Tycho, Kepler, & Newton : a Story in the Progress of Science

Mar 20 2007 Published by under Astronomy & Physics

I don't do this any more, but in the past I did what many astronomy professors do when teaching introductory astronomy: tell the tale of Tycho, Kepler, and Newton, as a way of introducing and describing planetary orbits. It's such a great story, as it shows the concrete struggle we as a race went through to fully codify and understand the heliocentric, Copernican picture of the Solar System. It also highlights the contributions of three very different sorts of scientists.

We have Tycho, the observer. We have Kepler, the phenomenologist. And, we have Newton, the theorist. Each played a crucial role, without which the contributions of each of the others would have been greatly lessened. The result was a revolution in our way of thinking about the Solar System, and the Universe at large.

Tycho Brahe was an observer. He compulsively took very precise data (for the time)— reams of data, huge amounts of data, on the positions of the planets as observed in the sky. Ultimately, this data would be used to once and for all show that the Copernican, Sun-centered picture of the Solar System was superior to the Earth-centered picture of the Solar System. Tycho, however, didn't believe it; he believed in a geocentric model. Like a good scientist, what he did was take lots of data, lots of very careful data, to test his theory. Perhaps he was doing it to prove the theory he favored— that is not the motivation that scientists are supposed to have, but as long as they approach it honestly and carefully, and don't fudge their data, it may be mere semantics whether they are trying to test their favorite theory, or whether they are trying to prove their favorite theory.

Ultimately, Tycho didn't really do either. He is the consummate observer or experimentalist. He excelled in the acquisition of first-rate data. He was the principal investigator who led and executed the project that produced the "planetary orbit survey" data of his time, a data set that later scientists would use for important and fundamental understanding about the nature of our world.

Kepler was a student and assistant of Tycho. Not the observer that Tycho was, Kepler's contribution came in the analysis of Tycho's data. And, yes, this is academia, so there are tales of acrimony and distrust on all sides, but we shall leave that aside for now.

Kepler took Tycho's data, and showed once and for all that you make a much simpler, much more straightforward, and much more powerful model of the Solar System if you place the Sun at the center and put the planets in orbit around it. This wasn't a new idea; Copernicus is generally credited, at least popularly, with the notion of the heliocentric model. The dominant model of the day, however, was Ptolemy's geocentric model, where the Earth was (sort of) at the center, and the planets (including, in the nomenclature of the time, the Sun and the Moon) orbited the Earth in a particularly complicated way. I suspect few really understood the model— heaven knows that I don't know all the details!— for the Earth wasn't exactly at the center. It was the thing closest to the center, but there were all sorts of ad-hoc offsets needed to make everything work right. Still, it wasn't bad; Ptolemy's model was able to predict the positions of the planets reasonably well, and as such was useful, even if cumbersome.

Kepler sat down with Tycho's data and, through a lot of work, was able to match all of the planet orbit data with three simple empirical laws:

  1. The planets orbit the sun in ellpises. Copernicus' original idea was that it was circles. At the time, there was still this notion that "the heavens" was a place of geometrical perfection, in contrast to the Earth. Circles are perfect geometrical figures, so there was a philosophical bias in favor of them. Kepler showed that circles didn't quite do it, but ellipses (which are slightly squashed circles, the amount of squashing being parameterized by the "eccentricity") did. The sun is not at the center of of the ellipse, but off center at the focus (a geometricall well-defined position). Most of the planets orbit in ellipses of very low eccentricity, so that they are almost circles. Mars' orbit is still very close to circular, but was eccentric enough that the difference between a circular and an elliptical orbit was easily discerned in Tycho's careful data.

  2. In their elliptical orbits, the planets move faster when closer to the sun than when farther from the Sun. (The actual law precisely specifies how this works.)

  3. The orbital period of a planet's orbit (how long its "year" is) is related to the "semi-major axis" of the orbit's ellipse (something like the average distance from the Sun), with larger orbits having longer periods according to the famous "P^2=A^3" law (P is period in Earth-years, A is the semi-major axis in astronomical units, or in units of the distance between the Earth and the Sun).

What Kepler had done was take Tycho's data, and through tremendous effort, distilled it down to a very small number of straightforward empirical laws. With those laws and a few free parameters— a semi-major axis, eccentricity, and position in the orbit on any one specified day— you could use Kepler's laws to predict where a planet would be any time in the future.

Why do I call these "empirical" laws? Because there is no underlying physics that says why these laws should be so. They are descriptions of the data. Elegant, extremely useful, beautiful, and compact descriptions of the data, yes. This is why I call Kepler a phenomenologist. He wasn't after the underlying fundamental theory, necessarily. Rather, he gave simple laws that described how all of the data worked.

Without Tycho, Kepler could never have discovered his three laws. Without Kepler, or another doing the work he did, Tycho's data would not have been nearly as important to the progress of human science as it turned out to be.

The last person in the story is Newton. Newton gave us his three laws of mechanics— the laws that include inertial (objects in motion stay in motion), reaction force (every action has an equal and opposite reaction), and the law of motion (the acceleration of an object is proportional to the force on that object; the constant of proportionality is the object's mass).

Newton also gave us his Universal Law of Gravitation. This was a single, simple equation that said that the gravitational force between two objects (which is the same on either object, thanks to the action/reaction law) is proportional to the masses of the two objects, and goes down as the square of the distance between the two objects. If you start from this law, you can derive that when a small mass is orbiting a large mass, the orbits are in ellipses, the small mass moves faster when closer to the large mass, and the period of the orbit goes up with the semi-major axis of the ellipse with P^2 proportional to A^3.

Notice what has happened. With universal laws of mechanics— not specific to planetary orbits at all— and with a single equation describing gravity, Newton is able to derive Kepler's three laws. What's more, there is now a physical theory that explains why Kepler's Laws are the way they are: it's just gravity.

There are two important, major contributions here. First is the unification of the heavens and the earth. No longer are the planets in a "celestial" realm that obeys "more perfect" laws of its own. The force that explains why planets orbit the way they do is exactly the same as the force that explains why apples fall to the ground. The force is described by exactly the same equation. Second, we have the conversion of Kepler's purely empirical laws into something that can be derived from a fundamental physical theory. Whereas Tycho was the observer and Kepler was the phenomenologist in this story, Newton is the fundamental theorist.

Could Kepler have been skipped? Perhaps. Perhaps Newton could have come up with his law of Universal gravitation, and then showed through long and arduous calculation that it is able to predict and explain Tycho's data. However, by distilling Tycho's data, Kepler gave a much more tractable and a much more meaningful set of observations which Newton's theory needed to describe. Newton's theory didn't need to be compared with each and every data point produced by Tycho, because Kepler had already distilled Tycho's data down to its core. At that point, if Newton's theory is shown to be consistent with Kepler's empirical laws, we know that Newton's theory is consistent with Tycho's data— because Kepler's laws are consistent with Tycho's data! Beyond that, the form of Kepler's laws can help guide the process of discovery. Just a lot of planetary positions themselves may not give much physical insight. The notion of planets orbiting in ellipses with the Sun at the focus, however, can. Those simple laws suggest that a simple underlying physical theory may be sufficient, and may even help guide the scientist in understanding the form of that theory.

The Copernican Revolution was complete. We had finally shown that not only is the heliocentric model much simpler and more tractable (according to Kepler), but we had a fundamental theory of gravity that showed that in a real way the Sun really is at the center of the Solar System— for the Sun has most of the mass of the Solar System, and is located very close to the "center of mass" of the Solar System. What's more, we had gone through the steps of understanding just the way science is supposed to. We had started with a lot of careful data. We had gone through the arduous process of trying to understand, manage, and simplify that data. And, finally, we had taken the understanding of that data we'd obtained and turned it into confirmation of a basic physical theory.

Tycho, Kepler, and Newton: observer, phenomenologist, and theorist. Respect them all, for all of their contributions to science are essential. Without any one, the contributions of the other two would have been less, or even impossible.

24 responses so far

  • Navneeth says:

    Wonderful article! I have read this 'story' umpteen number of times in popular-level books and textbooks, but this article gives it a better a perspective.Thanks.

  • tom says:

    Why don't you include this tale in your introductory courses anymore?

  • Matt says:

    The discussion of Kepler's laws in physics classes revolves around solving for a radial or planar angle in terms of time, or each other. This is often disconnected from what astronomers are directly measuring which is an angle across the sky and the time it takes to traverse that arc.
    How do astronomers go from one set of variables to the other? I imagine its a really really messy geometry problem having to take into account the various rotations of the Earth, plus positions and rotations of the object under observation.

  • Rob Knop says:

    Why don't you include this tale in your introductory courses anymore?
    Different focus. The "standard" intro astronomy class has just too much stuff in it. If you read any of the myriad introductory texts out there, there is lots and lots of stuff, and a whole host of "standard" topics. The result is a course that can be very good if taught by an engaging professor, but which can be very frustrating for the students if the professor tries to take the understanding much beyond the recall level-- because there's just too much, and it doesn't hang together.
    Last time I taught the course, I focused the whole thing on the questions "How old is the Universe? How do we know?" As a result, I didn't end up spending any time on Kepler's laws, and spent very little time on planetary orbits.
    Matt-- yes, it's fairly messy. You have to take into account the position of the Earth *and* the planet being observed to figure out where the planet is in the sky. It's the combination of the two that gives us fun things like retrograde motion.
    -Rob

  • Matt says:

    That was really neat, its easy to recognize each of those personalities here where I'm working

  • I go through this story every year in my high school physics class. This year I added a neat activity that I picked up from The Physics Teacher (journal published by AAPT). I drew an ellipse on a large piece of butcher paper using two pins and a string. Then I cut it up into pieces and showed the students how to calculate a force from the curvature of the section they had. We then plotted all the results and came up with an inverse-square force law.
    My conversation with the students went something like this: "Kepler found out that the planets travel in ellipses with the sun at one focus. But he couldn't explain why. Newton came along and explained why: Because our universe has a gravitational force law where the force falls off as the square of the distance between the two objects. If the force law was different, we'd have different orbits, but we don't."
    Having the students actually do Newton's geometric calculation helped them to appreciate the difference between describing something and explaining it.

  • Tom says:

    Nicely told.
    Though Kepler was certainly no phenomenologist! Phenomenology is the much later philosophical tradition that tries to characterise the /ways/ in which things appear, not what appears per se.

  • Rob -
    I think that this article would make and excellent addiition to the "basic concepts" series. Have you considered sending the link to John Wilkins at scienceblogs.com/evolvingthoughs?

  • Thony C. says:

    So Rob Kopp has given us a nice fairy tale about a small segment of the evolution of the new astronomy in the early modern period. Why do I say fairy tale? Mr Kopp himself calls it a great story but I'm afraid to say it deviates quite a long way from the historical facts, as we know them, concerning the evolution of the new astronomy.
    This is what I call the "back of the cornflake packet view of the history of science". I will add before he gets too offended that Mr Kopp tells his story well and with less factual errors than is normal in such presentations but this is still a major distortion of what actually took place and more important a major distortion of the actual scientific process. The real historical development of a scientific discipline or sub-discipline is a messy, complex, twisted struggle between competing ideas, theories, prejudices, superstitions and on occasions off the wall insanity with a grain of truth (e.g. Giordano Bruno). The type of story that Mr Kopp presents us with here is a sanitised, normative reconstruction produced with hindsight whilst looking down a telescope the wrong way.
    Don't get me wrong this is not a personal attack on the good Prof. Kopp who is only trying to animate his students or in this case his readers through real examples from the history of his discipline. I too was originally motivated to become an historian of science by reading Eric Temple Bell's Men of Mathematics when I was sixteen years old, historically a disaster of a book but wonderfully inspiring in its tales of heroic mathematicians. However, over the years, I have come to regard this form of presentation of the history of science with a jaundiced eye. If we wish students to understand what science is, how it's made and how it progresses then we should present them with the real history as it really happened and not some sort of pseudo-Whig-historical march of progress of the Titans of science.
    Unfortunately I have to work and so do not have time now to make a detailed criticism of what Mr Kopp has written but I shall return to do so within the next forty-eight hours, so if anybody is interested come back and look again.
    Just to keep you going some of the small points of criticism, which I shall elucidate in my next posting. Kepler was not a student of Tycho, they are not Newton's three laws of mechanics, Kepler was not a phenomenologist and his laws were not empirical (at least not in the sense Rob Kopp uses) and there never was a Copernican Revolution.

  • Rob Knop says:

    Well, that ought to be good....
    I'm also wondering who this Rob Kopp guy is.

  • David Harmon says:

    Oh. my, this is an interesting variation on the "concern troll"... a "Fermat troll" who promises to back up his condecension... at some unspecified future date.
    Bah....

  • Rob Knop says:

    "I have developed this excellent formulation of quantum gravity, but alas there aren't enough atoms within our Hubble volume to write it down."

  • MTW says:

    I will second David's comment that this is the most bizarre "concern troll" I have ever seen. Rob's comment seems to be an excellent variation of the "Its true, because the math works" idiocy regularly commented on by Mark over at Good/Bad Math.
    And being a history of science and physics student, I am ready and waiting for that eventual response. At least for a laugh.

  • Rob Knop says:

    Let me say that:
    The real historical development of a scientific discipline or sub-discipline is a messy, complex, twisted struggle between competing ideas, theories, prejudices, superstitions and on occasions off the wall insanity with a grain of truth
    is absolutely true.
    However.
    Hindsight is useful. It may all be a mess, it may have twists, etc. Later, after the fracas is over, perhaps even centuries later, we can look back and distill out what were the most important advances, what were the most important aspects. What mattered? What mattered was the picture of classical mechanics that was the fundamental basis of a lot of Physics for centuries, and remains extremely useful today as an "everyday limit" of our current basis. What also mattered was the roles that the key players had in the development of this extremely useful theory -- the roles that I outline here.
    The twists and turns and confusions and all of that: they can be interesting. But sometimes you have to simplify, perhaps even oversimplify, to get to the heart of what really matters, of what was really going on.
    For instance, when we are teaching students about planetary orbits, ellipses, and Kepler's laws, should we mention (a) effective mass in a two-body system, (b) gravitational effects of the other planets on any given planet, (c) chaos in a multiple-body system, (d) general relativistic effects, (e) non-gravitational effects such as the solar wind on very small particles, etc? Should we say, don't use Kepler's laws, because they're wrong, until you've calculated all of the above effects and have shown that they are unimportant in the given circumstance? Some or all of the above may be mentioned, but if you refuse to just teach Kepler's laws on the basis that they're an "untrue fairy story" given all of the above, then nobody will ever learn anything. Even mentioning most of the effects I've just described will serve primarily to convince the students that in reality it's much too hard, and that what they're learning is meaningless. Which is not right, and is not what we want to teach.
    Simplification through hindsight is essential.
    Don't forget the full history, but don't insist that it must be fully described in all of its obfuscating glory every time something is discussed.

  • Monte Davis says:

    Excellent synopsis -- and a *truly* excellent response, more even-tempered than many of us could manage, to the egregious Thony C.
    Every discipline knows the distinction between the messy, twisted way it really was and the pared-down pedagogical version. The difference is especially stark in the natural sciences, because they have been so successful -- so cumulative -- that they simply *must* trim away the false starts and dead ends and decades-long periods of confusion, or else Physics 405 would still be sorting out motion, inertia, and _vis viva_, in hopes of getting momentum cleared up before sending the students off to grad school.

  • Sage says:

    You're point about the necessity of streamlining history and highlighting the (in your case, pedagogically) relevant points is well-taken. However, I don't think it does justice to either history or how science works in general to strictly separate observations, phenomenology, and theory--it doesn't work well historically, and as a practicing scientist I'm sure you can appreciate the degree of overlap that between the three categories in modern scientific work.
    Simplification is one thing, but propagating historical myths is another. The above poster may be a bit strident in his approach, but a lot of what he is saying has meat to it. It's not just that the traditional story is an oversimplification; in some ways, it doesn't just leave out messy details, it it misses much of what was important in getting from there to here and replaces it with a story that is actually outright wrong in some ways. I won't go so far as to say there was no Copernican Revolution (how to characterize it is a matter of historical debate), but using this story as a parable for scientific method is dubious as best.
    The process of trimming and reinterpretation by which science progress that Monte Davis speaks of above is what your students likely don't understand about science. The basic "data to equations to theory" part, they no doubt learned in high school. I don't think it's fair to say that "every discipline knows" what's being left out; disciplinary myths are remarkably persistent and powerful. There are arguments to be made about the utility of such distorting myths, but one needn't conflate trying to present history accurately (which can still be done in a concise way) with teaching students how to do Aristotelian physics before they can learn Newton.
    A more useful point to get across to students is, perhaps, that one needn't get it all right to do useful science. So Kepler's theoretical work, while not well-remembered and it some ways quite wild, was actually very influential in the development of what Newton would eventually define as "force" (despite it's quasi-mystical origins). At the same time, Newton's theory of gravitation was explicitly phenomenological, since he had no way to approach the issue of what caused gravitational attraction. This lack of a causal explanation in Newton's work (i.e., because his work was in some sense atheoretical) was one of the main objections other natural philosophers had to it.

  • Thony C. says:

    Unlike Fermat I deliver on my promises, first a few comments on the reactions to my admittedly some over the top criticism of Rob Knop's original post.
    Above all a humble and sincere apology for consistently spelling your name wrong, I offer no excuse but an explanation. I suffer from dysgraphia, or as one of my pupils who is similarly afflicted expresses it, I'm an orthographic anarchist. At the best of times my orthography is dubious and sometimes my brain registers names completely wrongly and no mater how often I then read them afterwards I still consistently spell them the way my brain has registered them. Thank you for at least taking this unintentional insult with humour.
    I am not a troll. Trolls are Norwegian whereas I am English although I live in Southern Germany.
    An excellent reply to my criticism from Rob Knop but my objections still stand, if you wish to teach your students scientific methodology then teach them scientific methodology but don't falsify the history of science to do so. For example Kepler was not a phenomenologist and he did not produce "empirical laws" in the way that you describe. Kepler's entire life's work was theory driven and his attempts to find the fundamental underlying theory for his laws were an important step in the process that led to Newton's theory of universal gravitation, as Sage has already pointed out in his excellent reply.
    On the subject of my extremely provocative claim that there never was a Copernican Revolution I remain unrepentant and I shall now explain why. I in no way deny that there was a fundamental change in European astronomy and cosmology that took place in the early modern period, I would be mad to do so as I spend a fairly large part of my life studying this change and lecturing on it, I do however strongly object to labelling it "The Copernican Revolution" as this concept is highly misleading and factually incorrect. The concept consist of only two words but each of them is wrong in its own way so I will deal with them separately starting with "revolution".
    Revolution implies a radical, abrupt and even violent change this was most certainly not the case in the evolution of the "new astronomy". It was a long, complex, multi-facetted and very convoluted process that can be considered to have started in 1409 with the reappearance of the Geography of Ptolemaeus in Europe (you need accurate and reliable astronomical data in order to do cartography) and reached a provisional conclusion with Bradley's discovery of stellar aberration in 1725 (confirmation that the earth orbits the sun) and the various expedition in the middle of the 18th century that finally demonstrated the truth of the Newton/Huygens' hypothesis on the shape of the globe, a wonderfully deduced consequence of diurnal rotation. To describe this 350 years odyssey as a revolution is totally inaccurate and highly misleading.
    To label this process Copernican, even if one dispenses with the word revolution is equally misleading, it drastically over emphasises the role that Copernicus and his book played in the development of the new astronomy. One can and should not deny that it is one of the significant building blocks in this process but it is by no means the defining step or in anyway more significant than many other factors involved such as: The debate on the true astronomical nature of comets which began in the 15th C. with Toscanelli, Peuerbach, and Regiomontanus was continued in the 16th C. by Apian, Gemma Frisius, Cardano, Brahe and others was collated by Kepler in a fascinating paper in, I think, 1618 and then taken up again in the second half of the 17th century by the English mathematicians around Newton. One third of book three of Newton's Principia is taken up with the discussion of comets. Or the discussion of the correct mathematical measurement of the parallax of a moving body which accompanied the comet debate. Or the introduction of the teaching of mathematics and astronomy into the schools and university by Melanchthon from 1520 onwards for the Protestants, by Clavius from 1580 onwards for the Catholics and by Henry Savile in 1620 for England. Or the invention of printing in circa 1540 which made good quality accurate copies of the major works on astronomy and mathematics widely and comparatively cheaply available. Or the socio-political and economic demand for reliable and accurate astronomical data for astrology, cartography, chronometry and navigation. Or the development of telescopic astronomy in the 17th C. I could go on but I think that is enough to make my point. The publication of Copernicus' hypothesis of a helio-static universe (read solar system!) in Nuernberg in 1543 was one stone in a complex mosaic and append his name to the whole of the mosaic leads automatically to a massive historical distortion.

  • Rob Knop says:

    So, a couple of points. First: whatever Kepler's motivations, the fact remains that Kepler's Laws-- his most visible lasting contribution-- are empirical laws. Perhaps I misspoke when I said that Kepler wasn't after the deep theory behind it-- but in the end, the role he played in this story was that of empiricist, given what he produced.
    As for your extensive rant on the name of the "Copernican Revolution" -- I think the name "Revolution" applies, just as the name "Industrial Revolution" (which still hasn't even really reached some parts of the world) applies. That wasn't something that happened in a couple of years. It's something whose roots can probably be traced back to the development of the mill or the cotton gin or who knows what. Yes, there was a huge ramp of change right around the beginning of the 20th century, but I'd also say that there was a huge ramp of change in understanding during the Tycho-Kepler-Newton years. With hindsight-- an advantage that I really don't think it makes sense to give up-- we can clearly see a fundamental change in the thinking about the Universe. The notion of a heliocentric Solar System was the first thing that philosophically moved us away from "the center." It was an important step. It kept going with Shapley's model of the Galaxy, with the Curtis-Shapley debate-- and, indeed, is still a hot topic right now with the whole issue of cosmological parameter fine-tuning.
    AS for the other part:
    The publication of Copernicus' hypothesis of a helio-static universe (read solar system!) in Nuernberg in 1543 was one stone in a complex mosaic and append his name to the whole of the mosaic leads automatically to a massive historical distortion.
    Welcome to the real world.
    Was the Monroe Doctrine the sole creation of President Monroe? Was Peter Jackson the only one responsible for the "best picture" award of Return of the King? Was Riemannian Geometry conceived in a vacuum, or did he need work before-- and would anybody outside of mathematics care if it didn't turn out to be fundamental for the theory of General Relativity? For that matter, was Einstein really the only one to develop General Relativity? Was John Hancock the most important signatory of the Declaration of Independence? Did Gary Gygax create D&D ab initio? Are all of those cars really descendants of the design and creative work primarily of Ford? Does Tom Clancy even write a tenth of the books with his name on them any more? Was Columbus really such an outstanding European explorer of the 14th and 15th centuries that should receive either a national holiday, or specific individual revulsion for the evils resulting from European colonization?
    Etc.
    We like to identify with people. With individuals. That leads to a sometimes unfortunate tendency for hero worship and elevation of some individuals at the expense of others who deserve more credit than they get. But it also leads to us naming things after some individuals, and remembering some individuals, and remembering that all of these things are human accomplisments.
    Consider this year's Nobel Prize in Physics. Smoot and Mather were given the Nobel Prize for the CMB fluctuation discoveries by COBE. But, as my tabletop physics colleagues are fond of pointing out (usually in the context of questioning whether anybody from a big collaboration should ever get credit for anything), COBE was an effort of thousands. Even the data analysis was not done just by a couple of guys, but by teams. The same is true for all the Nobel Prizes given out over the years in particle physics. Hell, you can read my own rant on the matter here.
    We pick out and laud figures who stand out even though those figures had to stand on the shoulders of giants-- giants before, and giants after.
    What is the most identifiable feature of the new cosmology? The fact that the Earth is no longer at the center. Copernicus is identified as the figure who proposed that model. No, it wasn't just his work, but it gets that name because in retrospect, we see that his work distills the ultimate conclusion that was reached by the efforts of many.

  • Thony C. says:

    "Welcome to the real world."
    I would actually say welcome to the "unreal world" a point, which you amply illustrate in all that follows. We distort the historical process by apply the names of "prominent" individuals to complex historical developments that involved many individuals and also many non-individual i.e. social, economic etc factors. It is exactly this type of distortion that the current developments in the history of science are trying to dispel. There are serious attempts to get away from the "great names" school of historiography that your original post so wonderfully illustrates. Yes these things are human accomplishments but they are achieved by groups and in some cases generations of human beings working with, alongside and against each other and not by some isolated genial super human giant. This appears to be a point we both agree on but by presenting over simplified distortion of the history of science as you did in your original post you actual perpetuate the myths and strengthen the belief in many of your readers that for example the theory of universal gravity was the product of Isaac Newton sitting alone in his ivory tower in Cambridge and not the product of more than one hundred years of debate and dispute that starts, at the latest, in the first chapter of De Revolutionibus. In fact Copernicus in one passage comes so close to stating a theory of universal gravitation that Alexander von Humboldt in the 19th C. actually credits him and not Newton as its discoverer in his version of the great names game. The whole purpose of my original criticism of your original post is part of a personal crusade to get people to stop presenting the history of science as a litany of "great names" and naming major shifts in scientific thought after individuals rather than the events themselves, therefore "Evolution of the New Astronomy in the Early Modern Period" and not the "Copernican Revolution". Maybe I'm tilting at windmills but if I keep on trying I might just get one of them buggers to stop turning!

  • Sage says:

    Thorny C., you should become a Wikipedian and help with WikiProject History of Science:
    http://en.wikipedia.org/wiki/Wikipedia:WikiProject_History_of_Science
    We desperately need more professional historians of science, and Wikipedia is probably the best means of getting accurate history out to non-historians. Steve McCluskey (a medievalist archaeoastronomer), a real troll (one who shares your distaste for the traditional SciRev story but lacks your diplomacy and eloquence, and seems to oppose it for entirely different and idiosyncratic reasons), and I (a grad student historian of modern biology) had been trying to make progress on the "Scientific Revolution" article, but work has kind of petered out. Someone who really knew the SciRev historiography would be a great help.
    If you're interested but want some help getting started, leave me a note on my Wikipedia userpage:
    http://en.wikipedia.org/wiki/User:Ragesoss

  • Sage says:

    Rob, you clearly recognize the complexity of the way science actually works. This brings up two issues. One, regarding the usefulness of this story: are your students better served by an inspiring but inaccurate view of how science works, or a more accurate but messier one? Two, regarding hindsight: It seems to me that what you are applying is quite the opposite of hindsight. Newton was acutely aware of (and acknowledged) the contributions of Copernicus, Tycho and Kepler. The story you tell is the same one scientists have been telling for hundreds of years now. It is only with hindsight that we are now able to see a broader view of what scientists in the early 18th century left out (sometimes intentionally, sometimes not) when recounting the history of their science.

  • Sage says:

    Thorny C.,
    I left an earlier post for you that was lost or held up in moderation (because it included links). Anyhow, I want to invite you to participate in the history of science project on Wikipedia. It's probably the most effective way of actually making progress with dispelling historical myths and getting better history out to a (very, very) wide audience, and we desperately need more historians of science. My name in this post should link to my Wikipedia page; leave me a message if you're interested.

  • Thony C. says:

    "For instance, when we are teaching students about planetary orbits, ellipses, and Kepler's laws, should we mention (a) effective mass in a two-body system, (b) gravitational effects of the other planets on any given planet, (c) chaos in a multiple-body system, (d) general relativistic effects, (e) non-gravitational effects such as the solar wind on very small particles, etc?"
    Prof.Knop you probably intended the above quote as a rhetorical question but the answer is a resounding yes! If you do it historically then you can point out all of the things that Kepler ignored or rather didn't take into account because he didn't know that they existed. You can then explain why in his case it functioned despite the fact that he didn't take these things into account. His luck in being assigned Mars by Tycho and that if he had been assigned the Moon or Mercury instead, he would probably never have discovered his first two laws. You can then go on to show how Newton added those elements to the problem of which he was aware (mass etc.) and corrected Kepler's laws and also "truly proved" them for the first time. Continuing the theme you can explain that the three-body problem (let alone the multi-body problem) has not/can not be solved mathematically. Moving on we have the solution of the moon's orbit by Laplace, the solution of the Mercury problem through the discovery of relativity and so on and so forth. Done properly and with the right level of sensitivity you can, through the historical solutions of the problems that Kepler's laws entail, present a stimulating overview of the development of astro-physics and thereby encourage students to delve deeper into the subject.

  • Rob Knop says:

    Prof.Knop you probably intended the above quote as a rhetorical question but the answer is a resounding yes! If you do it historically then you can point out all of the things that Kepler ignored or rather didn't take into account because he didn't know that they existed.
    Well, I disagree, and very strongly.
    In a class that is just about planetary orbits, yes, you can do all that. But everything you describe— really doing that, and doing it so that students don't just hear all the words, but even understand some of it, is a full semester's worth of work— perhaps more for non-scientists, who might need more background to appreciate it all.
    But if you try to do that in a class that has anything else in it, you will kill the students with utter and extreme information overload.
    Believe me, I know. I didn't get anywhere near that level of complexity the first time or two I taught the non-majors intro astronomy here, and already I had too much stuff and information overload.
    Perhaps you're saying that no class should bite off more than it can chew, and that each class should explore all the details of anything it covers. No realistic person is going to have any kind of broad-based knowledge in that case, then, because nobody will have the time to hear about very much at all at the level of detail you are demanding!
    -Rob