Category Archives: History of Astronomy

The emergence of modern astronomy – a complex mosaic: Part XIX

Tycho and Kepler was one of the most important partnerships in the history of Early Modern science and a good counter example to those who mistakenly believe in the lone genius myth. Tycho the observational astronomer with an obsession for accuracy, who produced an unequalled volume of raw data


Tycho Brahe Source: Wikimedia Commons

and Kepler the theoretical astronomer with an equal obsession for accuracy, who would come to turn that data into a completely new heliocentric model of the cosmos.


Johannes Kepler Source: Wikimedia Commons

Superficially a marriage made in heaven but when the two men first met in Prague their future cooperation almost ended before it even started. Arriving in February 1600 at Tycho’s new home in Benátky Castle Kepler was initially welcomed as a guest and observer.


Benátky Castle Source: Wikimedia Commons

He was impressed by Tycho’s setup and his data collection to which he hoped to gain access to fine tune his Platonic solids model of the cosmos. Tycho was impressed by the young theoretician but, suspicious of possible plagiarism, was not prepared to make his data freely available. Kepler was of course desperate for paid employment and after two months entered negotiations with Tycho over some sort of fixed employment. The young, working class, German mathematician took umbrage at the arrogant attitude of the Danish aristocrat and in a strop broke off the talks, departing for Prague. Interestingly Tycho, needing fresh workers, proved himself surprisingly conciliatory and through the diplomatic efforts of the Bohemian physician Jan Jesenius (1566–1621) Kepler was persuaded to return to Benátky, where conditions of employment for him were eventually arranged.


Jan Jesenius

Kepler, who had left his family in Graz, now returned there and after a failed attempt to obtain employment from Archduke Ferdinand in August 1600 he finally set off for Prague with household and family. Initially he was employed directly by Tycho his first task being to write an account of the plagiarism dispute between Tycho and Ursus, probably as a punishment for having supplied Ursus with munitions in that dispute, and naturally he was expected to find in Tycho’s favour. This work, which turned out to be very impressive, was never published in Tycho’s or Kepler’s lifetimes and much more significant was the first real astronomical work that Tycho assigned to him.

When Kepler had first arrived in Benátky, Christen Longomontanus (1562–1647), who had returned to the fold having initially left Tycho’s circus when he quit Denmark, was working on the raw data for the orbit of Mars.


Christen Longomontanus

Tycho now removed him from this work, assigning him instead to the Moon’s orbit, and gave the task instead to Kepler under Longomontanus’ supervision. This turned out to be one of the most fateful decisions in the entire history of astronomy. Kepler initially thought that he could knock off this task in a couple of weeks but in fact it took him six years to complete but as well as the mathematical difficulties involved there were extenuating circumstances. Before turning to the results of what Kepler called his war with Mars, a play upon the fact that Mars was the Roman god of war, we need to take a look at some of those circumstances.

Tycho’s financial resources were stretched so he negotiated with Rudolf, the Emperor, for Kepler to be appointed directly to the court in order to produce a new set of planetary tables, using Tycho’s data, to replace the existing Prutenic Tables of Erasmus Reinhold and to be named, of course, after the Emperor. What seemed like a step up for Kepler proved to be very problematic, as Rudolf, always strapped for cash, was very bad at paying his staff.


Rudolf II Portrait by Martino Rota Source: Wikimedia Commons

The next major event was the death of Tycho on 24 October1601 barely a year after Kepler had started working with him. For Kepler this was both good and bad. Already appointed to produce planetary tables for Rudolph, he now inherited Tycho’s title as Imperial Mathematicus, as the obvious candidate Longomontanus had left Benátky and Tycho’s service the previous year. This was truly a major step up but with the same caveat that Rudolf was extremely bad at paying salaries. Kepler was, of course, now in physical possession of all of Tycho’s data but unfortunately not in legal possession. Although he had been Imperial Mathematicus, Tycho’s data did not belong to Rudolf but was his own private property and was on his death inherited by his family. Kepler was faced with the problem of negotiating with Tycho’s son in law Frans Gansneb genaamd Tengnagel van de Camp over the use of the data. Frans Tengnagel initially claimed that he would work with the data but he was a diplomat and not an astronomer or mathematician and in the end a compromise was reached in that Kepler could use the data but that Fans Tengnagel would be named as co-author in any resulting publications. In fact, in the end Frans Tengnagel’s only contribution was a preface to the Astronomia nova.


Frans Gansneb genaamd Tengnagel van de Camp

Even though he now possessed the desired data Kepler did not sit down solely to finish calculating the orbit of Mars. In 1604 he published his Astronomia Pars Optica, the most important work in optics since the Middle Ages, which laid the foundations of the modern science of optics.


Astronomiae Pars Optica

It included the first explanations of how lenses work to correct short and long sight and above all the first-ever correct explanation of how the image is formed in the eye. This work would, as will see, proved extremely important following the invention of the telescope at the end of the decade. Also in 1604 a supernova appeared in the skies and Kepler systematically observed it, confirmed it was definitively supralunar (i.e. above the moon’s orbit) and wrote up and published his findings, De Stella nova in pede Serpentarii, in Prague in 1606. This of course confirmed what had already been demonstrated in the 1570s that the heavens were not incorruptible, driving another nail into the coffin of Aristotelian cosmology.


Stella nova in pede Serpentarii title page

During this period Kepler also finished his determination of the orbit of Mars, in the course of which he changed the course of astronomy forever. Published in 1609 the Astronomia Nova ΑΙΤΙΟΛΟΓΗΤΟΣ seu physica coelestis, tradita commentariis de motibus stellae Martis ex observationibus G.V. Tychonis Brahe, to give it its full title, is without any doubt whatsoever one of the most important books in the whole history of astronomy, although it was not recognised as such until long after it appeared.


Astronomia Nova title page Source: Wikimedia Commons

Unique amongst major scientific publications the book appears to outline in great detail the path that the author took in his determination of the Planet’s orbit, including all the false paths he followed, the errors that he made and even his calculating mistakes. Normally scientists leave all of this out of their published work presenting only the successful conclusions of their battles with the evidence and data. So why did Kepler include all of his six years of strife in his finished product. The answer lies in the statement above, appears to outline. In fact the account presented is to some extent, to use an actual term, fake news. Kepler is deliberately misleading his readers but why?

Kepler was a convinced Copernicaner in a period where the majority of astronomers were either against heliocentricity, mostly with good scientific reasons, or at best sitting on the fence. Kepler was truly revolutionary in another sense, he believed firmly in a physical cause for the structure of the cosmos and the movement of the planets. This was something that he had already propagated in his Mysterium Cosmographicum and for which he had been strongly criticised by his teacher Mästlin. The vast majority of astronomers still believed they were creating mathematical models to save the phenomena, irrespective of the actually physical truth of those models. The true nature of the cosmos was a question to be answered by philosophers and not astronomers. Kepler structured the rhetoric of the Astronomia Nova to make it appear that his conclusions were inevitable; he had apparently no other choice, the evidence led him inescapably to a heliocentric system with a real physical cause. Of course, he couldn’t really prove this but he did his best to con his readers into thinking he could.

Kepler tested and refined his arguments in one of the most fascinating correspondences in the history of astronomy, which took place with the Frisian amateur astronomer David Fabricius (1564–1617) over a total of eight years; a correspondence that also makes a mockery of the lone genius myth. Fabricius was a Protestant pastor and a passionate amateur astronomer. He first emerged on the European astronomical scene when he took up contact with Jost Bürgi (1552–1632) in Kassel in 1592 to request his advice on constructing astronomical instruments. In 1596 having, as the first astronomer to do so, observed the variable star Mira he wrote a letter to Tycho Brahe in Hven describing his discovery. This was the start of an extensive correspondence between the two that lasted until Tycho’s death in 1601. In that year he visited Tycho in Prague, where he met Simon Marius (1573–1625) with whom he would also correspond but not Kepler who was in Austria on family business. The letters that Kepler and Fabricius exchanged were more in the nature of academic papers often running to forty or fifty pages.


Monument to David Fabricius & his son Johannes in the church yard in Osteel his parish Source: Wikimedia Commons

Fabricius was neither a geocentrist nor a heliocenrist but a solid supporter of Tycho’s geo-heliocentric compromise and so was an ideal sparing partner for Kepler. Kepler would outline his latest heliocentric theories and Fabricius would do his best to demolish them and his best was very good indeed. This meant that over the years of their correspondence Kepler could really develop and refine the complex arguments that he would then finally present in the Astronomia nova. Probably frustrated by his failure to convert Fabricius to his way of thinking, Kepler rather abruptly broke off the correspondence in 1609. Fabricius, who Kepler acknowledge as the best observational astronomer in Europe following Tycho’s demise, died tragically in 1617, beaten to death with a spade by a local farmer, who thought Fabricius had accused him of being a thief in a sermon.

Despite Kepler’s best efforts the Astronomia nova was largely a flop when first published. Those who read it largely rejected his argument for heliocentricity. The book however contains two of the most important discoveries in the history of astronomy, Kepler’s first two laws of planetary motion:

1) That planets orbit the Sun on elliptical paths with the Sun situated at one focus of the ellipse

2) That a line connecting the planet to the Sun sweeps out equal areas in equal periods of time.

Kepler actually developed the second law first using it as his primary tool to determine the actually orbit of Mars. The formulation of this law went through an evolution, which he elucidates in the book, before it reached its final form. The first law was in fact the capstone of his entire endeavour. He had known for sometime that the orbit was oval and had even at one point considered an elliptical form but then rejected it. When he finally proved that the orbit was actually an ellipse he knew that his battle was over and he had won.

Although, at the time, Kepler had temporarily lost the public battle in the larger war for the recognition that the cosmos, as it was then known, was indeed heliocentric the publication of the Astronomia nova represents one of the most important steps towards the final victory in that war. This would not remain Kepler’s only contribution to that war but before we look at his further efforts we need to turn to what was possibly the most important event in the history of Early Modern astronomy, the invention of the telescope.

[Attentive readers of this blog might have noticed that I have ‘plagiarised’ my own post on the Astronomia nova from December last year. I simply couldn’t be bothered to find new ways of expressing things that I had already expressed to my own satisfaction.]
















Filed under History of Astronomy, History of Optics, History of science

The emergence of modern astronomy – a complex mosaic: Part XVIII

Along with Copernicus, Galileo and Newton, Kepler is one of the historical icons of the heliocentricity story. I personally think he is the most important figure of them all but in the public perception he is the least well known of the major figures and the least acknowledged. It is often said that we live in a Copernican cosmos or universe but in fact it would be much more accurate to state that we live in a Keplerian cosmos. So who was this man and what did he contribute to the evolution of the heliocentric hypothesis and its acceptance?

Johannes Kepler (1571–1633) was born in the small town of Weil der Stadt, a Free Imperial City within the Duchy of Württemberg, the son of Heinrich Kepler, an innkeeper and sometime mercenary, and his wife Katharina Guldenmann, the daughter of an innkeeper.


Weil der Stadt 1682, Forstlagerbuch by Andreas Kieser Source: Wikimedia Commons

Kepler’s father disappeared when he was just five years old, not the most auspicious start in life. The young Kepler grew up in his grandfather’s inn. According to Kepler in one of his autobiographical sketches it was his mother, who first awakened his interest in astronomy. She took him outside in the night to view the Great Comet of 1577 and again in 1580 to view a lunar eclipse.


The Great comet of 1577, seen over Prague on November 12. Engraving made by Jiri Daschitzky. Source: W§Wikimedia Commons

Kepler must have been an intelligent child because he received a grant from the Duchy of Württemberg to study first at the convent-school, Adelberg, in 1584 then at the seminary at Maulbronn in 1586 he graduated BA at the University of Tübingen in 1588 but returned to Maulbronn for another year. In 1589 he entered the Tübinger Stift, the hall of residence of the Lutheran Protestant Church at the University of Tübingen. Kepler’s grant was part of scheme to train Lutheran pastors and schoolteachers to replace the Catholic ones lost through Württemberg becoming Protestant. He graduated MA in 1591.


Tübinger Still (left) and University (right) Source: Kepler-Gesellschaft e.V.

It is a widespread myth that Kepler now studied theology but in fact he remained at the university receiving instruction in the various practical aspects of his potential future career, teaching practice, basic theology for sermons and so forth until a suitable vacancy became available. Kepler, who was deeply religious, desired to become a pastor, however, when a vacancy for a maths teacher in Graz became available he was recommended for the post and after some hesitation he accepted reluctantly his new position, which included the post of district mathematicus and beginning in 1594.


Johannes Kepler (artist unknown) Source: Wikimedia Commons

During his studies in Tübingen he came under the influence of Michael Mästlin and was one of those, who received an introduction to Copernicus’ heliocentric hypothesis, which he immediately adopted with enthusiasm. He succeeded in acquiring a second hand copy of the first edition De revolutionibus in 1598–the book was by now 55 years old–which is still extant.

Kepler was still very miffed about the fact that he was teaching teenagers mathematics rather than serving his God as a pastor when he had what could be best described as an epiphany whilst teaching astronomy to a class on 19 July 1595. At the time Kepler was trying to find a conclusive argument as to why there are only six planets thus supporting a heliocentric model against a geocentric one that has seven planets. During his teaching he drew a diagram illustrating the cyclical pattern of the occurrences of the so-called Great Conjunctions of Saturn and Jupiter, something considered very important in astrology.

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Kepler’s diagram of the Great Conjuctions of Saturn and Jupiter

Viewing his own diagram he had a revelation and thought, the orbits of the planets are separated by geometrical figures! Initially he tried various regular polygons but couldn’t get a good fit between his figures and the known distances between the planetary orbits. His next thought was that space in naturally three-dimensional and the polygons are only two-dimensional, also there are infinitely many regular polygons so not a good potential argument for a specific limited number of planets. He now turned to polyhedra; then he had his second aha moment. There are only five regular Euclidian polyhedra, so the each of the five paths between the six planets was defined by one of these:

If, for the sizes for the relations of the six heavenly paths assumed by Copernicus, five figures possessing certain distinguishing characteristics could be discovered among the remaining infinitely many, then everything would go as desired.

The Earth is the measure of all other orbits. Circumscribe a twelve-sided regular solid about it; the sphere stretched around this around this will be that of Mars. Let the orbit around Mars be circumscribed by a four-sided solid. The sphere which is described around this will be that of Jupiter. Let Jupiter’s orbit be circumscribed by a cube. The sphere described about this will be that of Saturn. Now, place a twenty-sided figure in the orbit of the Earth. The sphere inscribed in this will be that of Venus. In Venus’ orbit place an octahedron. The sphere inscribed in this will be that of Mercury. There you have the basis for the number of planets.


Kepler’s Platonic solid model of the solar system, from Mysterium Cosmographicum (1596) Source: Wikimedia Commons

This astronomical epiphany led Kepler to the realisation that his God was a geometer and his call was to worship his God by revealing the geometrical structure of creation. His desire to become a pastor died and Johannes Kepler the astronomer was born.

He quickly turned his revelation into what became the first of his many books his Prodromus dissertationum cosmographicarum, continens mysterium cosmographicum, de admirabili proportione orbium coelestium, de que causis coelorum numeri, magnitudinis, motuumque periodicorum genuinis & proprijs, demonstratum, per quinque regularia corpora geometrica (Forerunner of the Cosmological Essays, Which Contains the Secret of the Universe; on the Marvelous Proportion of the Celestial Spheres, and on the True and Particular Causes of the Number, Magnitude, and Periodic Motions of the Heavens; Established by Means of the Five Regular Geometric Solids), usually known simply as the Mysterium Cosmographicum (the Cosmographic Mystery).


The fit between the Euclidian regular solids and the planetary orbits turned out to be fairly good with less that 10% error. Kepler would dedicate much of his later life to trying to eliminate that error through various strategies.

Supported by Mästlin, Kepler obtained permission from the University of Tübingen to publish this book, although the university insisted on removing some theological passages from the manuscript. Any doubts about Mästlin’s commitment to heliocentricity were removed by the publication of this book in 1596, which contains an introduction on the Copernican system written by Mästlin and his addition of Rheticus’ Narratio Prima to the book, as an appendix.

At this point in his life Kepler was a twenty-five year old schoolteacher in the Austrian provinces without any sort of reputation. To try and acquire some recognition he sent complimentary copies of his freshly printed tome to various notable European astronomers. As we shall see two of those complimentary copies played a significant roll in his future life, one of them causing him immense embarrassment the other setting him up for his future as a leading astronomer.

However, before we go down that path, there is a widespread myth that Kepler sent a copy of the Mysterium Cosmographicum to Galileo in Padua. At this point in his life Galileo was almost as unknown as Kepler and Kepler had certainly never heard of him. In fact Galileo did receive two copies of Kepler’s first book entirely by chance (you can read the full story here) and wrote a brief letter thanking the author. This letter was Galileo’s earliest known written commitment to the Copernican heliocentric hypothesis.

The two fateful copies that Kepler sent out were to Nicolaus Reimers Baer (1551–1600), known as Ursus, who was at the time Imperial Mathematicus on the court of Rudolf II in Prague and to Tycho Brahe (1546­–1601), Europe’s leading observational astronomer on his island of Hven. Kepler was unaware that the two recipients of his first efforts were at the time involved in a very public slanging match about who invented the geo-heliocentric system and whether Ursus has plagiarised it from Tycho. In fairly typical Renaissance manner Kepler had in his accompanying letter to Ursus addressed the Imperial Mathematicus in fawning heaps of praise of his abilities and achievements. Unknown to Kepler, Ursus then quoted that praise in one of his publications bitterly attacking Tycho. The result was that Kepler was in Tycho’s bad books long before he ever met him.

Graz is the capital of Styria in Austria an area that at the end of the sixteenth century was deeply Catholic with only a comparatively small Protestant minority. The Counter Reformation was in full swing and all of the Protestants were ordered to leave the province. Kepler was exempted from the ban on Protestant due to his successful astrological prognostica, part of his obligations as district mathematicus. However, as religious tensions rose the remaining Protestants were banned from the province and this time Kepler received no exemption. Now married and with children Kepler desperately needed a new position. He wrote to Mästlin in Tübingen but his one time mentor now refused to assist him in anyway. In the end he applied to Tycho, now installed in Prague as Imperial Mathematicus, for a position, any position. Due to the vagaries of the sixteenth century post system Kepler had not yet received any reply from Tycho when he set off in 1600 to Prague hoping to find a solution to his seemingly impossible situation but blissfully unaware that Tycho had a serious bone to pick with him. He also hoped to gain access to Tycho’s observational data, the most accurate available and several levels more accurate than the data Kepler had had available when he wrote his Mysterium Cosmographicum. With Tycho’s data he was convinced he would be able to remove that error in his model of the cosmos.










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Filed under History of Astronomy, History of science

A book for lunatics

The world has currently gone moon crazy, because it is now fifty years since a couple of American went for a walk on the moon. This has meant the usual flood of books, journal, magazine and newspaper articles, blog post and, Twitter and Facebook postings that now accompany any such #histSTM anniversary that is considered by the media world to be significant enough. With the following statement I shall probably lose half of my Twitter following overnight but personally I don’t find this particular anniversary especially interesting. I do have one peculiar biographical quirk in that I don’t think I actually watched that first moon landing; at least I have absolutely no memory of having done so. The last weeks of the school year 1968–69 were a highly emotional time for me. I had just been expelled from boarding school but was still living there as my fees were paid up to the end of the school year and my parents were away on sabbatical in Indonesia. Somehow all of that was more important in my life than some guys going for a walk on the moon.

Although I have skimmed the occasional newspaper/magazine/Internet article I have not and will not bother to buy and read any of the apparently X zillion books that have been thrown onto the market to celebrate the occasion. I will admit to having treated myself to Ewen A. Whitaker’s Mapping and Naming the MoonA History of Lunar Cartography and Nomenclature (CUP, ppb. 2003), which actually has little to do with the actual anniversary. I have however acquired and read one book written specifically for the anniversary Oliver Morton’s The Moon: A History for the Future (The Economist Books, 2019). I got this for free because I read and suggested corrections for those bits of the book dealing with the Early Modern Period. Although, I saved the author from making, what I consider to be a serious error but which the normal reader probably wouldn’t even have noticed, I think my contribution to the final product was so minimal that I can safely review it without fear of personal bias.


We’ll start at the top with the very simple statement; this is truly an excellent book. I would be very tempted to say, if you only read one book on the moon this year then you could do worse than choose this one. However, not having read any of the others, this would not be very fair to the other moon book authors. Back to the praise, Morton’s book is a wonderful literary tour de force, which is also incredibly informative. He combines the histories of astronomy, technology, the moon landings and science fiction to create a stimulating potpourri of lunar lore and selenology.

The book is divided into eight sections rather than chapters, each of which deals with a different aspect of humanity’s relationship with the Moon. Section I introduces the reader to the phenomenon of earthshine, the light reflected from the Earth that illuminates those parts of the Moon not lit by the Sun, both its discovery in the Early Modern Period and its use in modern times for scientific experiments. Section II deals with studies of the Moon’s appearance from the High Middle Ages down to the twentieth century. Section III takes us along the path of the development of rocketry up to Apollo and then with Armstrong, Aldrin and Collins on Apollo 11 to that first ever moon landing. Section IV takes a look at the various theories to explain the origins of the Moon and its geology. Section V deals with the end or better said the collapse of the Apollo program and then over the years the various suggestions for economically viable schemes to return to the Moon, here Morton demonstrates his strengths as a narrator. Although he is obviously a space fan he carefully details why such schemes were largely unrealistic or impractical. Section VI examines the various schemes currently being developed for a real return. Having got there, section VII discusses what to do when we get there if we do go back. Section VIII looks at negative literary depictions of the Moon illustrating rather nicely that maybe the Moon isn’t such an attractive place to visit.

This listing of the main themes of each section doesn’t do Morton’s inventiveness justice. He weaves lots of side topics into the weft of his main narratives taking his readers down many highways and byways, leaving the readers with the impression that he has consumed a vast library of lunar information, an impression strengthened by the extensive bibliography.  His real achievement is to pack so much fascinating information into so few pages, whilst retaining a wonderful light readable style. His book is both an encyclopaedia and a work of art.




Filed under Book Reviews, History of Astronomy, History of science, History of Technology

If you can’t tell your Cassini from your Huygens then you shouldn’t be writing about the history of astronomy.

There I was, mild mannered historian of early modern science, enjoying my first cup of tea on a lazy Sunday morning, whilst cruising the highway and byways of cyberspace, when I espied a statement that caused an explosion of indignation, transforming me into the much feared, fire spitting HISTSCI_HULKTM. What piece of histSTM crap had unleashed the pedantic monster this time and sent him off on a stamping rage?

The object of HSH’s rage was contained in an essay by Vahe Peroomian (Associate Professor of Physics and Astronomy, University of Southern California – Dornsife College of Letters, Arts and Sciences) A brief astronomical history of Saturn’s amazing rings, published simultaneously on both The Conversation and PHYS.ORG 15 August 2019. Peroomian writes:

I am a space scientist with a passion for teaching physics andastronomy, and Saturn’s rings have always fascinated me as they tell the story of how the eyes of humanity were opened to the wonders of our solar system and the cosmos.

He continues:

When Galileo first observed Saturn through his telescope in 1610, he was still basking in the fame of discovering the four moons of Jupiter. But Saturn perplexed him. Peering at the planet through his telescope, it first looked to him as a planet with two very large moons, then as a lone planet, and then again through his newer telescope, in 1616, as a planet with arms or handles.


Galileo Portrait by Ottavio Leoni Source: Wikimedia Commons

Galileo actually observed Saturn three times. The first time in 1610 he thought that the rings were handles or large moons on either side of the planet, “I have observed the highest planet [Saturn] to be triple bodied. This is to say to my very great amazement Saturn was seen to me to be not a single star, but three together, which almost touch each other.”


Galileo’s 1610 sketch of Saturn and its rings

The second time was in 1612 and whatever it was that he observed in 1610 had simply disappeared, “I do not know what to say in a case so surprising, so unlooked for and so novel.” The Earth’s position relative to Saturn had changed and the rings were no longer visible but Galileo did not know this. In 1616 the rings were back but with a totally altered appearance, “The two companions are no longer two small perfectly round globes … but are present much larger and no longer round … that is, two half eclipses with two little dark triangles in the middle of the figure and contiguous to the middle globe of Saturn, which is seen, as always, perfectly round.” [1]


Galileo’s 1616 sketch of Saturn and its rings

There is no mention of a new telescope and it is fairly certain that all three periods of observation were either carried out with the same or very similar telescopes. The differences that Galileo observed were due to the changing visibility of Saturn’s rings caused by its changing relative position to Earth and not to any change of instrument on Galileo’s part.

Although sloppy and annoying, the minor errors in Peroomian’s account of Galileo’s observations of Saturn are in themselves not capable of triggering the HSH’s wrath but what he wrote next is:

Four decades later, Giovanni Cassini first suggested that Saturn was a ringed planet, and what Galileo had seen were different views of Saturn’s rings. Because of the 27 degrees in the tilt of Saturn’s rotation axis relative to the plane of its orbit, the rings appear to tilt toward and away from Earth with the 29-year cycle of Saturn’s revolution about the Sun, giving humanity an ever-changing view of the rings.


Giovanni Cassini (artist unknown) Source: Wikimedia Commons

Now, Giovanni Cassini did record some important observations of Saturn; he discovered four of Saturn’s largest moons and also the gap in the rings that is named after him. Although, Giuseppe Campani, Cassini’s telescope maker, observed the gap before he did without realising that it was a gap. However, it was not Cassini who first suggested that what people had been observing were rings but Christiaan Huygens.

Christiaan Huygens first proposed that Saturn was surrounded by a solid ring in 1655, “a thin, flat ring, nowhere touching, and inclined to the ecliptic.” In 1659 he published his book, Systema Saturnium : sive, De causis mirandorum Saturni phaenomenôn, et comite ejus Planeta Novo detailing how the appearance of the rings varied as the Earth and Saturn orbited the sun.


Plate from Huygens’ Systema Saturnium showing the various recorded observations of Saturn made by astronomers before his own times


Plate from Huygens’ Systema Saturnium explaining why the appearance of Saturn and its rings changes over time and that all those different appearances can be explained by assuming the existence of the rings

Confusing Cassini and Huygens, two of the greatest observational astronomers of the seventeenth century, who were scientific rivals, is not a trivial error and shouldn’t be made anywhere by anyone. However, to make this error in an essay that is published  on two major Internet websites borders on the criminal. I have no idea what the reach of PHYS.ORG is but The Conversation claims to have a readership of ten million plus. This means that a lot of people are being fed false history of astronomy facts by a supposed expert.

If the good doctor Peroomian had bothered to check his facts, a thing that I thought all scientists were taught to do when receiving their mother milk, he could have easily discovered his crass error and corrected it, even the much maligned Wikipedia gets it right, but apparently he didn’t consider it necessary to do so, after all it’s just history and not real science.

[1]The Galileo and Huygens quotes are taken from Ron Baalke’s excellent time line, Historical Background of Saturn’s Rings.



Filed under History of Astronomy, History of science, Myths of Science

The emergence of modern astronomy – a complex mosaic: Part XVII

As I stated earlier in this series only a comparatively small number of astronomers accepted the whole of Copernicus’ theory, both cosmology and astronomy. More interestingly almost none of them had any lasting impact during the final decades of the sixteenth century on the gradual acceptance of heliocentrism. Although he appears to have abandoned Copernicus’ astronomy later in life, Rheticus did have a strong impact with his Narratio Prima(1540), which through its various editions was the first introduction to the heliocentric hypothesis for many readers. Two others, whose impact was principally in the seventeenth century, were Kepler and Galileo, who will be dealt with later. However, one astronomer who did play an important role in the sixteenth century was Michael Mästlin.


Michael Mästlin portrait 1619 artist unknown

Michael Mästlin (1550-1631) stood at the end of a long line of important Southern German astronomers and mathematicians. A graduate of the University of Tübingen he was a student of Philipp Apian (1531–1589),


Philipp Apian, artist unknown Source: Wikimedia Commons


who was a student of his more famous father Peter Apian (1495–1552) in Ingolstadt. Peter Apian had studied under Georg Tannstetter (1482–1535) in Vienna, who had studied under Andreas Stiborius (c. 1464–1515) and Johannes Stabius (1450–1522) first in Ingolstadt then in Vienna. In 1584 Mästlin succeeded his teacher Philipp Apian as professor for astronomy and mathematics at Tübingen. An active astronomer since the beginning of the 1570s Mästlin was regarded as a leading German astronomer and consulted by the Protestant princes on matters astronomical, astrological and mathematical.

Mästlin represents the transitional nature of the times probably better than any other astronomer. His Epitome Astronomiae (1582), a university textbook, which went through a total of seven editions, was a standard Ptolemaic geocentric text that he continued to teach from until his death in 1631.


However, at the same time he taught selected students the fundaments of Copernican heliocentric astronomy. Earlier accounts claimed that he did this in secret but all of the available evidence suggests that he did so quite openly. This quasi revolutionary act of teaching famously produced one significant result in that Mästlin introduced Copernican astronomy to the young Johannes Kepler, who would go on to become the most important propagator of heliocentric astronomy in the early seventeenth century.

One subject on, which the German Protestant princes consulted Mästlin was the proposed Gregorian calendar reform from 1582. Mästlin launched a vitriolic polemic against it largely on religious grounds with his Gründtlicher Bericht von der allgemeinen und nunmehr bei 1600 Jahren von dem ersten Kaiser Julio bis jetzt gebrauchten jarrechnung oder kalender (Rigorous report on the general and up till now for 1600 years used calculation of years or calendar from the first Caesar Julio) (1583). The Protestant princes accepted his advice and as a result didn’t adopt the new calendar until 1700.

On the other side of the religious divide the man charged by the Pope to promote and defend the new calendar was the Jesuit professor of astronomy and mathematics at the Collegio Romano, Christoph Clavius (1538–1612).


Christoph Clavius. Engraving Francesco Villamena, 1606 Source: Wikimedia Commons

Although Clavius was a convinced defender of the Ptolemaic system until his death, he did play a central role in the developments that led to the eventual acceptance of the heliocentric system. The Catholic universities in the last quarter of the sixteenth century still didn’t really pay the mathematical disciplines much attention and their teaching of astronomy had not really progressed beyond the High Middle Ages. Clavius introduced modern mathematics and astronomy into the Jesuit educational reform programme, following the fundamental principle of that programme, if you want to win the debate with your non-Catholic opponents you need to be better educated than them. Many Jesuit and Jesuit educated mathematicians and astronomers, who came out of the pedagogical programme established by Clavius, would, as we shall see, make significant and important contributions to the developments in astronomy in the seventeenth century.

Clavius was also the author of a number of excellent up to date textbooks on a full range of mathematical topics. His astronomy textbook In Sphaeram Ioannis de Sacro Bosco commentarius, the first edition appearing in 1570 and further updated editions appearing in 1581, 1585, 1593, 1607, 1611 and posthumously in 1618, was the most widely read astronomy textbook in the last decades of the sixteenth and early decades of the seventeenth centuries. It was strictly Ptolemaic but he presented, described and commented upon Copernicus’ heliocentric hypothesis. Although he showed great respect for Copernicus as a mathematical astronomer, he of course rejected the hypothesis. However, anybody who read Clavius’ book would be informed of Copernicus work and could if interested go looking for more information. One should never underestimate the effect of informed criticism, and Clavius’ criticism was well informed, for disseminating a scientific hypothesis. Many people certainly had their first taste of the heliocentric hypothesis through reading Clavius.

Another group who had a positive impact on the propagation of the heliocentric hypothesis in the last quarter of the sixteenth century was the so-called English School of Mathematics. Whilst Robert Recorde (1510–1558) and John Dee (1527–c. 1608) were not committed supporters of Copernicus, they did much to spread knowledge of the heliocentric hypothesis. As we have already seen John Feild (c. 1520–1587) was a declared supporter of Copernicus but as his Copernican ephemerides proved no more accurate than the Ptolemaic ones his influence diminished. Not so Dee’s foster son Thomas Digges (c. 1546–1595).

His 1576 edition of his father’s A Prognostication everlastingcontained an appendix A Perfit Description of the Caelestiall Orbes according to the most aunciente doctrine of the Pythagoreans, latelye revived by Copernicus and by Geometricall Demonstrations approved, which is an annotated translation of part of the cosmological first book of De revolutionibus into English, which continued to have an impact on English readers long after Digges’ demise.


Source: Linda Hall Library

Thomas Harriot (c. 1560–1621) was another, who was committed to the heliocentric hypothesis.


Portrait often claimed to be Thomas Harriot (1602), which hangs in Oriel College, Oxford. Source: Wikimedia Commons

His biggest problem was that he published none of his scientific or mathematical work but he was well networked and contributed extensively to the debate through correspondence. The influence of this group would, as we will see, have an impact on the early acceptance of Kepler’s work inEngland.

Another figure in the last quarter of the sixteenth century, who, although not an astronomer, made a very important contribution to the cosmological debate, was the physician William Gilbert (1544–1603).


William Gilbert (1544–1603) artist unknown. Source: Wellcome Library via Wikimedia Commons

Gilbert is well known in the history of science as the author of the first modern scientific investigation of magnetism in his De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure (On the Magnet and Magnetic Bodies, and on That Great Magnet the Earth).


Gilbert carried out many of his experiments with spherical magnets, which he called terella, from which he deduced his belief that the Earth itself is a spherical magnet. Based on his erroneous belief that a suspended terella rotates freely about its axis he came to accept and propagate diurnal rotation. Book VI of De magnete, the final book, is devoted to an analysis of the Earth as a spherical magnet based on the results of Gilbert’s experiments with his terella.

In Chapter III of Book VI, On the Daily Magnetic Revolution of the Globes, as Against the Time-Honoured Opinion of a primum mobile: A Probable Hypothesis, Gilbert gives a detailed review of the history of a geocentric system with diurnal rotation starting with Heraclides of Pontus and going through to Copernicus. Gilbert rejects the whole concept of celestial spheres, dismissing them as a human construction with no real existence. He brings the standard physical arguments that it is more logical that the comparatively small Earth rotates once in twenty-four hours rather than the vastly larger sphere of the fixed stars. In the following chapter he then argues that magnetism is the origin of this rotation. In Chapter V he discusses the arguments for and against movement of the Earth. At the end of Chapter III Gilbert writes, “I pass by the earth’s other movements, for here we treat only of the diurnal rotation…” so what he effectively promotes is a geocentric system with diurnal rotation. Later in his De Mundo Nostro Sublunari Philosophia Nova (New Philosophy about our Sublunary World), Gilbert propagated a full heliocentric system but this book was first published posthumously in 1651 and had no real influence on the astronomical discussion.


Diagram of the cosmos De Mundo p. 202 Source: Wikimedia Commons

Gilbert’s De magnete was a widely read and highly influential book in the first half of the seventeenth century. Galileo praised it but criticised its lack of mathematics. As we shall see it had a massive influence on Kepler. Because of its status the book definitely had a major impact on the acceptance of geo-heliocentric systems with diurnal rotation rather than without later in the seventeenth century.

We will stop briefly and take stock in 1593, fifty years after the publication of De revolutionibus. We have seen that within Europe astronomers had already begun to question the inherited Ptolemaic system during the fifteenth century. In the sixteenth century a major debate developed about both the astronomical and cosmological models. The Aristotelian theories of comets, the celestial spheres and celestial immutability all came under attack and were eventually overturned. Alternative models–Aristotelian homocentricity, the Capellan system and geocentricity with diurnal rotation–were promoted.  With the publication of Copernicus’ De revolutionibus with its heliocentric hypothesis the debates went into overdrive. Only a comparatively small number of astronomers propagated the heliocentric system and an even smaller number of them actually went on to have a real impact on the discussion. A much larger number showed an initial strong interest in the mathematical models in De revolutionibus and the planetary tables and ephemerides based on them, in the hope they would generate better, more accurate data for applications such as astrology, cartography and navigation. This proved not to be the case as Copernicus’ work was based on the same inaccurate and corrupted ancient data, as Ptolemaic geocentric tables. Recognising this both Wilhelm IV in Kassel and Tycho Brahe on Hven began programmes of extensive new astronomical observations. However, this very necessary new data only became generally available well into the seventeenth century. Other astronomers partially convinced by Copernicus’ arguments turned to Capellan models with Mercury and Venus orbiting the Sun rather than the Earth and full geo-heliocentric models with the Moon and the Sun orbiting the Earth and all the other five planets orbiting the Sun. This was the situation at the beginning of the 1590s but a young Johannes Kepler (1571–1630), who would have a massive impact on the future astrological and cosmological models, was waiting in the wings.







Filed under History of Astrology, History of Astronomy, Renaissance Science

Vienna and Astronomy the beginnings.

Vienna and its university played a very central role in introducing the study of mathematics, cartography and astronomy into Northern Europe in the fifteenth and sixteenth century. In early blog posts I have dealt with Georg von Peuerbach and Johannes Regiomontanus, Conrad Celtis and his Collegium poetarum et mathematicorum, Georg Tannstetter and the Apians, and Emperor Maximilian and his use of the Viennese mathematici. Today, I’m going to look at the beginnings of the University of Vienna and the establishment of the mathematical science as a key part of the university’s programme.

The University of Vienna was founded in 1365 by Rudolf IV, Duke of Austria (1339–1365) and his brothers Albrecht III, (c. 1349–1395) and Leopold III (1351–1386) both Dukes of Austria.


Rudolf IV, Duke of Austria Source: Wikimedia Commons

Like most young universities it’s early decades were not very successful or very stable. This began to change in 1384 when Heinrich von Langenstein (1325–1397) was appointed professor of theology.


Presumably Heinrich von Langenstein (1325-1397), Book miniature in Rationale divinorum officiorum of Wilhelmus Durandus, c. 1395

Heinrich von Langenstein studied from 1358 in Paris and in 1363 he was appointed professor for philosophy on the Sorbonne advancing to Vice Chancellor. He took the wrong side during the Western Schism (1378–1417) and was forced to leave the Sorbonne and Paris in 1382. Paris’ loss was Vienna’s gain. An excellent academic and experienced administrator he set the University of Vienna on the path to success. Most important from our point of view is the study of mathematics and astronomy at the university. We tend to think of the curriculum of medieval universities as something fixed: a lower liberal arts faculty teaching the trivium and quadrivium and three higher faculties teaching law, medicine and theology. However in their early phases new universities only had a very truncated curriculum that was gradually expanded over the early decades; Heinrich brought the study of mathematics and astronomy to the young university.

Heinrich was a committed and knowledgeable astronomer, who established a high level of tuition in mathematics and astronomy. When he died he left his collection of astronomical manuscripts and instruments to the university. Henry’s efforts to establish astronomy as a discipline in Vienna might well have come to nothing if a successor to teach astronomy had not been found. However one was found in the person of Johannes von Gmunden (c. 1380–1442).


Initial from British Library manuscript Add. 24071 Canones de practica et utilitatibus tabularum by Johannes von Gmunden written 1437/38 by his student Georg Prunner Possibly a portrait of Johannes Source: Johannes von Gmunden (ca. 1384–1442) Astronom und Mathematiker Hg. Rudolf Simek und Kathrin Chlench, Studia Medievalia Septentrionalia 12

Unfortunately, as is often the case with medieval and Renaissance astronomers and mathematicians, we know almost nothing personal about Johannes von Gmunden. There is indirect evidence that he comes from Gmunden in Upper Austria and not one of the other Gmunden’s or Gmund’s. His date of birth is an estimate based on the dates of his studies at the University of Vienna and everything else we know about him is based on the traces he left in the archives of the university during his life. He registered as a student at the university in 1400, graduating BA in 1402 and MA in 1406.

His MA was his licence to teach and he held his first lecture in 1406 on the Theoricae planetarum by Gerhard de Sabbioneta (who might well not have been the author) a standard medieval astronomy textbook, establishing Johannes’ preference for teaching astronomy and mathematics. In 1407, making the reasonable assumption that Johannes Kraft is Johannes von Gmunden, thereby establishing that his family name was Kraft, he lectured on Euclid. 1408 to 1409 sees him lecturing on non-mathematical, Aristotelian texts and 1410 teaching Aristotelian logic using the Tractatus of Petrus Hispanus. In the same year he also taught Euclid again. 1411 saw a return to Aristotle but in 1412 he taught Algorismus de minutiis i.e. sexagesimal fractions. The Babylonian sexagesimal number system was used in European astronomy down to and including Copernicus in the sixteenth century, Aristotelian logic again in 1413 but John Pecham’s Perspectiva in 1414.


Johannes von Gmunden Algorismus de minutiis printed by Georg Tannstetter 1515 Source: Johannes von Gmunden (ca. 1384–1442) Astronom und Mathematiker Hg. Rudolf Simek und Kathrin Chlench, Studia Medievalia Septentrionalia 12

Around this time Johannes took up the study of theology, although he never proceeded past BA, and 1415 and 16 see him lecturing on religious topics although he also taught Algorismus de minutiis again in 1416. From 1417 till 1434, with breaks, he lectured exclusively on mathematical and astronomical topics making him probably the first dedicated lecturer for the mathematical disciplines at a European university. Beyond his lectures he calculated and wrote astronomical tables, taught students how to use astronomical instruments (for which he also wrote instruction manuals), including the construction of cheap paper instruments.


Johannes von Gmunden instructions for constructing an astrolabe rete Wiener Codex ÖNB 5296 fol. 6r Source: Johannes von Gmunden (ca. 1384–1442) Astronom und Mathematiker Hg. Rudolf Simek und Kathrin Chlench, Studia Medievalia Septentrionalia 12

He collected and also wrote extensive astronomical texts. As well as his teaching duties, Johannes served several times a dean of the liberal arts faculty and even for a time as vice chancellor of the university. His influence in his own time was very extensive; there are more than four hundred surviving manuscripts of Johannes Gmunden’s work in European libraries and archives.

When he died Johannes willed his comparatively large collection of mathematical and astronomical texts and instruments to the university establishing a proper astronomy department that would be inherited with very positive results by Georg von Peuerbach and Johannes Regiomontanus. Perhaps the most fascinating items listed in his will are an Albion and an instruction manual for it.


Albion front side Source: Seb Falk’s Twitter feed


Albion rear Source: Seb Falk’s Twitter feed

The Albion is possibly the most fascinating of all medieval astronomical instruments. Invented by Richard of Wallingford (1292–1336), the Abbot of St Albans, mathematician, astronomer, horologist and instrument maker, most well known for the highly complex astronomical clock that he designed and had constructed for the abbey.


Richard of Wallingford Source: Wikimedia Commons

The Albion, ‘all by one’, was a highly complex and sophisticated, multi-functional astronomical instrument conceived to replace a whole spectrum of other instruments. Johannes’ lecture from 1431 was on the Albion.

Johannes von Gmunden did not stand alone in his efforts to develop the mathematical sciences in Vienna in the first half of fifteenth century; he was actively supported by Georg Müstinger (before 1400–1442), the Prior of the Augustinian priory of Klosterneuburg.



Müstinger became prior of Klosterneuburg in 1418 and worked to turn the priory into an intellectual centre. In 1421 he sent a canon of the priory to Padua to purchase books for over five hundred florins, a very large sum of money. The priory became a centre for producing celestial globes and cartography. It produced a substantial corpus of maps including a mappa mundi, of which only the coordinate list of 703 location still exist. Scholar who worked in the priory and university fanned out into the Southern German area carrying the knowledge acquired in Vienna to other universities and monasteries.

Johannes’ status and influence are nicely expressed in a poem about him and Georg von Peuerbach written by Christoph Poppenheuser in 1551:

The great Johannes von Gmunden, noble in knowledge, distinguished in spirit, and dignified in piety                                                                                                                                         And you Peuerbach, favourite of the muses, whose praise nobody can sing well enough                                                                                                                                           And Johannes, named after his home town, known as far away as the stars for his erudition

The tradition established in Vienna by Heinrich von Langenstein, Johannes von Gmunden and Georg Müstinger was successfully continued by Georg von Peuerbach (1423–1461), who contrary to some older sources was not a direct student of Johannes von Gmunden arriving in Vienna only in 1443 the year after Johannes death. However Georg did find himself in a readymade nest for the mathematical disciplines, an opportunity that he grasped with both hands developing further Vienna’s excellent reputation in this area.







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

The emergence of modern astronomy – a complex mosaic: Part XVI

One of the things attributed to Tycho Brahe is the geo-heliocentric model of the cosmos. In this system the Earth remains at the centre and the Moon and the Sun both orbit the Earth, whereas the other five planets orbit the Sun. This system combines most of the advantages of Copernicus’ heliocentric system without the problems caused by a moving Earth. As such, as we shall see, the Tychonic system became one of the two leading contenders later in the seventeenth century. The only problem is that although it is named after him, Tycho wasn’t the only person to suggest this model and he almost certainly wasn’t the first to think of it.


A 17th century illustration of the Hypothesis Tychonica from Hevelius’ Selenographia, 1647 page 163, whereby the Sun, Moon, and sphere of stars orbit the Earth, while the five known planets (Mercury, Venus, Mars, Jupiter, and Saturn) orbit the Sun. Source: Wikimedia Commons

The first to publish a version of the geo-heliocentric model was Nicolaus Reimers Baer (1551–1600), known as Ursus, in his Nicolai Raymari Ursi Dithmari Fundamentum astronomicum (Straßburg 1588). Ursus’ system differed from Tycho’s in that he included diurnal rotation.


Nicolaus Reimers Baer, Fundamentum Astronomicum 1588 geo-heliocentric planetary model Source: Wikimedia Commons

Ursus was a self-taught astronomer, who in his youth had worked as a pig-herd until Heinrich Rantzau (1526–1598), a humanist scholar and astrologer, recognised his talents and employed him as a mathematician.


Heinrich Rantzau Source: Wikimedia Commons

There followed a period as a private tutor and a year, 1586–87, in Kassel with Wilhelm. During his time in Kassel he translated De revolutionibus into German for Jost Bürgi, who couldn’t read Latin. In exchange Bürgi taught Ursus prosthaphaeresis, a method of using trigonometrical formulas to turn multiplications into sums to simplify calculations. From 1591 till his death, in 1600, Ursus was Imperial Mathematicus to Rudolf II in Prague.

Tycho was outraged that somebody published “his system” before he did and immediately accused Ursus of plagiarism, both of the geo-heliocentric system and of prosthaphaeresis, citing an earlier visit to Hven together with Rantzau, when Ursus was in his service. The two astronomers delivered a very unseemly public squabble through a series of publications; Tycho emphasising Ursus’ lowly birth and lack of formal qualifications and Ursus giving as good as he got in return. However, when Tycho left Hven and approached Prague, Ursus fled fearing the aristocrat’s wrath. When Kepler came to Prague to work with Tycho the first task that Tycho gave him was to write an account of the dispute, naturally expecting Kepler to find in his favour. Kepler wrote his report but didn’t ever publish it. Nicholas Jardine published a heavily annotated English translation in his The Birth of History and Philosophy of Science. Kepler’s ‘A Defence of Tycho against Ursus’ with Essays on its Provenance and Significance, CUP (2nd rev. ed. 1988)[1].

Tycho’s false accusation of theft of the trigonometrical method of prosthaphaeresis is, however, very revealing. Tycho was not the discoverer/inventor[2] of prosthaphaeresis. As far as can be ascertained, the method was originally discovered by Johannes Werner (1468–1522) but was actually taught to Tycho by the itinerant mathematician/astronomer from Breslau, Paul Wittich (c. 1546–1586). It turns out that that Wittich was probably the inspiration for both Tycho’s and Ursus’ decision to adopt a geo-heliocentric system. Wittich played around with the Capellan system, in which Mercury and Venus orbit the Sun in a geocentric system. He sketches of his thoughts are contained in his copy of De revolutionibus.


Paul Wittich’s 1578 Capellan geoheliocentric planetary model – as annotated in his copy of Copernicus’s De revolutionibus in February 1578 Source: Wikimedia Commons

Following Wittich’s, comparatively early, death Tycho went to a lot of trouble and expense to obtain both of Wittich’s copies of Copernicus’ book, suggesting he was desperately trying to cover up the origins of “his system.” Another indication of Wittich’s possible or even probable influence is the fact that David Origanus (1558–1629), who had been influenced by Wittich at the University of Frankfurt an der Oder, also “independently” invented a geo-heliocentric system but with diurnal rotation like Ursus’ system.


David Origanus Source: Wikimedia Commons

The route from a Capellan system to a full geo-heliocentric system was probably the route taken by both the physician and astrologer Helisaeus Roeslin (1545–1616) and the court mathematicus Simon Marius (1573–1625), who both claimed independent discovery of the system.


Simon Marius Source: Wikimedia Commons

Geoheliocentric cosmology, 16th century

I think it should be clear by now that a geo-heliocentric system, whether with or without diurnal rotation was seen as a logical development by several astronomers following the publication of De revolutionibus, for it combined most of the advantages of Copernicus’ system, whilst not requiring the Earth to orbit the Sun, solving as it did the problem of the missing, or better said undetectable, solar stellar parallax. Such a system also solved another perceived, empirical problem, which has been largely forgotten today, that of star size.

If the cosmos were heliocentric then the lack of detectable parallax would mean that the so-called fixed stars were absurdly distant and much worse, given the naked-eye false perception the size of the star discs, all the more absurdly immense. Tycho used this as a valid empirical argument alongside religious ones to categorically reject a heliocentric system. Because the geo-heliocentric system didn’t require stellar parallax then the distance to the fixed stars was considerably shorter and thus the star size also much smaller. The apparent star size argument would continue to play a significant role in the astronomical system debate until the end of the seventeenth century.

Tycho, naturally, hoped to use his vast quantity of freshly won, comparatively accurate celestial data to prove the empirical reality of his system. Unfortunately, he died before he could really set this project in motion. On his deathbed he extracted the promise from Johannes Kepler, his relatively new assistant, to use the data to prove the validity of his system. As is well known, Kepler did nothing of the sort but actually used Tycho’s hard won data to develop his own totally novel heliocentric system, of which more later.

However, a geo-heliocentric model of the cosmos, with or without diurnal rotation, remained, as we shall see later, one of the leading contenders amongst astronomers right up to about 1660-70. The definitive version based on Tycho’s own data was produced by Christen Sørensen, known as Longomontanus, (1562-1647),


Tycho’s longest serving and most loyal assistant, in his Astronomia Danica (1622).


Longomontanus’ system was published in direct opposition to Kepler’s heliocentric one. Unlike Tycho’s, Longomontanus’ system had diurnal rotation.

Today we tend to view the various geo-heliocentric systems, with hindsight, as more than somewhat bizarre, but they provided an important and probably necessary bridge between a pure geocentric model and a pure heliocentric one, delivering many of the perceived advantages of heliocentricity, without having to solve the problems created by an Earth flying at high speed around the Sun.

[1]A highly recommended read

[2]Chose your word according to your philosophy of mathematics


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