NOTE: This is an outline for a set of lectures on the Copernican Revolution. It includes references to Ptolemaic astronomy, which was the precursor of the Copernican system. These are all topics that are addressed in class lectures. 




Between 1500-1700 there was a vast change in viewpoint of educated public in Europe toward the natural world. At the end of period a generally accepted notion was that science was the arbiter of truth and that the world was rational and within the powers of humans to manage.


This is the scientific revolution. The first step in it, at the beginning of this period is the Copernican Revolution.




Copernicus' life:


Born in 1473 of German parents in Torun, Prussia--now Poland--about 100 miles south of Gdansk


Father died when Copernicus was 10.


Raised by uncle who became a bishop in the Catholic Church.


Went to study at the University of Cracow.

Studied medicine, but discovered ancient classics of math and astronomy


Summoned home by uncle who had arranged for C. to take post as Canon of Frauenberg Cathedral.


          missed getting the post by a few days because incumbent failed to die in an even numbered month when the uncle had the power to appoint successors to such positions. (The pope appointed in uneven months.)


Copernicus returned to his studies, but this time went on to the universities at Bologna and then Padua. His uncle eventually was able to appoint him to the sinecure as a Canon at Frauenberg Cathedral; this provided him with income and security, but little duties. In fact Copernicus continued his studies for an additional eight years.


Eventually he took a doctorate in Canon Law at the University of Ferrara (which he never actually attended) and then returned to Poland.


Even then he did not take up his post as Canon, but instead lived at his uncle's castle as house physician (ostensibly) for six years. During this time he formed his ideas about astronomy and made an outline of them which was not published until centuries later (The Commentary).


When his uncle died in 1512, Copernicus finally took up residence and duties as Canon at Frauenberg where he remained the rest of his life.


Officially, Copernicus functioned as a physician and church administrator, but had much leisure time and devoted much of it to his interest in astronomy.


He completed a draft of On the Revolutions of the Heavenly Spheres in 1530, but locked it away, making only occasional corrections after that. In 1543, he was eventually persuaded to publish it. He died in the same year.


Copernicus' interests:


Copernicus was a prototype Renaissance Man. Studied widely in many subjects, but took a special interest in mathematics and astronomy, as these seemed crucial and central to his philosophical understanding.


He was especially the flaws perceived in the current astronomical theory.


          Julian Calendar out by about 10 days.


          Council of Trent called to deal with this and other problems.


To understand Copernicus' interests we need to understand the classical tradition that he inherited and why astronomy was crucial to it.




Ancient natural philosophy sought universal, unchanging aspects of nature. These were eternal and worthy of attention. Other events were random and not worthy.


For Plato in 4th century B.C., the unchanging forms were the ultimate realities; their physical manifestations were not important. Therefore abstract thinking was the only kind of real value. This emphasis aided the development of mathematics a great deal because it focused on abstract relations. Ancient Greeks were excellent mathematicians. But Plato's appeal to the abstract was to disembodied to gain general approval and understanding. His view remained a very influential one among a certain segment of the educated society.


Plato's student, Aristotle, had much more success in characterizing nature in a way that made sense to his culture and to generations and generations after. Like Plato, Aristotle focussed attention upon those aspects of Nature which were in some sense eternal. But unlike Plato Aristotle's eternal forms existed only in physical manifestations.


These two outlooks provided philosophy with its major contrasting viewpoints. The dissonance between the two views has been responsible for much lack of communication among intelligent people for centuries. Also it provided issues to focus the attention of thinkers where the two points of view seemed to clash.


Such a clash is involved in the Copernican Revolution.




What was eternal was what never changed, or what repeated in a cycle. In antiquity there was nothing more obviously cyclic than the constant east-west motion of the objects in the heavens.


          General pattern of star motions remained the same. As though a large ball was viewed from the inside with the stars painted on its inner surface and it turned slowly and constantly.


          Sun and moon also moved with regularity, though not in step with the stars. They could be viewed as having a circular motion of their own in addition to sharing the motion of the stars.


          Circles were the ideal, perfect pathways because they were eternal (endless) and unchanging. Likewise, a sphere was the perfect shape because it had no sharp edges and was the same everywhere.


          Hence it seemed only fitting that the eternal motions of the heavenly bodies were somehow composed of the motions of circles and/or rotations of spheres.




          In addition to the stars, which seemed to be fixed on some large rotating sphere at the outer edge of the universe, and the sun and moon which dominated the sky when visible, there were a handful of other bodies which appeared regularly in the sky but were not so well behaved.


          These appeared to be stars, but stars that wandered. The Greeks called them wandering stars, which in Greek was the word planet. A planet was a star that did not remain in position relative to the other stars. Planets seemed to have an irregular motion in the sky, but one which repeated.


          For a web site illustrating and discussing the problem of the planets go to:


Another site, with extensive analysis of different ways of dealing with planetary motion, from the ancients to the Renaissance is
This site has animations and explanations of all aspects of this problem. Check this out by all means.



          Irregular but repeating was a self-contradiction to the ancient Greek mind. There must be something wrong here.


          Plato called attention to the problem and called upon philosophers to solve the paradox. He enjoined them to "save the phenomena" by which he meant to find out how it is that the motions of the planets which appear irregular really were some combination of regular eternal motions, that is, were really circular and unchanging.




The first real elaborated attempt to work out such a solution was made by Plato's student Eudoxus. Eudoxus' system was adopted by Plato's more famous student, Aristotle, and then considerably elaborated. It became a cornerstone of Aristotle's view of the cosmos, which itself came to dominate scientific thought for nearly two thousand years.


The spheres of Eudoxus


Eudoxus proposed that the planets were really bright spots imbedded on otherwise invisible spherical shells concentric with the earth. Each planet was part of a system of 4 concentric shells, connected to each other by their axes of rotation, which were all different. Each system was imbedded within the inner sphere of the system of the next farther planet. The outermost planet's system (Saturn) was imbedded in the sphere of the fixed stars.


Thus each planet had the possibility of considerable apparent irregularity in motion while really moving only in perfect circles within circles as the various spheres rotated, communicating the motion of one to the other.


Eudoxus's system was adopted in an amended and expanded version by Aristotle.


Aristotle's appeal


Aristotle's great power and appeal as a thinker had to do with his determination to have an answer for everything. For virtually every philosophical question that might have been raised in his day, Aristotle either had an answer, with arguments to support it, or had an argument to assert that the question was of no importance.


Moreover Aristotle's answers were all readily understandable. He appealed to the evidence of the senses and analysed them in a straightforward way.


The two sphere universe


For Aristotle, the most obvious distinction that could be made about the world around him was that in the heavens things went on and on, repeating themselves apparently forever, whereas on earth the general trend was for everything to have a single span of existence. Animals and plants were born, lived, and died and that was the end of them. Likewise motions all seemed to begin and then end. An object thrown in the air falls to the ground and then stops. Anything that stayed in motion on earth did so because something was pushing it along. But in the heavens, events went on forever.


Aristotle reasoned that there were really two different worlds visible to man. Everything below the moon existed somewhere within a life span from generation to corruption (beginning to end), while everything from the moon outwards was eternal.


In the sublunar world, below the moon, the substance of the world was in the form of the four elements, earth, air, fire, and water. Everything was imperfect and existing for a finite time. Motion, unless it was forced otherwise, was in straight lines (because straight lines had natural beginning and end points).


In the superlunar world, above the moon, everything that was consisted of a different material altogether, because it was perfect and could hardly be made from the imperfect elements. Beyond the moon, the substance of the world was another element, which Aristotle called simply the "fifth" element. The name has stuck, but we know it by the Latin for "fifth element," "quintessence." In the superlunar world, all motion was eternal and changless. To the Greek mind it therefore had to be circular motion at constant velocity. Nothing else made philosophical sense, but perhaps equally important, the mathematics of antiquity could not cope with any other kind of motion.


Aristotle's system of the world beyond the moon was essentially the system of Eudoxus, with each planet having several spherical shells associated with it, communicating motion from one to the other. Saturn nearest the outer sphere of the fixed stars and the moon nearest the boundary to the inner world which included the motionless earth. Aristotle determined, somehow, that more spheres were needed than Eudoxus had proposed and fixed the required number at 55.


Though Aristotle's views on most subjects prevailed, after the conquest of the surrounding world by (Aristotle's former pupil) Alexander the Great, Greek thinkers came into contact with the vast astronomical records of ancient Babylon. From these it became obvious that Aristotle's system was really inadequate for describing the motion of the planets. It did not "save the phenomena."

CLAUDIUS PTOLEMY 150 AD -- Alexandria


mathematical representation only (Platonic)




epicycle - deferent


          retrograde motion



          Greek math only handled stasis and regular motion



Ptolemy's system "impossible" to be physically real

Not a problem if true reality is realm of ideas


A web site on the Aristotelian world view and the Ptolemaic system:





Retained and elaborated by Arabs ("Almagest")

Attempts to reconcile with Aristotle system.

Epicycles as ball bearings between shells


Efforts to update Ptolemy and make more accessible.

Culminated in publication in 1496 of The Epitome of the Almagest by Regiomontanus (Johann Müller).




Copernicus took an interest in astronomy in part because it was perceived as a critical subject (understanding the order of the heavens = understanding the mysteries of nature = understanding God, etc.) and one that was in need of attention.


          Julian calendar out of date

          General revival of interest in classical theories & mathematics

          Something clearly wrong with Ptolemy that a clever person might discern


Big issue was the apparent conflict between Ptolemy's strictly mathematical representation and the Aristotelian literalist view.


Some devices of Ptolemy's did not appear to be possible physically.




The equant particularly troubled Copernicus because it was not possible for a sphere to rotate with stability evenly around a point which was not its geometrical centre.


In the Epitome of the Almagest, Regiomontanus had shown that the effect of the equant could be produced by the introduction of another epicycle. However, calculations could be so complex as to render this impractical.


(One epicycle is required to explain retrograde. Another for uniform motion.)


However, it is possible to explain retrograde differently if instead of having the planets revolve around the earth, they revolve around the sun. (Also suggested by Regiomontanus).


Copernicus, seeking to get rid of the philosophically repugnant equant, tried to revise the Ptolemaic system by substituting the sun as the center of motion of the planets. (But the earth is still motionless.) (This is the same as the Tycho Brahe system.)


Problem of Mars' orbit. If the planets circled the sun, but the earth was stationary, then the orbit of Mars (1.5 x radius of orbit of sun round earth) cuts into the orbit of the sun around the earth. Impossible if the orbits are physical spheres.


If the sun were motionless and the earth moved around it, that would solve this problem.


In the prevailing Aristotelian climate of thought, putting the earth in motion was an absurdity, as it violated common sense.


But Coppernicus was influenced as well by a strong Neo-Platonist tradition which sought the meaning of life in mysteries that may seem to defy common sense. Also the neo-platonist tradition (and the Hermetic tradition, which Copernicus also learned about at Bologna and Padua) placed greater emphasis on the symbolic value of the sun as the "giver of life". Therefore for the sun to assume a position of greater importance was also more natural.


Copernicus ultimate theory hung on to the physical reasoning of the Aristotelians in the construction of his model (physically real spheres carrying planets), but discarded the common sense perception of the motionless earth.


Copernicus realized his conception would make little sense to the public. Being secretive, he kept it to himself (and a few trusted colleagues) for 30 years, until finally urged to publish in the year of his death, 1543.




Earth a planet, like others, all circling the sun (no longer a planet)


Moon circling earth (no longer a planet)


Earth has three motions:

          Daily rotation -- replacing the movement of the sphere of the fixed start


          Annual revolution around sun -- accounting for retrograde motion


          3rd motion -- an annual rotation about an axis perpendicular to the ecliptic (to correct for change in earth's axis relative to the sun -- seeking symmetry around a point instead of inertial orientation relative to the stars)


Fixed stars truly fixed now.  Sphere of the fixed stars motionless.


No equant.


A web site on the basics of the Copernican system:



Problems to be explained (away) by Copernicus


1. moving earth -- no answer, really. Copernicus said that it was okay for the earth to move because it was a sphere and spherical motion was natural for spheres. Clouds and other objects in the air do not rush off to the west because being earthly, they partake of the earth's motion.


2. phases of Venus -- since Venus is held to orbit the sun in a smaller orbit than the earth, it will be seen from the earth at different angles with respect to the sun and therefore should exhibit phases, like the moon does. But Venus does not appear to exhibit phases. -- Copernicus' answer is that Venus is not lit by the sun, but has its own light.


3. stelar parallax. -- if earth is not the centre of the sphere of the fixed stars, but in orbit around the centre, it should see the stars at varying angles at different times of year. Therefore there should be stellar parallax seen. But none is seen. -- Copernicus' answer (actually correct, but seemed preposterous at the time) is that stellar parallax was not visible because the stars were too far away. (In relation to the heavens, the orbit of the earth is but a point.) (Stellar parallax discovered in 1838 by Bessel.)


Everything about Copernicus's reasoning was ancient. Difficulties solved by ad hoc arguments. His system just as complex as Ptolemy's. Copernicus solved some problems in Ptolemy but replaced them with others just as bad, perhaps. Orbits all circular and at constant speed--as required by ancients.

Copernicus saved the phenomena in a Platonic fashion.


His original appeal was to Neo-Platonists only.  Too much defying common sense.


Osiander's preface


A web site from a course that covers much the same ground on Copernicus as my lectures. These are also lecture notes, but with a few good illustrations, especially of retrograde motion as explained by Copernicus. This is one of the sites pointed to by the site for the astronomy course listed at the bottom of this document.







One of the few converts to Copernicus' theory in next 70 years was Johannes Kepler, a Lutheran mathematics professor in Austria and astrologer. Kepler could be considered a neo-Platonist as well.


Kepler had achieved fame as an astrologer early in his career by correctly predicting a cold winter one year, and also the Turkish invasion of Austria.


Kepler was obsessed with numerical and geometrical relationships and invested them with great mystical meaning. (Pythagorean)


Kepler found Copernicus' more mystical arguments amenable.


Kepler believed he too had found order in the heavens -- a particular geometrical symmetry.


Kepler's 5 solids:


At the age of 25 Kepler had a great insight:

          According to Copernicus, there were now six planets:

                   Mercury, Venus, Earth, Mars, Jupiter, Saturn

          Each planet was a blip on the surface of an invisible    spherical shell concentric with the sun.

          What determined the relative size of the spherical shells?      (Or what amounts to the same, the spaces between each?

          Euclid had shown that there were only 5 regular solids possible.

                   A regular solid can be inscribed and circumscribed in a         sphere.

                   cube -- between Saturn and Jupiter

                   tetrahedron -- between Jupiter and Mars (4 triangles)

                   dodecahedron -- between Mars and Earth (12 pentagons)

                   icosahedron -- betwen Earth and Venus (20 triangles)

                   octohedron -- between Venus and Mercury (8 triangles)


          The cosmic mystery is solved: the planetary orbs are separated by the distances required to fit the five regular solids between them as shown.


The answer seemed right to Kepler, but to prove it he needed to consult the most accurate observations of the planetary positions available. He sought out Tycho Brahe.


Tycho Brahe (1546-1601), like Copernicus, thought astronomy immensely important, but saw the problem with its state not with inadequate theory, but with innacurate observations. Gave his life to getting the positions right. Adopted a system much like Regiomontanus with earth stationary but planets revolving around sun.


A web site on Tycho Brahe:


Kepler came to Tycho's attention because of his Cosmographic Mystery and other achievements that gave Kepler some reputation. When Kepler sought out Tycho, Tycho hired him as an assistant to work out the mathematics involved in his observations (and thereby help Tycho prove that Tycho's own system was correct).


Kepler went to work for Tycho in Prague, but in a few months Tycho died. After a wrangle with Tycho's heirs, Kepler became Tycho's successor as Imperial Mathematician in Prague and therefore came into Tycho's observational data.


Kepler wanted the data to prove his own system, with the 5 regular solids. In working with Tycho's data, especially on Mars which has a very irregular orbit, Kepler uncovers several other mathematical mysteries of the heavens, which he publishes.


Three of these mysteries have survived, primarily because Newton later showed that they were explained by his (Newton's) physics.

We know these as Kepler's laws:


          1. Planets travel in elliptical orbits, with the sun at one focus.


          2. Planets sweep out equal areas in equal times (line from sun to planet sweeps out)


          3. T2 = k d3 (square of time of revolution proportional to cube of mean distance from sun).


A web site discussing and illustrating Kepler’s laws:

Another site on Kepler’s laws. The main (only?) virtue of this site is that it has another visual demonstration of the three laws if you want another look at them.

And another:



Point is, these were all magical numerological hocus pocus, the appeal of which was purely their elegance. Note also the sun's magnetic power of drawing the planets closer and infusing the planets with the ability to move more quickly as the sun is neared. Action at a distance -- an occult quality.


Kepler no more than Copernicus could have brought about a sea change in public opinion about astronomy and the place of the earth.



Born in Pisa, same year as Shakespeare

Son of musician

Studied medicine (to earn a good living) at the University of Pisa. Hated it.


Got interested in mathematics and began studying it privately.


Left university without a degree, but was appointed professor of mathematics at Pisa at age of 25.


(Paid 1/10 of what a philosophy professor was paid.)

Galileo detested philosophers. Thought they merely mouthed dogma. Their dogma was Aristotle, who was a great empiricist, but the philosophers no longer used their eyes to gain first hand experience of the world, they only learned what Aristotle and his commentators said. Galileo liked nothing better than to show up philosophers to be fools.


Mathematician = engineer in XVI -- a person good with instruments and calculations

          Galileo became a fine instrument maker and inventor of instruments (e.g. one like a slide rule)

Moved to the University of Padua in 1592 for 3 times his Pisa salary (near Venice). Had only light teaching duties: Euclid and Ptolemaic astronomy.


A web site on Galileo’s early work. Same topics as above. Good pictures.



Galileo became interested in Copernicus to explain Galileo's theory of the tides.

          Galileo believed the tides were explained by mechanical motion -- the sloshing of water due to the changes in speed of the earth as the daily and annual motion would be combined and opposed at different times of day.


The telescope


A spyglass was invented in Holland in 1609 which magnified about 3 times. Galileo heard of it, realized the principle, and made his own version which magnified 8 times. Later he improved it to 30 times magnification.


Used his telescope to spots ships at sea coming into harbor. Sold the telescopes to merchants who wanted to get a jump on the competition.


After a while, he got the idea to turn the telescope on the heavens. There, what he saw astounded him. He realized that he saw so much more clearly with a telescope than with the naked eye that he was seeing things no one had ever seen before.


It seemed to Galileo that what he saw proved the general correctness of Copernicus, or, more to the point, proved the incorrectness of the philosophers, who were all committed to the Aristotelian-Ptolemaic earth-centered view.


The Starry Messenger


In 1610, Galileo published a slim volume recounting his observations, The Starry Messenger.


          Moon he found rocky and uneven. Had mountains as large as on earth. Its craters he thought were seas. Therefore, the earth was not different in kind from the heavenly bodies, as Aristotle had thought, but instead the heavenly bodies were like the earth.


          Earthshine on the moon. Therefore irregular bodies can reflect light.


          Venus did indeed have phases. But they could only be seen with the greater resolution of the telescope.


          Jupiter has moons. Galileo saw four satellites of Jupiter. Therefore the earth is not an anomaly in having a moon.


          Milky way was not just a blur, but a conglomerate of stars. Indeed many more stars were visible than with the naked eye.


Galileo invited the public to make their own telescopes and see for themselves.


Galileo became famous. Moved to Florence to become the Imperial Mathematician to the Duke of Tuscany, where he would have no teaching duties and could devote himself to research. (Big mistake.)


Galileo began to undermine Aristotle as the privileged interpreter of the Bible.


          In letter to the Grand Duchess Christina, Galileo suggests that the Bible needs to be interpreted figuratively. Viz: when Joshua commands the sun to stand still (to prolong the day indefinitely), Galileo argues that this must be taken merely as a convenient way to express the thought to ordinary people who knew nothing of astronomy. (Because in Aristotelian-Ptolemaic astronomy, the explanation would actually be more complex.)


Galileo was playing with fire by suggesting that the authority of the Church needed to be re-examined. This was the middle of the Counter-Reformation. Those who opposed any aspect of Church authority were on thin ice.


In 1616 Galileo was forbidden by the Vatican to hold or defend the Copernican World System.


But the temptation is too great. Galileo itches to show that the Aristotelians are wrong, and that his theory of the tides is right (or at least might be). He decides that discussing the Copernican view is not the same as holding and defending it as true.


The Dialogue


In 1632 he completes a dialogue, in the style of Plato, which discusses the explanation of the tides. After some trouble he obtains no less than 4 imprimateurs giving permission of the censors for it to be published. He planned to call it the Dialogue on the Tides, but perhaps realizing that it really was about much more, dropped the reference to tides, and the work appeared under the simple title, Dialogue. History has come to know it better by the expanded title that was appended to later editions and translations: Dialogue Concerning the Two Chief World Systems--Ptolemaic and Copernican.


Dialogue has 3 characters:


          Salviati = Galileo = Copernican

          Sagredo = impartial observer, converted to Copernican view

          Simplicio = Aristotelian = fool = pope


The Dialogue systematically refutes every tenet of Aristotelian cosmology. And upsets the authority of the Church, which was based upon Aristotelian authority.


Galileo was called before the Inquisition. Convicted of vehemently suspected heresy, and sentenced to house arrest for the rest of his life.


A web site on Galileo’s astronomical work:



The Dialogue was banned, of course, which made it immensely popular, and Galileo had made Copernican astronomy understandable and reasonable (by simplifying it) and also made a shambles of the Aristotelian/Ptolemaic world view.


Galileo caused the Copernican Revolution (or completed it).


Galileo died in the year Newton was born.


Here is a web site from a course in the history of astronomy that pretty well encapsulates everything covered here. This link takes you to the beginning of a unit on Renaissance astronomy with links to all the people mentioned above.