileo, Courtier: on Galileo's professional and political context

• Richard Westfall, Never at Rest: the definitive Newton biography

• Peter Dear, Discipline and Experience: on the changing epistemological status of mathematics during the 16th-17th century and its importance in the "Scientific Revolution"

Holy makeral, this is an enormous question. I've tried to answer it and it got unbelievably long, so let me try to touch on some of the factors involved.

First of all, a thing you should note is "in a similar time period" is a problematic assertion here. Copernicus' De Revolutionibus, was published in 1543 shortly before his death. Newton's Principia was published in 1687 and he went on to have a career well into the 18th century. That's nearly 150 years between text. What happened in those 150 years is part of your answer and it is a huge amount of history. They are not living in a similar time period.

Second of all, "scientific inquiry" is a long conversation by itself. What is "scientific inquiry"? And what is "acceptable"? Clearly, Copernicus' heliocentricism was acceptable to many people, it just wasn't accepted or considered important or real until years later--when it suddenly was controversial, until it was acceptable again. By this example, scientific inquiry still isn't all that acceptable. Many people in the world do not fully buy scientific argument and yet to do science is very acceptable.

"Doing Astronomy" was acceptable for all four of the men you mentioned above. What wasn't necessarily acceptable happens in the details, and a lot of the issues these people faced weren't about science at all, but about politics (individual or general), religion (individual or general) or about what they believed their particular brand of mathematics could do.

Some of the issues that are at stake in that 150 Years and within those four people:

• Religious Upheval or Lack Thereof (Catholics vs. Protestants vs. ?)

Kepler and Galileo are the closest in time and belief here and had different experiences with respect to the church(es). Part of that is down to the differences in religion between Northern and Southern Europe. Copernicus was closely affliated with and supported by the church but no formal opposition to heliocentricism existed at the time of his publication. Kepler was a Calvinist and that was a problem for a while, but his astronomy was not.

• Political affiliation and visibility

Galileo was a highly visible astronomer with (read more in Galileo, Courtier) strong political affiliations. Kepler also had strong religious and political affliations. Both were to some extent shunted around by the great and powerful who employed them but faced different challenges and rules.

• Physics vs. Astronomy vs. Cosmology

When Copernicus was writing, astronomy was a mathematical discipline largely limited to predictions for the movements celestial bodies, mostly for astrological purposes. It had little connection to cosmology (although I think its highly arguable that Copernicus was advancing a theory intended to be real, not merely handy) and even less connection to physics. Kepler, on the other hand, as well as assuming cosmological implications for his observations (as Galileo did) slammed Physics into his astronomy in a way that was overlooked until the latter part of the 17th century.

This was problematic for many partly just because it was new, but also because of its cosmological and theological impacts.

The Book that Nobody Read is a great text covering the progression of Copernicus' ideas through Europe in the second half of the 16th century and on into Galileo's time.

• Type of Evidence

Galileo's early use of evidence found with a telescope (e.g. the phases of the inner planets) is very different from Kepler's and Copernicus' use of mathematics. He was popularly known among the intelligensia, rather than just the academics of his field.

• Development of Evidence as Supporting Discovery

I wrote a paper that traced the use of evidence (actually, experiment) in the 16th century. I found a distinctive difference between things written in the beginning half of the 16th century (when Copernicus was writing) and the end (around where Kepler and Galileo began their work).

My paper focused partly on the less academic use of evidence--navigators and such writing practical books for practical use. I wanted to see how experiment and evidence came out of unequivocal experience of, say, the ancients being wrong about the geography of the world or claims about magnets and garlic.

It wasn't a great paper, but I did notice a progressive change towards the popular expectation of and reliance on claims of experiential evidence over the course of the 16th century. What was seen or experienced became more meaningful, over references to authority. Readers and writers were accepting more that there would be some modern-day proof that could be shown and tested and experienced for yourself, that could back up what was asserted.

I think this change must have some relevance to how Galileo and Kepler's ideas were received, Galileo particularly. He could say, "hey look through the telescope, you can see for yourself!" and that was both an expected and accepted practice in a variety of fields. The "general population" (e.g. the wealthy and/or educated) expected new ideas to be put forth and then in order for those ideas to stand against received knowledge, had a mechanism to determine which one was right.

Ultimately, I think the short and scrappy answer to your question is that scientific enquiry came into its own sometime at the beginnning of the 17th century, around when Galileo published Siderius Nuncius. By then, people seemed to be starting to be consistantly convinced of new ideas with real-world applications and implications by new evidence or argument or experiment.

Uh, this was kind of shoddy, but if you have any questions, ask them and I'll see what I can add!