Comets and Heliocentricity: A Rough Guide

In the standard mythologised history of astronomy of the Early Modern Period comets are only mentioned once. We get told, in classical hagiographical manner, how Tycho Brahe observed the great comet of 1577 and thus smashed the crystalline spheres of Aristotelian cosmology freeing the way for the modern astronomy. That’s it for comets, their bit part in the drama that is the unfolding of the astronomical revolution is over and done with, don’t call us we’ll call you. The problem with this mythological account is that it vastly over emphasises the role of both Tycho and the 1577 comet in changing the view of the heavens and vastly under rates the role played by comets and their observations in the evolution of the new astronomy in the Early Modern Period. I shall deal with the crystalline spheres and their dissolution in a separate post and for now will follow the trail of the comets as they weave their way through the fifteenth, sixteenth and seventeenth centuries changing our perceptions of the heavens and driving the evolution of the new astronomy. I have dealt with various aspects of this story in earlier posts but rather than simple linking I will outline the whole story here.

In antiquity comets were a phenomenon to be marvelled at and to be feared. Strange apparitions lighting up the skies unpredictably and unexplainably, bringing with them, in the view of the astrology priests of earlier cultures, doom and disaster. As with almost all things Aristotle had categorised comets, fitting them into his grand scheme of things. Aristotle’s cosmology was a cosmology of spheres. In the centre resided the spherical earth, on the outer reaches it was enclosed in the sphere of the fixed stars. Between theses two were the spheres of the planets centred on and spreading outwards from the earth, Moon, Mercury, Venus,  Sun, Mars, Jupiter Saturn. This onion of celestial spheres was split into two parts by the sphere of the moon. Everything above this, superlunar, was perfect, unchanging and eternal, everything below, sublunar, imperfect, constantly changing and subject to decay. For Aristotle comets were a sublunar phenomenon and were not part of astronomy, being dealt with in his Meteorology, his book on atmospheric phenomena, amongst other things.

However Aristotle’s was not the only theory of comets in ancient Greek philosophy, the Stoics, whose philosophy was far more important and influential than Aristotle’s in late antiquity had a very different theory. For the Stoics the cosmos was not divided into two by the sphere of the moon but was a single unity permeated throughout by pneuma (whatever that maybe!). For them comets were not an atmospheric phenomenon, as for Aristotle, but were astronomical objects of some sort or other.

In the High Middle Ages as higher learning began to flourish one more in Europe it was Aristotle’s scientific theories, made compatible with Christian theology by Albertus Magnus and his pupil Thomas Aquinas, that was taught in the newly founded universities and so comets were again treated as atmospheric phenomena up to the beginning of the fifteenth century.

The first person to view comets differently was the Florentine physician and mathematicus Paolo dal Pozzo Toscanelli (1397–1482), best known for his letter and map supplied to the Portuguese Crown confirming the viability of Columbus’ plan to sail westwards to reach the spice islands. In the 1430s Toscanelli observed comets as if they were astronomical object tracing their paths onto star-charts thereby initiating a new approach to cometary observation. Toscanelli didn’t publish his observations but he was part of a circle humanist astronomers and mathematicians in Northern Italy who communicated with each other over their work both in personal conversation and by letter. In the early 1440s Toscanelli was visited by a young Austrian mathematician called Georg Aunpekh (1423–1461), better known today by his humanist toponym, Peuerbach. We don’t know as a fact that Toscanelli taught his approach to comet observation to the young Peuerbach but we do know that Peuerbach taught the same approach to his most famous pupil, Johannes Müller aka Regiomontanus (1436–1476), at the University of Vienna in the 1450’s. Peuerbach and Regiomontanus observed several comets together, including Halley’s Comet in 1456. Regiomontanus wrote up their work in a book, which included his thoughts on how to calculate correctly the parallax of a comparatively fast moving object, such as a comet, in order to determine its distance from earth. The books of Peuerbach and Regiomontanus, Peuerbach’s cosmology, New Theory of the Planets, published by Regiomontanus in Nürnberg in 1473, and their jointly authored epitome of Ptolemaeus’ Almagest, first published in Venice in 1496, became the standard astronomy textbooks for the next generation of astronomers, including Copernicus. Regiomontanus’ work on the comets remained unpublished at the time of his death.

Whereas in the middle of the fifteenth century, as Peuerbach and Regiomontanus were active there were very few competent astronomers in Europe the situation had improved markedly by the 1530s when comets again played a central role in the history of the slowly developing new astronomy. The 1530s saw a series of spectacular comets that were observed with great interest by astronomers throughout Europe. These observations led to a series of important developments in the history of cometary observation. Johannes Schöner (1477–1547) the Nürnberger astrologer-astronomer published Regiomontanus’ book on comets including his thoughts on the mathematics of measuring parallax, which introduced the topic into the European astronomical discourse. Later in the century Tycho Brahe and John Dee would correspond on exactly this topic. A discussion developed between various leading astronomers, including Peter Apian (1495–1552) in Ingolstadt, Nicolaus Copernicus (1473–1543) in Frauenburg, Gemma Frisius (1508–1555) in Leuven and Jean Péna (1528 or 1530–1558 or 1568) in Paris, on the nature of comets. Frisius and Pena in Northern Europe as well as Gerolamo Cardano (1501–1576) and Girolamo Fracastoro (circa 1476–1553) in Italy propagated a theory that comets were superlunar bodies focusing sunlight like a lens to produce the tail. This theory developed in a period that saw a major revival in Stoic philosophy. Apian also published his observations of the comets including what would become known, incorrectly, as Apian’s Law that the tails of comets always point away from the sun. I say incorrectly because this fact had already been known to Chinese astronomers for several centuries.

These developments in the theory of comets meant that when the Great Comet of 1577 appeared over Europe Tycho Brahe (1546–1601) was by no means the only astronomer, who followed it’s course with interest and tried to measure its parallax in order to determine whether it was sub- or superlunar. Tycho was not doing anything revolutionary, as it is normally presented in the standard story of the evolution of modern astronomy, but was just taking part in in a debate on the nature of comets that had been rumbling on throughout the sixteenth century. The results of these mass observations were very mixed. Some observers failed to make a determination, some ‘proved’ that the comet was sublunar and some, including Tycho on Hven, Michael Maestlin (1550–1631), Kepler’s teacher, in Tübingen and Thaddaeus Hagecius (1525–1600) in Prague, all determined it to be superlunar. There were many accounts published throughout Europe on the comet the majority of which still favoured a traditional Aristotelian astrological viewpoint of which my favourite was by the painter Georg Busch of Nürnberg. Busch stated that comets were fumes that rose up from the earth into the atmosphere where they collected and ignited raining back down on the earth causing all sorts of evils and disasters including Frenchmen.

On a more serious note the parallax determinations of Tycho et al led to a gradual acceptance amongst astronomers that comets are indeed astronomical and not meteorological phenomena, whereby at the time Maestlin’s opinion probably carried more weight than Tycho’s. This conclusion was given more substance when it was accepted by Christoph Clavius (1538–1612), who although a promoter of Ptolemaic astronomy, was the most influential astronomer in Europe at the end of the sixteenth century.

By the beginning of the seventeenth century comets had advanced to being an important aspect of astronomical research; one of the central questions being the shape of the comets course through the heavens. In 1607 the English astronomer, Thomas Harriot (circa 1560–1621), and his friend and pupil, the MP, Sir William Lower (1570–1615), observed Halley’s Comet and determined that its course was curved. In 1609/10 Harriot and Lower became two of the first people to read and accept Kepler’s Astronomia Nova, and Lower suggested in a letter to Harriot that comets also follow elliptical orbits making him the first to recognise this fact, although his view did not become public at the time.

The comet of 1618 was the source of one of the most famous disputes in the history of science between Galileo Galilei (1564–1642) and the Jesuit astronomer Orazio Grassi (1583–1654). Grassi had observed the comet, measured its parallax and determined that it was superlunar. Galileo had, due to an infirmity, been unable to observe the comet but when urged by his sycophantic fan club to offer an opinion on the comet couldn’t resist. Strangely he attacked Grassi adopting an Aristotelian position and claiming that comets arose from the earth and were thus not superlunar. This bizarre dispute rumbled on, with Grassi remaining reasonable and polite in his contributions and Galileo becoming increasingly abusive, climaxing in Galileo’s famous Il Saggiatore. The 1618 comet also had a positive aspect in that Kepler (1571–1630) collected and collated all of the available historical observational reports on comets and published them in a book in 1619/20 in Augsburg. Unlike Lower, who thought that comets followed Keplerian ellipses, Kepler thought that the flight paths of comets were straight lines.

The 1660s again saw a series of comets and by now the discussion amongst astronomers was focused on the superlunar flight paths of these celestial objects with Kepler’s text central to their discussions. This played a significant role in the final acceptance of Keplerian elliptical heliocentric astronomy as the correct model for the cosmos, finally eliminating its Tychonic and semi-Tychonic competitors, although some Catholic astronomers formally continued paying lip service to a Tychonic model for religious reasons, whilst devoting their attentions to discussing a heliocentric cosmos hypothetically.

The 1680s was a fateful decade for comets and heliocentricity. John Flamsteed (1646–1719), who had been appointed as the first Astronomer Royal in Greenwich in 1675, observed two comets in 1680, one in November and the second in mid December. Flamsteed became convinced that they were one and the same comet, which had orbited the sun. He communicated his thoughts by letter to Isaac Newton (1642–1727) in Cambridge, the two hadn’t fallen out with each other yet, who initially rejected Flamsteed’s findings. However on consideration Newton came to the conclusion that Flamsteed was probably right and drawing also on the observations of Edmund Halley began to calculate possible orbits for the comet. He and Halley began to pay particular attention to observing comets, in particular the comet of 1682. By the time Newton published his Principia, his study of cometary orbits took up one third of the third volume, the volume that actually deals with the cosmos and the laws of motion and the law of gravity. By showing that not only the planets and their satellite systems obeyed the law of gravity but that also comets did so, Newton was able to demonstrate that his laws were truly universal.

After the publication of the Principia, which he not only edited and published but also paid for out of his own pocket, Halley devoted himself to an intense study of the historical observations of comets. He came to the conclusion that the comet he had observed in 1682, the one observed by Peuerbach and Regiomontanus in Vienna in 1456 and the one observed by Harriot and Lower in London in 1607 were in fact one and the same comet with an orbital period of approximately 76 years. Halley published the results of his investigations both in the Philosophical Transactions of the Royal Society and as a separate pamphlet under the title Synopsis of the Astronomy of Comets in 1705. Halley determined the orbit of the comet that history would come to name after him and announced that it would return in 1758. Although long lived Halley had no hope of witness this return and would never know if his was right or not. Somewhat later the French Newtonian astronomer and mathematician Alexis Clairaut (1713–1765) recalculated the return date, introducing factors not considered by Halley, to within a one-month error of the correct date. The comet was first observed on Newton’s birthday, 25 December 1758 and reached perihelion, its nearest approach to the sun, on 13 March 1759, Clairault had predicted 13 April. This was a spectacular empirical confirmation of Newton’s theory of universal gravity and with it of heliocentric astronomy. Comets had featured in the beginnings of the development of modern astronomy in the work of Toscanelli, Peuerbach and Regiomontanus and then in the final confirmation of that astronomy with the return of Halley’s Comet having weaved their way through they whole story over the preceding 350 years.




Filed under History of Astronomy, History of science, Newton, Renaissance Science

23 responses to “Comets and Heliocentricity: A Rough Guide

  1. A beautiful post, as usual.

    Somewhat later the French Newtonian astronomer and mathematician Alexis Clairaut (1713–1765) recalculated the return date, introducing factors not considered by Halley, to within a one-month error of the correct date.

    Craig Waff has written a nice article about this, “Predicting the mid-eighteenth-century return of Halley’s Comet” (in Planetary astronomy from the Renaissance to the rise of astrophysics, CUP 1995), with an appendix by Curtis Wilson on the details of Clairaut’s calculations.

    Clairaut’s work was hardly a routine exercise in Newtonian mechanics. Clairaut based his calculation on his work on the three-body problem, where he had already bested Euler in resolving the famous lunar anomaly. (See Bodenmann, “The 18th-century battle over lunar motion”, Physics Today Jan 2010).

    Stepping back from the details, this is a superb example of what Kuhn labeled “normal science”. Kepler’s first law, after all, isn’t 100% true: it’s the two-body approximation. One of the big issues in 18th-century astronomy was, is the inverse-square law strictly accurate, or itself an approximation? Triumphs like those of Clairaut helped dispell lingering doubts.

  2. Between theses two were the spheres of the planets centred on and spreading outwards from the earth, Moon, Venus, Mars, Sun, Jupiter Saturn.

    Mercury appears to have been left out here?

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  4. Øystein

    An off-topic question here, if I may.

    I’m having a discussion somewhere on the net as to whether the Galileo affair was the church fighting tooth and nail to hinder scientific progress or not. At some point the books on the Index came up, and I started looking around for what was placed there and when. Now, I don’t have any sources on this myself, and looking online sort of fast, I found this and this. Looking through those for Kepler (whom I was unsure of), I find he’s not mentioned in the second, while in the first lists Epitome Astronomiae Copernicanae. However, I’ve read a couple of places that Astronomia Nova also was on the list. So I’m sort of wondering which of his works were banned, and if there is an online place I could link?

  5. Quoting from the at Rice university:

    Kepler’s New Astronomy, his Epitome of Copernican Astronomy, and his World Harmony were quickly placed on the Index. None of Galileo’s books were placed on the Index at this time [1673].

    The notion that the Church (I assume you mean the Catholic church) was “fighting tooth and nail to hinder scientific progress” has been debunked many times on this blog and elsewhere. The web page I linked to also says, for example, “In the cases of the Copernican System, the Church was slow to act because it did not see immediate danger to the faithful in De Revolutionibus (1543)”, and only placed it on the index 73 years later. Papers by Christopher Graney, freely available through the arXiv, document valid scientific qualms that the Church’s astronomers had about the Copernican hypothesis.

    I imagine Thony or other posters will have more to say on this. I will mention that one shouldn’t go to the other extreme, and pretend that scriptural issues played only a minor role in the Galileo affair.

    • Once again, I messed up on the html anchor tag syntax: here’s the link (correctly I hope)

      Galileo Project”.

    • Øystein

      Michael Weiss, thanks for your reply.

      Just to clarify, I’m the one arguing against the notion of the Catholic church fighting tooth and nail to hinder scientific progress. However, I haven’t really entered into this theme on the back of strong reading (that is, book reading), and I’m familiar with the arguments only in blog form.

      As my opponent wants primary sources (not that he knows how to read them, but that’s another matter), I try to search for what I don’t already know. Basically trying to be as historically correct as I can.

      • Where is this debate going on?

      • Øystein

        Over at, membership forum, subforum Literature

        ..bit embarassing to admit, as I’ve gotten .. a bit heated..

      • Øystein

        Sorry, bit hard to find if you’re not familiar, I guess.

        I start arguing on this page, as Rorshach

      • Rorshach —
        Quite a thread. I would say that the Galileo affair was a real giambotta of theology, scripture, legal technicalities, personality conflicts, geopolitical concerns, and bad luck. (Or good luck, if you think it’s a good thing it happened. As I do.) In short, add a gallon of historical nuance to understand it.

        It was pretty much inevitable that the Astronomia nova would be banned once Galileo’s Dialog was. Book by a Protestant astronomer. Introduction contains an extensive discussion of the scriptural issues, at least as explicit as anything Galileo ever wrote. (Those Protestants!) And this introduction was reprinted as an addendum to the Latin translation of Galileo’s Dialog.

        The “formally heretical” and “foolish and absurd in philosophy” has been discussed previously in this blog, in the comments. The former phrase addresses theological matters, the latter scientific.

      • Øystein

        Heh. I think I’ll agree it’s not my proudest moment. I do have a bit of a temper, and, experience aside, I have not yet mastered the art of *not* replying when I’m agitated..

        Should think such wisdom would kick in once you reach a certain age (I’m 36)

      • The ‘debate’ you link to is a perfect example of why I don’t take part in such discussions. The anti-Church participants play out half chewed statements like trump cards in a game of bridge. For such people historical context, subtle detail, or nuanced interpretation play no role what so ever. They “know” that the Church persecuted Galileo because he was a “truth defending scientist” and anything one might say to the contrary is per definition wrong. I prefer to stay here and write for people with open minds who even if the disagree with me bring substantial well argued reasons for doing so, it’s called learning, something that your opponents are not willing to undertake.

      • I suspect that both the Epitome and the Rudolphine Tables were both much more widely distributed and read in the 1600s than Astonomia nova. Possibly also his book on comets, which was a sort of standard reference work on the subject.

    • laura

      I was looking this subject up awhile ago and I think that source is wrong (although it’s a credible source; maybe that’s why it gets reposted everywhere.) Only the Epitome of Copernican Astronomy went on the Italian Index and only because Kepler wrote a criticism of the censor Ingoli’s attack on Copernicus referring Ingoli to his own book. As I understand it, Kepler didn’t know at the time who Ingoli was or even that the Inquisition had temporarily banned De Revolutionibus; this was in 1617. When he found out he was very upset and worried they would also ban Harmony, but they didn’t. Also, I think Epitome was banned not for being Copernican but for positing a vitalistic/ ensouled sun.

      Lansberg and Bouilleau’s books didn’t go on the Italian index either. I think they weren’t really that militant about banning technical books even if they were Copernican.

      By contrast, all of Kepler’s books went like clockwork onto the Spanish Index. But neither De Revolutionibus nor Dialogue ever made it on, mainly due to bureaucratic snafus.

      My main source for the above is Aviva Rothmann’s phD thesis (with Anthony Grafton) which is available free online; just google her name and it comes right up. Also Heilbron’s Galileo biography.

      • laura

        One other comment on the thread at Westeros: I always have to roll my eyes when people get on about “the horrors” faced by Galileo. 40% of the population of Germany and 50% of the population of Ireland died in wars while Galileo was growing old and writing Two New Sciences in his villa. A little perspective maybe?

      • Most interesting. Especially comparing the scriptural discussion in the intro with Galileo’s Letter to the Grand Duchess. Donahue says that “Kepler’s introduction to the Astronomia nova, especially the part that discusses the relation between scripture and astronomy, was the most widely disseminated of his works during the seventeenth century… [it] was the only writing of Kepler’s to appear in English prior to the nineteenth century.”

        I am retrospectively shocked at this sloppy work by the Roman Inquisition! Defenders of the faith indeed! 🙂

        Thanks for the thesis reference, it looks fascinating. The stuff about Haffenreffer persuading Kepler to leave the scriptural chapter out of the Mysterium cosmographicum, and why Kepler wanted to include it in the first place: “His mathematical work, that is, could be mobilized to settle some of the sharpest confessional disputes [between Calvinists and Lutherans], in ways that would brook no dissent.”

      • laura

        I really enjoyed her thesis! It’s rare to find non-technical work on Kepler.

        The Inquisition was really sloppy! I’m not sure the Inquisition even bothered to formally ban to Latin version of Dialogue (translated by a Protestant!) If they did, they banned the intro to Astronomia Nova that was included with it — that might be what people mean when they say AN was banned. But that was only five pages of the work.

        Also just to be totally contrarian, I’m not sure I think Donahue is right that the intro to New Astronomy was the most widely disseminated of Kepler’s work in the 1600s. The Latin Dialogue with the 5 pages from AN only went through 2 printings before 1699. As far as I know (and I’ve looked), it was never translated into French, Dutch or German and the English translation (which included the non-Galileo parts) didn’t fare very well. Most copies burned in a warehouse during the Fire of London and hardly any copies exist today (but Newton had one). Both Epitome and Somnium also went through two Latin editions so I don’t know why they were necessarily read less (outside of Italy). Dioptrice was reprinted 7 times as part of Gassendi’s textbook on astronomy, though it’s not really astronomy so I guess it doesn’t count.

  6. Given where the debate was taking place (, I’m wondering why no one pointed out that the world is a hollow sphere with the sun at the center.

  7. Pingback: “…realigning the heavens with a single stroke of the brush.“ – Really? | The Renaissance Mathematicus

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