Prompted by a question from Brian Cox, on Twitter, I wrote a post outlining the history of Galileo’s engagement with heliocentricity and the Catholic Church giving it the sub-title “A Rough Guide”. This post in turn provoked a series of question and answers on Twitter between myself and my #histsci soul-sister Dr Rebekah “Becky” Higgitt, which I developed into a post on the role played by the observations of the phases of Venus in the gradual acceptance of heliocentricity; a second post to which I added the sub-title “A Rough Guide”. I have now decided to go with the flow and produce a series of posts dealing one by one with the various things that contributed to the gradual transition from a geocentric to a heliocentric astronomy during the sixteenth and seventeenth centuries, each post bearing the sub-title “A Rough Guide”.
The aim is to demonstrate that this transition was not a simple question of the one is right and the other wrong, as it is unfortunately all too often presented today, particularly by those of a gnu atheist persuasion, but that within the context of the times the various factors involved often required subtle and careful interpretation and were not the clear cut evidence that hindsight seems to make them now. For example, I hope I have already achieved this in the post on the phases of Venus. To make it easier for readers to put the whole series together and to form, for themselves, the big picture, I have added a new separate page to the Renaissance Mathematicus, which will contain a list of all the posts, with links.
Suggestions, from readers, for topics to be dealt with in this series are welcome; I already have a list of eight, the first of which will be posted some time next week.
The Renaissance Mathematicus 
Epicycles and simplicity in Ptolemy and Copernicus, perhaps?
Good suggestion.
And the limited and approximate equivalence between Ptolemaic and Keplerian astronomy.
Oh yes, equants.
Oh, wow! Great!
Since you’re asking for suggestions:
A question that bugs me a lot: what was the relative impact of so-called crucial experiments/observations compared with the fall-out from the Principia?
Let’s pretend someone took opinion polls in 1725 and again in 1730, asking what people believed and why. Do we see a big swing? Just among astronomers, or more broadly? Because of Bradley, or because of the 3rd edition of the Principia? Did Guglielmini’s 1789 experiments change many minds, or was it pretty much game before then?
If we did one of those opinion poll timelines, what would it look like?
I also wonder about the impact of popularizations of Principia, like Voltaire’s, and the effect of the vortex theories, which were basically heliocentric, although Descartes claimed neutrality.
Hard questions to answer, I imagine, but I’m sure historians have been digging into these sorts of issues.
My series stops before Newton!
Oh. OK. Does that mean that heliocentrism had pretty much won the day before Newton? Well, I guess you’ll tell us.
What about the precursers? (Nicholas of Cusa, etc.) You’ve touched on them over the years.
Actually, I realize I’m not clear on what you mean by “heliocentrism”. Kinematic only? Physical? Is diurnal motion implied? Maybe you should state your preferred terminology up front.
Just to add the reason for my confusion: you’ve said once or twice that the accuracy of the Rudolphine tables was the decisive factor leading to widespread acceptance of heliocentricity. If this is true for physical and not just kinematic heliocentricity, then I’m curious why that was.
To what extent were people convinced by neo-Platonic number woo-woo (Kepler’s math was so simple and easy compared to Tycho or Copernicus) and to what extent by Aristotelian empiricism (evidence of actual motion).
Why the stars were supposedly much closer than they are: ignorance of Airy disks.
I believe that actually doing computations with Kepler’s system was a deal harder than with the traditional Ptolemaic techniques. (For example, see Victor Thoren, “Kepler’s Second Law in England”, BJHS7:3 pp. 243-258.) Conceptually of course Kepler is simpler — at least if you can make your peace with non-circular motion.
I read somewhere or other that, although the theoretical explanation for Airy disks didn’t arrive until 1835 (from Airy, of course), it was known well before then, just from better instruments, occultations, etc., that the apparent stellar disk sizes weren’t real. Unfortunately I can’t find the reference.
Yeah. I love that Thoren article. Also, Noel Swerdlow, in his article on Maria Cuhna (I can’t remember the title), remarks that it takes three times longer to calculate a position with the Rudolphine Tables than with any of the other competing tables available at the time. Plus, no closed form solutions!
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What kinds problems, mathematical, theoretical, practical, were not solved by the various systems.
How pressing were these problems to the scientific community and to the public?
What were the actual stumbling blocks, be they philosophical, political, scientific or religious, to the acceptance by the Church and 17th c. astronomers of the Heliocentric system?
The role of almanacs?
Changing ideas about instrumentalism vs. realism in astronomy?
There are several good suggestions in the comments above, some of which were already on my list the others I have now added. However some of you have obviously not understood the general title, A Rough Guide. The idea is to write articles that are simple, uncomplicated, without too many technical details but which are factually accurate for non experts. Some of the discussion above are too technical and advanced to fit into this concept. However those knowledgeable commentators are more than welcome to add such details in the comments as they see fit.