Talk:Johannes Kepler/Archive 1

comments
someone has defaced the page. Specifically the area about his death. Just thought I should let someone know. ---

Removed. It's not clear that previous generations of astronomers had been content to accept authority of ideas. Kepler had new data which other astronomers had, and it took him 20 years to process it all.


 * whereas previous generations of astronomers had been content to accept the authority of ideas from previous generations

Removed reference to God. The people that initially came up with the idea that planets moved in circles were the Greeks who did not believe that planets moved in that way because God wanted them to. They were polythestic. The reasons for circles came from Plato, which got absorbed into Christian theology, but that's a whole other article.

Also emphasized the fact that before Tycho, all the data suggested that the planets did move in circles, and that showing that they weren't circles was not obvious (it took Kepler decades.)

Roadrunner

Are the two titles The Cosmic Mystery and Misterium Cosmographicum the same book ? It's a bit confusing with alternating Latin and English translated titles.Norwikian 10:34, 4 Oct 2003 (UTC)
 * They're the same. Caesar Lexicorum, 00:46, 30 December 2005 (UTC)

Kepler
1620 Kepler´s mother was arrested in Leonburg. the name of the city is Leonberg not Leonburg.

Kepler
He was a exermly smart man who knew what he was doing but should not be regarded as just an asrtomer. His work should be study be all to fully understand the orbits of the planets an d other things in the night sky.

The 'See also' link
Removed the 'See also" link pointing to his laws of planetary motion. The link was superfluous, as there was already a link to that topic within the body of the text! Eilthireach 03:57, 27 Mar 2005 (UTC)

Balance
When I came across the article earlier today, it was extremely unbalanced between his mysticism and his scientific work. Of course these are modern categories, but from the amount of space devoted to them, it came across as though his speculation about the platonic solids were somehow ten times more important than his laws of planetary motion! Part of this may be simply because the treatment of his laws of motion was in the Kepler's laws of planetary motion article, but I thought it was just plain goofy. Given some of the controversy there's been over astrology-related articles, I may also be hypersensitive to what I see as attempts by believers in astrology to push a POV that legitimizes astrology, and blurs the line between science and pseudoscience. I've beefed up the discussion of Kepler's laws with a couple of figures and more text. (Most of this is taken directly from a copylefted book I wrote.) Although this may be seen as duplicating the article on Kepler's laws, it is much shorter and less mathematical, so I think it's appropriate to have it in here.--Bcrowell 5 July 2005 16:35 (UTC)


 * It is also hard to understand why so much space is devoted to his nonsensical books whereas there's no mention of Astronomia nova. Bambaiah 13:37, July 12, 2005 (UTC)


 * Certianly mathamatical observations outway mystologicalb observations? no?-- Hello  'from ' SPACE undefined 00:12, 15 November 2005 (UTC)

Kepler's Third Law
There a request for Kepler's Third Law from ACF Regionals 2000 answers

If this is another name for a page that already exists could someone more knowledgeable than me make a redirect. Or if not could some make an article.--BirgitteSB 15:55, July 12, 2005 (UTC)


 * Hi -- The article you refer to has been nominated for deletion. No, there should not be a separate article on the third law. It's covered here.--Bcrowell 17:02, 12 July 2005 (UTC)

Quote
There seems to be a typo in this quotation:
 * As one historian, John North, put it, 'had he not been an astrologer he would very probably have failed to produced his planetary astronomy in the form we have it.'

Can someone check it? It's probably from:
 * John North, The Fontana History of Astronomy and Cosmology, London 1994, pp. 309-26

Kepler's Equations
There is a very recent paper entitled "Kepler's Equations : A Kinematical Deduction" by Raul Nunes (a copy of which can be downloaded from http://ThreeBirds.com.br/KE.pdf) which contains a new purely kinematical deduction of Kepler's equations for all types of conics. It also includes a lot of bibliographic references about Kepler's works and life.

I have added some information about exactly how Kepler was able to use Tycho's observational data to deduce the orbit of Mars and thus his various laws. Peter Maggs 22:12, 15 October 2005 (UTC)

To Kepler the three laws were a part of his theory. He never thought them so important. It took Newton to make them so. BernardZ 14:32, 10 December 2006 (UTC)

Harmonices Mundi or Harmonice Mundi?
Is there an "s" in the name of the book? I'm asking because someone chopped the "s" out in the on Harmonices Mundi article. Curiously, each of these get a lot of Google hits. See here for the hits without the "s", and see here for the hits with the "s". It's not clear to me which is right. (I'm posting this here because this article seems to have more traffic.) --A bit iffy 08:16, 18 October 2005 (UTC)

I have a copy of the book (not an original mind you!) and the author refers to it in the introduction and such as Harmonice Mundi. However, on the facsimile of the original title page it's Harmonices Mundi. The difference could be "Harmony" vs. "Harmonies", but it would still need to be one or the other. Perhaps it's some nuance of Latin I'm missing, but I think the reference should be Harmonice Mundi since so many scholars refer to it like that, without the "s". --DanielCD 12:22, 18 October 2005 (UTC)

Anyone here better at Latin than I? --DanielCD 12:26, 18 October 2005 (UTC) --- The correct title should be given as Harmonices Mundi Libri V, which in English is "Harmonics of the World, Five Books" in deference to the Ptolemaic work on harmonics with which Kepler saw himself in dialogue. The confusion arises because 'Harmonice' might be considered an ablative and thus the title would read "De Harmonice Mundi" or "Concerning the Harmony of the World." When one considers that Kepler was dealing with an entire system of harmonics on many levels, the plural makes more sense, and Ed Rosen has written extensively on this subject, although the reference escapes me at the moment. The 's' is included on the 1858 facsimile of the title page in C. Frisch's edition of the Opera Omnia, which can be accessed via Gallica.bnf.fr. --PaulRWagner 28 Nov MMV

Copied from Main Page discussion March 8, 2006
 * The anniversaries section today says that on this day some years ago, Kepler discovered the third law of planetary motion. Huh? You don't discover something like that until years, possibly decades of observing data or reading collected data. Is March 8 the day he settled on its final form? The day he first proposed it? Thought of it? The day it was published in a journal? They day it was submitted to a journal? No discovery of a scientific law happens all in one day. The article on Kepler doesn't specify which. Can we clarify this entry please? 24.243.188.42 02:07, 8 March 2006 (UTC)


 * Google shows that the third law of planetary motion was published in 1619 in Harmonice Mundi. The Wiki article states that it took 2 decades to find the form of the 3 laws. This would make March 8 the anniversary of the day he settled on its final form -- by extensive number crunching (two decades worth). --Ancheta Wis 05:06, 8 March 2006 (UTC)
 * Note: The Kepler article Revision as of 08:36, 9 March 2003 stated the initial March 8, 1618 discovery (and the confirmation on May 15, 1618). But it has apparently been dropped from the article. By the policy of Selected anniversaries we need to reinstate this fact into the article. --05:29, 8 March 2006 (UTC)

First SF writer?
Kepler's posthumous 1634 book Somnum is sometimes called SF. (So is The Divine Comedy...) Trekphiler 01:01, 30 December 2005 (UTC)


 * What's even more wild than that is that Somnium, in manuscript form, may have been what led people to accuse his mother of witchcraft. He wrote it shortly after moving to work with Tycho (I think), and passed it around to a few friends.  But the main character was sort of like Kepler; details were different, but a lot of it was pseudo-autobiographical.  And the main character figures out how to get to the moon (that's what the main of it is, going to the moon and observing Earth from there, showing how a change of perspective makes the Copernican system more believable) by having his mother, a healer and spiritualist, commune with spirits.  So that may have been the basis for the witchcraft rumors that eventually grew into an actual trial.  I hope to do some more work on this soon, but if you're interested in improving the article, check out Kepler's Dream by Lear. --ragesoss 09:15, 30 December 2005 (UTC)

Lutheran vs. German in intro
PhilipC, I've reverted your changed of "Lutheran" to "German" in the first sentence, as Lutheran was much more key to his identity than German, since this was the time of the Holy Roman Empire and he worked in both present-day Germany and Austria. It may be appropriate to include something about Germany later in the intro if you can find a way to do it elegantly.--ragesoss 01:06, 31 December 2005 (UTC)

That's a good point, but I was thinking more of encyclopaedic convention than biographic emphasis. "Lutheran astronomer, astrologer and mathematician" read a bit oddly to me, as though the article were claiming the existence of some kind of "Lutheran school" for these disciplines. Personally I'd be happier something like: "an astronomer, astrologer and mathematician who followed the Lutheran faith and was born in Weil-der-Stadt in what is now Germany"; but all the relevant information appears in the body of the article, so this may be sheer pedantry on my part. PhilipC 17:07, 31 December 2005 (UTC)


 * Actually, a "Lutheran school" isn't too far off. Even though it wasn't peculiar to those disciplines, being a Lutheran academic at that time meant something very different (and perhaps more coherent) than, say, being a Catholic or Calvinist (perhaps on par with "Jesuit").  The education system and the "Philippist" (after Melancthon) educational philosophy were important for the way Kepler thought about the world, and the way he did his (what we would call) science.  The Barker and Goldstein reference goes into some detail about this.  But your concerns about encyclopedic convention are significant.  Let's wait and see if anyone else chips in or comes up with a better way to reword the intro while maintaining the proper emphasis and flow.  Thanks, PhilipC.--ragesoss 00:56, 1 January 2006 (UTC)

Kepler's birth place Weil der Stadt then was part of the "Holy Roman Empire of German Nationality". It is located in today's Germany. Kepler spoke german. He was imperial mathematician of the emperor of the "Holy Roman Empire of german nationality". So, there's absolutely no reason to object the claim that Kepler is a german.(anonymous user, January 18, 2006)


 * I grant that German may be a valid descriptor, but I think Lutheran is still far more central for his biography. Your revision also makes the sentence somewhat awkward.  I'll try to think of a way to include German in the first sentence without disrupting it.--ragesoss 21:08, 18 January 2006 (UTC)

astrology edits
Theodore7, I've reverted your recent edits to Kepler. While I appreciate you point about the importance of astrology, this article was already clear about it being a significant part of Kepler's professional work. Many of the people in the article (Tycho, Galileo) were also astrologers, but in the context of this article "astronomer" or "astonomer/astrologer" are fine concise descriptions the way they are, and should not be simply replaced with "astrologer." Replacing "Lutheran mathematician, astrologer and astronomer" with simply "astrologer" is the kind of edit that requires discussion and consensus. I hope you will try to contribute something substantial (and sourced) to Kepler article, but please use the talk page to argue your point before making any more such changes--ragesoss 14:46, 7 January 2006 (UTC)

First to predict a transit of Venus?
In the article it's stated that "he was the first astronomer to successfully predict a transit of Venus (for the year 1631).", now this is not my field of expertise but didn't ancient civilizations already notice this and where able to predict it, like for example the Maya Civilization?

http://en.wikipedia.org/wiki/Mayan_Calendar

http://www.experiencefestival.com/venus_transit

http://www.astrologycom.com/venustransit.html

http://www.mayanmajix.com/art1034.html

http://www.crystalinks.com/workshop666.html

http://www.world-mysteries.com/gw_whart2.htm

Some (if not all) of these links have some extra baggage of information regarding other things then just the Venus transit but it should show the point that I am trying to make, could someone well informed on this clear this up?

Cultural depictions of Johannes Kepler
I've started an approach that may apply to Wikipedia's Core Biography articles: creating a branching list page based on in popular culture information. I started that last year while I raised Joan of Arc to featured article when I created Cultural depictions of Joan of Arc, which has become a featured list. Recently I also created Cultural depictions of Alexander the Great out of material that had been deleted from the biography article. Since cultural references sometimes get deleted without discussion, I'd like to suggest this approach as a model for the editors here. Regards,  Durova  15:42, 18 October 2006 (UTC)
 * Very few biography subjects warrant a separate page just for cultural references. Separating them detracts from the completeness of the article and forces the reader to follow a link for information that belongs in the same article. Cultural references frequently get deleted because they are unsourced or are too trivial to be meet encyclopedic standards. Finell (Talk) 16:36, 18 October 2006 (UTC)
 * I agree that very few biography subjects warrant a separate page, which is why I've posted this suggestion only to Wikipedia's core biographies. Because, as you say, these references often get deleted I've relied on the core biographies list rather than the size of a current cultural references section to suggest this solution.  If you think it's inappropriate in this case I'll defer to that opinion.  However, I would like to suggest that even "trivial" references can become useful educational tools for important biographies.  In my music history class (dare I say at Columbia University?) a good portion of the class thought they had never heard Richard Wagner's music until the instructor reminded them of the soundtrack to Apocalypse Now and the Warner Bros. cartoon "What's Opera, Doc?"  Respectfully,  Durova  05:33, 20 October 2006 (UTC)

Oct 19 edit by non-user
I am that guy. No account. I just removed some redundancy as it was pretty redundant to say the same thing twice, pretty much in succession and repeating itself. So I took the first instance of the redundant info out so that the redundancy would be no longer be present.

"To his disappointment, Kepler's attempts to fix the orbits of the planets within a set of polyhedrons never worked out, but it is a testimony to his integrity as a scientist that when the evidence mounted against the cherished theory he worked so hard to prove, he abandoned it.

His most significant achievements came from the realization that the planets moved in elliptical, not circular, orbits. This realization was a direct consequence of his failed attempt to fit the planetary orbits within polyhedra. Kepler's willingness to abandon his most cherished theory in the face of precise observational evidence also indicates that he had a very modern attitude to scientific research."

The first paragraph of those two has been removed so as to eliminate some redundancy in the article, with the result of one less instance of the article repeating itself. -- Pat (not-a-user)

Tycho Brahe's Mars Observations - plot
It would be nice to include a plot of Tycho's data Kepler used in formulating his laws. I have the raw data (from "Brahe, Tycho. Tychonis Brahe Dani Opera Omnia (in Latin). Vol 1-15. 1913-1929. Edited by I.L.E. Dreyer.") and created a plot using R (see below). I would like to add some regression analysis in order to highlight the periodic nature of the data. This can be a bit tricky with R for non-linear fits. If anyone knows an easy way, let me know and I can recreate the plot. I can also upload the raw data somewhere, if someone would like it?--Thorwald 04:35, 5 November 2006 (UTC)



Caps on book titles?
Capitalization of the Latin book titles in this article is inconsistent. Is it not true that conventionally only the first word and proper nouns in Latin titles should be capitalized? In any case (sorry about that) let's set a convention and conform to it.Myron 13:53, 16 November 2006 (UTC)

Total re-write
I've re-written this article, mostly from scratch. Any feedback will be greatly appreciated; I would like to work this into a Featured Article.--ragesoss 06:59, 16 December 2006 (UTC)

Well done as its definitely better. I think it should be made clear that Kepler did believe in astrology. He not onlyed used it professionally but also privately e.g to help pick his wife. It was not commonsense that he used but genuine astrological methods and he was very lucky that he was surprisingly correct often. BernardZ 05:19, 18 December 2006 (UTC)
 * I think the article is pretty clear about him being an astrologer, though I agree that the ways in which he used astrology in his personal life are telling and could due for some elaboration.--ragesoss 05:22, 18 December 2006 (UTC)

I think you have edited a bit too much out. It was not just personal. Kepler sincerely believed in astrology, he had a good reputation as one and it was also a good source of income for him. For example in 1595 he predicted correctly bitter cold, a Turkish attack and a peasant uprising. These predictions certainly were not from common sense but luck. BernardZ 12:07, 18 December 2006 (UTC)

Logicus Criticisms
Unfortunately the article is fundamentally defective from the philosophy of science point of view, with its central interest in the logic of scientific discovery. And as the Wikipedia article on history of science used to tell us, the very rationale of the history of science is to provide a testbed for the theories of philosophy of science such as its theories of the rationale of theory change. But what it does not tell us is that history of science is itself already constructed and biassed according to various philosophies of science, and Ragesoss adopts standard mistaken inductivist and revolutionist philosophies of the standard mistaken positivist theory of a scientific revolution. Here I make just three major corrective points.


 * (1)	Kepler's kinematical laws of planetary motion are most certainly not the foundation of Newton's gravity theory: As Duhem, Popper, Feyerabend and others have periodically pointed out, the planets do not move in ellipses and Kepler's laws are therefore false according to Newtonian dynamics. If they were true, then Newton's theory of mutual gravitational attraction and his planetary gravitational perturbation theory must be false. Newton's astro-dynamics and theory of gravity contradicted Kepler's and falsified his kinematical laws. In fact whilst writing the Principia Newton was greatly concerned with falsifying Kepler's Rudolphine Tables with such as the non-elliptical gravitationally perturbed motion of Saturn. In fact refuting the Rudolphine Tables based on Kepler's laws was something of a sport amongst English astro-physicists. Thus the opening claim that “Kepler's laws would be the foundation of Isaac Newton's theory of universal gravitation”  must be deleted as illogical nonsense.


 * (2)	Circular orbits were not replaced by ellipses:  One of the sillier and scientifically ignorant positivist myths of a scientific revolution is that Kepler successfully replaced circular planetary orbits with elliptical ones, which was supposedly revolutionary. But on the one hand since Appollonian epicycles in antiquity, planetary orbits were not circular but were at most epitrochoid, as even the Wikipedia article on the epicycle points out, and planetary orbits were most certainly not thought to be circular immediately before Kepler's astronomy. And on the other hand planetary orbits are not elliptical according to Newton's dynamics. 'From circles to ellipses' is a total myth. Of course Galileo and Newton and others supposed planetary orbits to be circular or indeed elliptical as simplified models posited for specific theoretical purposes. But false kinematical assumptions made for hypothetical dynamical modelling purposes should not be confused with reality.  Unfortunately the article has been influenced by this basic error. Thus such false claims as the following two and others must be deleted or corrected:

"Since antiquity, it was assumed a priori that the natural motion of planets was circular; retrograge motion was acccounted for, in Ptolemaic astronomy, through circular epicycles, ..."

"All earlier astronomers, including Copernicus, conceived of the planets as dense spots within a system of orbs, spherical shells that rotated to produced the observed motion of planets; a planet's distance from its center of rotation based on many points was assumed constant."

In general I presume it is an interesting unanswered question whether the orbital trajectories of the solar planets are best approximated on average by a circle, ovoid, epitrochoid, ellipse or any other closed curve, noting Newton's observation that in humanly scientifically unfathomable complex reality, they are not recurrent closed curves at all, since in dynamically complex reality no planet repeats its orbit.


 * (3)	Kepler's major historical achievement lay in producing a scientifically progressive Aristotelian inertial astro-dynamics:   Kepler's astro-dynamics from his Astronomia Nova onwards explodes the standard positivist narrative of an astro-dynamical revolution according to which a heliocentric revolution in kinematical astronomy precipitated an anti-Aristotelian revolution in dynamics because a moving earth necessitated an 'anti-Aristotelian' dynamics in which such motion does not require an external mover.  But this narrative is obviously logical nonsense inasmuch as there is no logical reason why heliocentrism cannot be associated with a dynamics that requires external movers for such motion, and indeed it was. For both Copernicus and Kepler posited external movers of the planets - Copernicus posited the planets were moved by rotating celestial spheres within which they were embedded, Kepler posited the planets were pushed around by the sunspecks of the rotating Sun, and Descartes that they were swept around by vortices, and heliocentrism was accepted long before the Thomist-Keplerian doctrine of inertia that bodies inherently resist ALL motion was rejected in favour of Newton's minor revision of it that they resist all motion EXCEPT uniform straight motion. In particular Kepler adopted a Thomist 'inertial' variant of Aristotelian dynamics, according to which all bodies universally have a non-gravitational inherent resistance to motion proportional to their mass 'm', and whereby v α F/m. The radical historical importance of Kepler's 'inertial' astro-physics may be that it was the first astro-physics to theoretically anticipate novel facts before they were observed, for it successfully predicted the dramatic novel facts that the Sun and planets with satellites rotate, first confirmed by rotating sunspots in 1609(?) by the telescopic observations of Kepler's research assistant, John Fabricius. Because on Kepler's Aristotelian inertial dynamics orbiting satellites must be pushed around by something, he therefore posited the Sun and planets with orbiting moons such as Jupiter  must all rotate in order to push their satellites around somehow. These were apparently the first successful theoretical novel predictions of heliocentric astro-physics, and on the Huyghens-Leibniz criterion that the greatest commendation of a hypothesis next to absolute proof is that it successfully predicts novel facts, they might explain the major conversion to heliocentrism soon thereafter. It is a major defect of the article that it entirely omits any mention of this historically highly important scientific development achieved by Kepler and contains no mention whatever of sunspots and of the dramatic theoretical significance of rotating sunspots. Arguably rotating sunspots provide the grail no historian of science has yet discovered, namely what makes the heliocentric revolution rational.

I shall leave you some time to revise the article yourself or else rebutt my criticism before I make any corrective deletions/revisions. But to make clear, you have my constructively critical support in making this a featured article. Whilst I cannot agree with Hegel and Popper that Kepler's scientific achievement was greater than that of Newton, I certainly agree they were far nearer the truth than the standard positivist account, if not for reasons they realised. For without Kepler's notion of 'inertia', rejected by Galileo but most keenly noted and critically revised by both Descartes and Newton, we would never have had Newton's historically crucial inertial dynamics. Season's Greetings. Logicus 20:40, 26 December 2006 (UTC)


 * Testing the Rudolphine Tables: Re point (1) above, it seems that on the one hand the 1639 transit of Venus, specifically observed by the English astronomer Jeremiah Horrocks for that critical purpose, was regarded as a falsification of the Rudolphine Tables because they did not predict Venus would appear in the sun’s disc, and on the other hand a confirmation of Lansberg’s competing astronomical tables based on epicyclical astronomy which did predict it. [See Dreyer.] Logicus 15:44, 7 January 2007 (UTC)

Circular motion, etc.
Logicus has raised some interesting points; I've tried to address one of his comments that deals with circular motion by disentangling the concern of the natural philosophers with the causes of celestial motion from that of the mathematical astronomers' concern with geometrical models. Of course, these traditions interacted in complex ways, as many medieval astronomers also accepted the natural philosophers' teachings on the physical nature of the celestial spheres (remember Copernicus wrote De revolutionibus orbium celestium) and many medieval natural philosophers discussed the physical nature of the astronomers' epicycles and eccentrics. I hope my changes address some of his concerns about circular motions.

On a different point raised in the same paragraph, I'm not happy with Ragesoss's phrase "Further geometrical techniques were necessary to account for observed eccentricities:" The term "eccentricities" doesn't get at what the astronomers observed and what they were trying to account for using equants and the Tusi-couple. The principle astronomical phenomena at issue here included: I'd like any suggestion for how to replace "observed eccentricities" with a compact phrase that encompasses what the astronomers were up to. "Observed zodiacal anomalies" would do it, but is too much heavy jargon for an encyclopedia article -- I never used it in an undergraduate lecture.
 * The varying size of the retrograde arc in different portions of the zodiac.
 * The varing intervals (either measured in space or in time) between successive synodic phenomena (i.e., first and last visibility, stationary points, and oppositions), which also varied as a function of the planets' position in the zodiac.

Happy Christmas to all SteveMcCluskey 15:14, 28 December 2006 (UTC)

Kepler did not discover non-circular planetary motion


 * Logicus comments: In 'Logicus Criticisms' above Logicus pointed out that the 'from circles to ellipses Kepler astronomical revolution' story is one of the sillier ahistorical aspects of the positivist Scientific Revolution fairy tale. But its arch-defender, Steve McCluskey, apparently wishes to preserve the myth of the alleged circularity of celestial motion of all pre-Keplerian celestial astronomy somehow. However, his 29/12/06 edit of the article's claim that
 * "Since antiquity, it was assumed a priori that the natural motion of the planets was circular..." to become
 * "Since antiquity, natural philosophers considered that the natural motion of celestial bodies was circular..."
 * to try and avoid Logicus's criticism completely fails for the most elementary logical reason. For of course the planets are themselves celestial bodies and indeed the only relevant ones for the modern reader who does not believe in or even know of 'the celestial spheres'. Yet their motion was thought to be non-circular ever since Apollonius's eccentric epicyclical astronomy in antiquity. And the planetary orbits were certainly not thought to be circular in the immediately preceding astronomical orthodoxy at the time of Kepler's Astronomia Nova, namely Tycho's Heraclidean geocentric astronomy in which planetary orbits were at least epitrochoidal around the Earth.


 * Thus the logic of scientific discovery and development is fundamentally misrepresented by such ahistorical positivist mythology, i.e. Kepler did not discover planetary orbits are non-circular. And McCluskey's 'natural philosophers versus astronomers' distinction is surely a red herring here, and anyway probably largely if not wholly a myth invented by positivist historians of science. Probably all or most astronomers since antiquity have been concerned with giving a physically realistic portrayal of the cosmos.


 * The whole 'Keplerian circular to elliptical planetary orbits revolution' claim is a historically untenable fundamentalist dogma of positivist revolutionist historiography, and must be totally rejected. For it does nothing but introduce obfuscatory and insoluble pseudo-problems without advancing our understanding of the logic of scientific discovery, which is the purpose of rational history of science. It is at best a misplaced kinematical misrepresentation of the really significant fundamental change in astro-physics, namely the dissolution of the solid celestial spheres and of the Plato-Aristotle heuristic programme of explaining planetary orbits by some mechanism of (nested and interconnected) uniformly rotating spheres. But as Kepler himself pointed out, this dissolution of the solid spheres was already accomplished in Tycho's prevailing geocentric cosmology. The latter implied solid spheres were impossible because of the intersecting orbits of Mars and the Earth. And their impossibility was further claimed to be supported by Tycho's independent evidence of the superlunary trans-spherical paths of comets that would have shattered any such solid spheres. So this fundamentally important change in astro-physical modelling is not attributable to the heliocentric revolution and moreover it preceded Kepler's Astronomia Nova. (Here I shall not enter into the ongoing fascinating debate over the possible novelty of the hypothesis of non-solid fluid celestial spheres in the 16th century and Kepler's (retro- ?) commitment to fluid orbital spheres that became Cartesian vortices.)


 * But not only is it false that planetary orbits were circular before Kepler, but the article's claim that in Astronomia Nova Kepler abandoned 'the Aristotelian principle of the primacy of uniform circular motion' is also apparently false. For according to Kepler's astronomy, the planets were primarily pushed in a circle around the Sun, but their essentially circular orbits were perturbed by alternating solar magnetic attractions and repulsions that produced non-circular elliptical orbits overall thereby. If so, from a logical point of view rather than abandoning the primacy of circular motion, surely Kepler's astro-dynamics retained it, as indeed did Galileo's. And Newton himself was not averse to charactersing the planetary orbits as essentially circular, such as in the Principia's final Scholium: "The six primary planets revolve about the sun in circles concentric with the sun, ..." (p940, Cohen & Whitman 1999 Principia)


 * In provisional conclusion, I propose the article's whole section from "Since antiquity..." to "...an ad hoc mathematical fix." in the Astronomia Nova subsection be deleted as logically and historically irrelevant, confused and highly misleading, and only raising problems it cannot resolve. (e.g. As philosophers of science know, ad hoc mathematical fixes are always logically possible, contrary to the article's claim that they were not.)


 * This proposal disposes of McCluskey's second point, but just to note that 'observed eccentricities' could be replaced by 'variations', then stating what these two variations are.


 * It would be helpful and timesaving if McCluskey could try to think through Logicus's criticisms and edits logically and desist in his swift knee-jerk usually logically mistaken responses, perhaps giving a day or so of serious coherent thought to the issue ? Logicus 18:55, 2 January 2007 (UTC)

Butterfield says [p64 The Origins of Modern Science: "Some people have said that Kepler emancipated the world from the myth of circular motion. This is hardly true, for from the time of the ancient Ptolemy men had realised that the planets themselves did not move in regular circles. Copernicus had been aware that certain combinations of circular motion would provide an elliptical course, and even after Kepler we find people accounting for the new elliptical path of the planets by reference to a mixture of circular movements. The obsession on the subject of circular motion was disappearing at this time, however, for other reasons, and chiefly because the existence of the hard crystal spheres was ceasing to be credible. It had been the spheres, the various inner wheels of the vast celestial machine, that had enjoyed the happiness of circular motion, while the planet, recording the resultant effect of various compounded movements, had been realised all the time to be pursuing a more irregular course. It was the circular motion of the spheres themselves that symbolised the perfection of the skies, while the planet was like the rear lamp of a bicycle - it might be the only thing that could actually be seen from the earth, and it dodged about in an irregular manner; but just as we know that it is is really the man on the bicycle who matters, though we see nothing save the red light, so the celsetial orbs had formed the essential machinery of the skies, though only the planet that rode on their shoulder was actually visible. Once the crystal spheres were eliminated, the circular motion ceased to be the thing that really mattered - henceforward it was the actual path of the planet itself that fixed one's attention. It was as though the man on the bicycle had been proved not to exist, and the rear lamp, the red light, was discovered to be sailing on its own account in empty space." Butterfield's cosmological cyclist metaphor no doubt stems from the fact that as in China the bicycle is the preferred mode of transport in Cambridge." Logicus 19:20, 23 January 2007 (UTC)

Logicus's corrective commentary on Butterfield: Whilst Butterfield was right here just on the obvious point that planetary orbits had been thought to be non-circular before Kepler since antiquity, and, contra Butterfield, even before Ptolemy, on the other hand he was also crucially wrong in various other historical respects.


 * "...and even after Kepler we find people accounting for the new elliptical path of the planets by reference to a mixture of circular movements."

This makes the false presupposition that after Kepler it was accepted planetary paths were elliptical, whereas it was not. In his 1632 Dialogo Galileo posited concentric circles, and I doubt Lansberg's epicylical heliocentric astronomy and his 1632 tables entailed elliptical orbits. And the Cartesian vortex theory that dominated the latter half of the 17th century and later seems to have posited circular vortices. It is reported Huygens, for example, rejected Kepler's first two laws, whilst accepting the third law. At the end of Principia Bk 2 Newton of course argued Cartesian vortices forbad elliptical orbits. We must also remember it seems Kepler himself never gave any evidential proof that all planets move in ellipses. Who, if anybody, accepted elliptical orbits but accounted for them by circular motion, as Butterfield claims some people did, is an interesting question. Is the answer 'Nobody ?'


 * "The obsession on the subject of circular motion was disappearing at this time, however, for other reasons, and chiefly because the existence of the hard crystal spheres was ceasing to be credible."

This is obviously false re the disapearing obsession claim for the same reasons stated above, and also for the further critical logical point re the alleged cause of this pseudo-fact that basing astronomy on circular motion does not require hard crystal spheres, as in the case of Tycho's circularist cosmology, Galileo's, Lansberg's and Descartes' circular vortices. The Cartesian cosmology can be seen as the simple replacement of solid spheres by systems of fluid spheres, that is, circular whirlpools within whirlpools rather like epicyclical systems of circles upon circles.


 * "Once the crystal spheres were eliminated, the circular motion ceased to be the thing that really mattered - henceforward it was the actual path of the planet itself that fixed one's attention."

Nonsense ! Once the hard crystal spheres were eliminated, and post-Tycho, the focus of attention became not the actual path of the planet any more than it ever had been, but rather exactly what alternative physical mechanism did propell the planets, be it e.g. Kepler's solar 'cartwheel' or Cartesian vortices, etc. As Kepler put it 'What moves the planets ?' became the central problem. Arguably neither Galileo nor Cartesian's cared too much about the exact orbit as opposed to the mechanism, and nor even did Newton in some contexts, being quite happy with concentric circles in the 1727 final Scholium.


 * "and the rear lamp, the red light [i.e. the planet], was discovered to be sailing on its own account in empty space."

But it was not, except in Galileo's cosmology, in which it is driven around by its own permanently conserved internal impetus originally acquired in its primeval gravitational fall from its point of creation by God into its orbit. In Kepler's cosmology it is pushed around by rotating sunspecks without which it would stop on Kepler's theory of inertia. And then Cartesian cosmology posited the planets were carried around floating in a vortical plenum, a view which was influential well into the 18th century. And then afterwards, until Einstein there was the aether. Nowadays there is dark matter.

Like many 20th century historians of science, Butterfield was more concerned with rhetoric than logical analysis of science and historical reality, or even with proof-reading his own work for logical consistency apparently. Thus, for example, apparently contrary to his own claims pp64-5 of the disappearance of the obsession with circular motion in Kepler's time and that it ceased to matter once the solid spheres were eliminated on, on pp147-8 he then writes of the strong and long influence of the subsequent Cartesian vortical system of circular whirlpools and even says the Cartesian vortex theorist Huygens "believed that circular motion was natural and fundamental - not a thing requiring to be specially explained - and that rectilinear motion...was...a by-product of circular motion."[p150-1] Given such incoherence and unreliability of the conclusions and judgments of historians of science, the educationally responsible encyclopedist must obviously form their own logically coherent conclusions from the conflicting and internally confused literature.

Thus on this critical analysis McCluskey's claim "after Kepler astronomers shifted their attention from orbs to orbits—paths that could be represented mathematically as an ellipse." is mistaken. Logicus 19:15, 25 January 2007 (UTC)


 * It seems the very ignorant myth that Kepler successfully replaced circular orbits by elliptical orbits may be so strong that unless the article itself specifically dispells it, rather than just the Talk page, people are likely to edit it in again, as somebody did recently, presumably not having read the Talk page discussion of it. It is also educationally important this very misleading myth about the nature of scientific development and discovery should anyway be explicitly dispelled in a learned encyclopedia article. Thus I insert a brief statement about this, but with lengthy informative footnotes for the moment that can ideally be worked into the main text at a later point when the historical situation has been clarified. But as the literature stands it is wholly unclear whether Kepler himself ever gave any full evidential proof of elliptical orbits and his three laws, and Ferguson's book, notably proof-read by Gingerich, implies he never did since he never did before he published the Rudolphine Tables, and apparently nor did they offer any evidential proof of his laws but rather only a general computing method, plus Tychonic data.


 * And there is then the question of whether elliptical orbits ever were accepted, and if so when ? The brute fact of the matter is that orbits are not recurrent ellipses (e.g. Mercury performs a rosetta that 'refutes' Newtonian gravitation), and so the only tenable question is what are they better approximations than ? Note that even the great English Kepler fan Horrocks reportedly used Lansberg's non-elliptical epicyclical tables to successfully predict the 1639 transit of Venus that the Rudolphine's entirely failed to predict. Note that the episode of Patrick Moore’s long standing BBC television astronomy programme ‘The Sky at Night’ on the 2004 transit of Venus reported that in the historically very first observation of the transit of Venus by Horrocks in 1639 he was specifically trying to refute the Rudolphine Tables. And of course the refutation of ellipses in gravitationally holistically complex reality was crucial for the confirmation of Newton's theory of gravity in such crucial facts as the gravitationally perturbed orbits of Saturn and Jupiter at conjunction and the perturbation of Uranus's orbit by Neptune at conjunction that led to its discovery, all presumably refuting the Rudolphine Tables and certainly Kepler’s cognate gravitation theory.] Logicus 17:02, 26 January 2007 (UTC)

Kepler's Laws and Newton
Logicus's discussion minimizing the relation between Kepler's laws and Newton's theory of gravitation raises a good point and then takes it too far. Admittedly Keplerian elliptical orbits only apply rigorously in a simple two-body problem, and Newton spent part of his Principia struggling to deal with motions involving three or more bodies. Furthermore, as Curtis Wilson long ago pointed out, Newton was concerned over the lack of precision of Kepler's laws ("Newton and Some Philosophers on Kepler's 'Laws'," Journal of the History of Ideas, 35 (1974): 231-258).

However, Newton deduced the inverse square law in the annus mirabilis of 1665 from considerations of the motion of the Moon and "from Kepler's rule of the periodical times of the Planets being in sesquialterate proportion of their distances from the center of their Orbs." (Westfall, Never at Rest, pp.143, 152). In 1684 Newton's manuscript De motu corporum in gyrum demonstrated all three of Kepler's laws from physical principles (Westfall, p. 404) Newton's Principia (1687) expands on those, including a demonstration that bodies moving under an inverse square force travel in paths described by conic sections, of which Kepler's elliptical orbits provide a special case(Principia, Book I,Sect. III, Prop. XI, Prob. VI; Prop. XII, Prob. VII; Prop. XIII, Prob. VIII; Prop. XVII, Prob. IX) a demonstration that bodies moving under a centrally directed force sweep out equal areas in equal times (Principia, Book I, Sect. II, Prop. I, Th. I; Prop. II, Th. II) and demonstrations that Kepler's 3/2 power law follows from inverse square gravitation (Principia Book I, Sect. III, Prop. XV, Theorem VII) and that Kepler's 3/2 power law is inconsistent with Cartesian vortices (Principia, Book II, Prop. LII, Theorem XL, Scholium). Addressing the more complex case of many bodies, Newton found that these bodies "may move among themselves in elipses; and that the radii drawn to the foci describe areas very nearly proportional to the times" (Principia, Book I, Proposition LXV, Theorem XXV).  To speak of perturbed elliptical orbits does not sound at all like a falsification of Kepler's theory.


 * Theres a highly readable account of these demonstrations in Feynman's Lost Lecture - The Motion of the Planets Around the Sun by Goodstein & Goodstein - if you're interested! Fizzackerly 16:17, 26 February 2007 (UTC)

The influence of Kepler on Newton is complex and should not be oversimplified, but it cannot be ignored, to say nothing of being turned into opposition. --SteveMcCluskey 01:57, 29 December 2006 (UTC)


 * Logicus comments: Thanks for all this, and will respond as most appropriate. But since at least you do not disgree that Kepler's laws were not the foundation of Newton's gravity theory, I shall delete the logically mistaken claim that they were. Logicus 17:04, 29 December 2006 (UTC)


 * Sed contra. I thought I made it clear that one of Newton's two original derivations of his law of gravity was based on Kepler's third law and that the third law (as well as the other two) continued to play an important role in Newton's Principia.  That's pretty clear evidence that Kepler's laws were one of the foundations of Newton's gravity theory.  I don't want to get into a revert war, but Kepler's influence on Newton is an important element of Kepler's significance and should remain in the article. --SteveMcCluskey 17:43, 29 December 2006 (UTC)

Logicus Delete re Orbits
"The very idea of an orbit, a trajectory through space, may have been the most revolutionary aspect of the New Astronomy. All earlier astronomers, including Copernicus, conceived of the planets as dense spots within a system of orbs, spherical shells that rotated to produced the observed motion of planets; a planet's distance from its center of rotation based on many points was assumed constant. [17]"

This paragraph must be deleted. Contrary to its first sentence, Field 1988 [See Further References] tells us Kepler "does not use the word orbis in a way which would allow us to translate it as 'orbit' i.e. the planet's actual path in space." [p86, Field 1988] And contrary to the second sentence, (i) Tycho's geocentric astronomy did not 'conceive of the planets as dense spots within a system of orbs' since it abolished the solid orbs, and (ii) a planet's distance from its center of rotation based on many points was not assumed constant at least since epicyclic astronomy.Logicus 19:13, 2 January 2007 (UTC)
 * I'll have to re-check out the book I had cited for that, and compare some other sources. I know that Andersen, Barker and Chen, among others put a lot of emphasis on Kepler's orbits being revolutionary, but re-reading what I wrote it seems a bit off (especially with respect to the Tychonic system, as you point out).  Something should definitely be said about the emergence of the orbit concept, balancing the different interpretations.--ragesoss 17:18, 6 January 2007 (UTC)


 * Logicus to Ragesoss: In general re your ideological interest here in finding something revolutionary in the astronomy of Kepler's Astronomia Nova, the only significantly historically novel aspect of it I am aware of is that it was the first development of the Aristotelian inertial dynamics developed by Averroes and Aquinas for a heliocentric model. But it was not thereby revolutionary nor in any other respect I am aware of. But of course in the advertising industry and revolutionist historiography of science everything is 'a revolutionary new product', and so possibly Kepler's orbits are for such as revolutionists Andersen, Barker & Chen. But obviously such claims without serious proof are not to be taken seriously. For clearly the concept of a planet having a non-circular re-entrant closed curve trajectory was not original to Kepler; see for example the ovoid orbit for Mercury depicted in the 1558 Rheinhold edition of Peuerbach's astronomy on p341 of Gingerich's 1993 book The Eye of Heaven cited in the Bibliography. And since the notion of a planet performing a trajectory in space without being embedded in an orb is obviously also pre-Kepler and indeed ancient, why bother with such an abstruse issue in an article on Kepler ? Inasmuch as the purpose of history of science is to help determine the logic of scientific discovery and development, identifying exactly what was specifically historically novel in Kepler's work and its problem-solving rationale by means of critical logical thinking is surely more important than repeating the unreliable illogical nonsense spouted by historians of science about what was. Logicus 19:06, 9 January 2007 (UTC)
 * First of all, I deny any ideological interest in finding something revolutionary in Astronomia Nova; I simply wrote this article based on the sources I was most familiar with, on the assumption that others could help balance the article in areas of historical dispute. Granting that the source I had used might not be significant enough to warrant inclusion, the idea of Astronomia Nova being revolutionary is a strong and recurring idea in the historiography; mistaken or not, it's an issue that needs to be in the article (along with contrary views attributed to other historians).  It is beyond the proper domain of a Wikipedia article to make the kind of decisions about which experts are right and which are wrong that you seem to be asking for.  It's not our place to investigate the logic of scientific discovery, but simply to provide a biography of Kepler, based on existing literature by experts.--ragesoss 19:20, 9 January 2007 (UTC)

Kepler never abandoned his Mysterium Cosmographicum's polyhedral-spherist astronomy
The article currently claims "[In his 'Astronomia nova'] Kepler set about creating - literally - a new astronomy. Though it meant abandoning his system from Mysterium Cosmographicum,...."

But Astronomia Nova was not the abandonment of the 1596 Platonist polyhedral-spherist cosmology of Mysterium Cosmographicum, but rather an integral part of its further development concerned with determining more accurate dimensions of the planetary orbs/spheres. This claim that Kepler abandoned the Platonist astronomical cosmology of Mysterium Cosmographicum in his Astronomia Nova and thereafter is just yet another apocryphal part of the positivist fairy tale of a Scientific Revolution that typically air-brushes out the fact that Kepler republished a much expanded version of the former in 1621. This article's current list of 'Writings by Kepler' very notably omits it, apparently in line with positivist air-brushing. In fact Kepler's 1619 Harmonices Mundi and his 1621 Mysterium Cosmographicum Ed2 were both further developments of his 1596 polyhedral-spherist astronomy. As Field, the English historian of science and student of Rupert Hall, wrote in his 1988 'Kepler's Geometrical Cosmology' (his PhD thesis supervised by Hall) cited in the article's Bibliography: "The fact that Kepler allowed a second edition of the Mysterium Cosmographicum to be printed in 1621, in itself suggests that the amount of astronomical work which he had done in the meantime had not led him to reject the theory put forward in this early publication." [p72 Field 1988]

The anti-positivist analyses of Kepler's astro-physics in the works of both Field and Stephenson cited in the Bibliography provide a valuable antidote to the historically mistaken positivist analysis of it favoured by Ragesoss and McCluskey. Logicus 18:54, 3 January 2007 (UTC)


 * I'm going to check out the Field and Stephenson books this coming week. I find this plausible, yet it squarely contradicts what I've read in several other sources to the effect the Astronomia nova was in fact an abandonment of the MC cosmology.


 * In the added paragraph, you put "p 72f" in the citation. I took this to indicate that the information comes from a footnote, and indicated that when I re-wrote and reformatted the new paragraph.  Please change it back if the "f" was a typo or meant something else.--ragesoss 16:32, 13 January 2007 (UTC)

Logicus Deletes
(i) The introductory Carl Sagan quote "Nevertheless he was, in the words of Carl Sagan, "the first astrophysicist and the last scientific astrologer" must be deleted as patent historical nonsense given there were scores of ancient Greek astrophysicists and no doubt preceding ancient Egyptian and many others. And Kepler himself was essentially a developer of Plato's Timaeus astro-physics.

(ii) p4 "Though the essay did not earn him a place in Ferdinand's court, its proto-gravitational theory became the basis for his later work on planetary motion." Kepler's gravitation theory was not the basis of his later work on planetary motion. Kepler held and developed a Platonic cognate mutual attraction theory of gravity such as adopted in 14th century Parisian physics and also held by Galileo, a theory analogous to Plato's theory of mutual human attraction in which like bodies (cognates) attract each other. And according to Kepler's version of it, the Earth and Moon are cognates and thus mutually attract each other, but the planets are not cognates of each other nor of the Sun, whereby there are no gravitational attractions between these latter bodies. (In Galileo's universal gravitation theory, at least in his celestial cosmogony, the planets are cognates of the Sun and thus fall towards it according to Galileo's radically mistaken universal law of gravitational fall, s α tt.) Hence Kepler's gravitation theory was not the basis of his later theory of the causes of planetary motion. To what extent it may have played a role in his theories of the motions of planetary satellites such as the moons of the Earth and of Jupiter is another matter.

(iii) p6 "Having given up on circular orbits,..." is nonsense since he had never proposed circular orbits in the first place.

(iv) The Caspar quotation "Epitome ranks next to Ptolemy's Almagest and Copernicus' Revolutiones as the first systematic [complete] presentation of astronomy to introduce the idea of modern celestial mechanics founded by Kepler." is confused gobbledegook and must be deleted. What on earth does it mean? What kind of ranking is being claimed here, rank 2 or 3 in respect of what ? For neither Ptolemy's Almagest nor Copernicus's work were introductions to Kepler's celestial mechanics and thus unrankable in that league. And nor did Kepler found modern celestial mechanics, but rather Newton did, unless the reference is to Kepler's Thomist inertial-dynamics further refined by Newton. And surely it was the 1609 Astronomia Nova, not the 1618 Epitome, that founded Kepler's celestial mechanics of the Sun pushing the planets around in circles perturbed into ellipses by secondary magnetic forces. Logicus 19:09, 4 January 2007 (UTC)


 * Instead of deleting these things, which are cited and attributed to the people who made the claims, you should add balancing information from contradictory sources. I've restored these three deletions; it's not our place to argue against sources, but rather to show the different interpretations that have been published.--ragesoss 16:40, 6 January 2007 (UTC)
 * I'm grateful for all the attention you're giving this, as I would like to keep this article as neutral as possible and I realize that the sources I've used are not the final word (and in many cases, probably not the best). But it seems like the traditional interpretation (a la Caspar) is the most widely known, so alternate interpretations should be in addition to that.--ragesoss 16:45, 6 January 2007 (UTC)

Re the relative popularity of Caspar's interpretation, the Amazon sales rank of his book is c450,000th, whilst Koyre's Astronomical Revolution is c360,000th, and Koestler's Sleepwalkers is c44,000th, noting Gingerich's Preface to Caspar acknowledges its greater popularity and that it puts a different spin on Kepler to Caspar. Logicus 19:19, 18 January 2007 (UTC)

Logicus justifies his deletes contra Ragesoss reverts


 * - Delete (ii): But contrary to what Ragesoss claims at 16:40 6 Jan, no source is given for the blatantly false claim that "...its proto-gravitational theory became the basis for his later work on planetary motion." And re the proximately surrounding footnote references 9 & 10, certainly Caspar makes no such claim on his pages 108-111. But as Dreyer correctly wrote "gravity had no place in Kepler's theory of celestial mechanics." [p398, Dreyer], meaning it played no role whatever in explaining planetary orbital trajectories dynamically. I therefore propose deletion at least until Ragesoss can find a source that makes this apparently ludicrously mistaken claim.


 * - Delete (iii): Thanks at least for accepting this deletion. My critical comment was of course intended to refer to 'concentric' circular orbits, since of course Kepler attempted an eccentric circular solar orbit for Mars, whereas the logical contrast of varying distance you make supposes concentricity.


 * - Delete (i): I disagree with Ragesoss's advice here to add balancing information rather than simply delete the claim made by Wikipedia that Kepler was the first astrophysicist. Historians of science make all sorts of claims, including very many very silly ones, so why repeat them all and set many mad hares running, rather than judiciously ignore those that are blatantly false ? Arguing against sources is also avoided by not quoting them in the first place. Contra Sagan and some others, very obviously Kepler was not historically the first astro-physicist, but was simply restoring causal astro-physics against Tycho's immediately preceding abandonment of it. The polemical 'New' of 'The New Astronomy' was only directed against the prevailing Tychonic astronomy, not the whole history of astronomy. Thus Gingerich gets it right that Kepler's astronomy was only a RESTORATION of celestial physics, contra Tychonic purely kinematical astronomy, rather than its wholly novel historical innovation, when he says:
 * "[Tycho Brahe] had considerable difficulty in accepting [Copernican astronomy] as a physically real system because it contradicted the accepted Aristotelian physics and apparently also the Bible. Unwilling and unable to forge a new physics, he chose instead to modify the cosmology to the geo-heliocentric form. Of course, this shattered the crystalline spheres, a radical step he eventually espoused. That left the heavens with no obvious means of generating their motions, something previously supposed to have been supplied by God at the outside edge of the nested spheres and transmitted inward through the crystal machinery. It is at this point in the story that the young German astronomer Johannes Kepler arrived on the scene, eager to RESTORE some kind of celestial physics." [p36, Gingerich 1993]


 * So I propose deletion rather than repeating patently silly opinions that then require correcting sources. Or do you want to add something like '...however Gingerich has pointed out Kepler's was only restoring astro-physics after its recent abandonment by the prevailing Tychonic astronomy.' But why get into such a silly issue in the first place ?


 * Whether Kepler was or was not the first astrophysicist (an arbitrary designation in any case) is beside the point of quote, in my view. I agree with you that Sagan's quote is, historically speaking, indefensible.  But it emphasizes the way Kepler is seen as a central figure in the foundation of modern science; Sagan is was not a historian but (in this context) a science popularizer, and it is that capacity that the quote is most significant.  By "astrophysicist", Sagan implied "modern astrophysicist" and thus implied that modern physics (in the traditional Sci Rev sense) began with Kepler; this is a lot of philosophical baggage in the quote, but it's pithy.  Fortunately, by using Sagan's word's, the article does not commit itself to any of that philosophical baggage.  I think a good solution to your objection would be to expand the footnote for that quote to include something along the lines of your summary of Gingerich here.  Of course, Gingerich largely endorses the standard idea of the Scientific Revolution; by "some kind of celestial physics", I think Gingerich means to emphasize that the physics that developed following Kepler was a different kind of physics.--ragesoss 19:06, 10 January 2007 (UTC)


 * Can you read the weasel words you have written with a straight face (-:? The primary point here is that Wikipedia itself is currently making the radically historically mistaken claim that Kepler was the first astrophysist, and just using Sagan's words to assert it. The proper title of Kepler's book was in fact The New Causal Astronomy or Celestial Physics to distinguish it from the old causal astronomy of rotating spheres and the non-causal purely kinematical astronomy of Brahe. And re your historically mistaken claim that "modern physics (in the traditional Sci Rev sense) began with Kepler", of course it is now widely accepted (e.g. by Curtis Wilson, Koyre and even McCluskey's mentor Westfall) that Kepler's celestial mechanics and its fundamental concept of 'inertia' was a development of Aristotelian dynamics (e.g. see Westfall The Construction of Modern Science p5, see Koyre Astronomical Revolution 'Kepler and the New Astronomy Part 1 The Beginning, Ch IV A Quo Moventur Planetae.) But I am quite happy to accept the (historically correct) view that modern physics was a development of Aristotelian dynamics (and the Scientific Revolution fairy tale is nonsense)(-: Logicus 18:51, 17 January 2007 (UTC)


 * By the way, the Preface to the Reader of Book 4 of Epitome announces
 * "This book is designed to serve as a supplement to Aristotle's On The Heavens" [See p845 Great Books of the Western World Vol 16, p845] This seems to imply Kepler saw his causal astronomy as in the tradition of Aristotle's celestial physics. Thus if the very silly Sagan quote is retained, the following edit would seem appropriate: "He was, in the words of Carl Sagan, "the first astrophysicist and the last scientific astrologer."[2], but Kepler himself regarded his celestial physics as a supplement to Aristotle's."  But it is far too silly and misleading to retain. Logicus 19:19, 18 January 2007 (UTC)


 * -Delete (iv): Ragesoss seems to completely miss the illiteracy point here, which is that with or without the missing word 'complete', Caspar's quotation simply does not make any plain English sense. Even if Epitome was the first complete systematic presentation of Kepler's celestial mechanics for all the planets, nevertheless how on earth can it be compared with Almagest and De Revolutionibus in that respect ? The claim is incoherent gobbledegook, unlike for instance Dreyer's intelligible equal ranking claim about Astronomia Nova, also quoted by Gingerich, "In the history of astronomy there are only two other works of equal importance, the book De revolutionibus of Copernicus and the Principia of Newton." [p410] The Caspar quotation must be deleted simply on the grounds of its unintelligibilty, and if required, replaced by some intelligible claim.


 * Logicus will respond more fully to the issues raised in 16:45 6 Jan later. But Caspar's interpretation is surely not the traditional nor most widely known interpretation of Kepler, who in school physics is misrepresented as a positivist scientist who just discovered some kinematical laws of astronomy by deducing them from data. As I recall Caspar's book was much concerned with challenging this Gradgrind positivist conception of Kepler's theorising. Logicus 18:39, 10 January 2007 (UTC)

Was Kepler's first law a rash conclusion ?
The article claims "Finding that an elliptical orbit fit[ted] the Mars data perfectly, [Kepler] immediately concluded that all planets move in ellipses, with the sun at one focus - the first law of planetary motion."

This claim seems to be asserting that Kepler irrationally concluded all planets move in ellipses with the sun at one focus from just one example, namely Mars, before first checking whether it was also true of the data of any of the other 5 planets' orbits, hence practicing a remarkably non-empirical and 'unscientific' method. But was this so ? This is notably the traditional illogical farce of the positivist inductivist fairy tale told by such as Caspar and Koestler of Kepler's supposedly revolutionary scrupulous commitment to the 'empirical' precision of his hypotheses in conforming to the data on the one hand. But on the other hand, in this tale, after intensely indulging this worthy empirical commitment for the case of Mars, Kepler then suddenly leaps to the conclusion that his elliptical hypothesis must be true for every planet without any mention of him ever checking it against the data for any other planet, and thus checking such as whether their orbits were ovoid or elliptical, for example.

Are the claims made true ? Did the ellipse hypothesis really curve-fit the Mars data PERFECTLY ? Did Kepler really not check his first law against the data for any other planet first before publishing it ? Did Tycho's data for Saturn confirm the ellipse law ? What are the literary references for discussion of these centrally important issues with respect to the logic of scientific discovery ? The article should surely discuss such issues. Meanwhile I propose this sentence be deleted unless or until its two claims are reliably referenced.

One of the key elements of Kepler's historical significance is his supposed steplifting the criterion of observational accuracy in theoretical astronomy and his innovation of the notion of 'experimental error'. This reputation needs serious qualification if he did not test his orbital hypotheses for every planet. Logicus 19:09, 4 January 2007 (UTC)


 * Logicus explores this issue further: It seems likely Kepler did publish his law of elliptical planetary orbits in Astronomia Nova before testing it for any planets other than Mars. In his book The Astronomical Revolution Koyre published a letter of March 1607 from Kepler to his patron Emperor Rudolph II for more money to extend his Astronomia Nova analysis and its successful 'war against Mars' to all the other planets. But none was forthcoming. [See Part 2 Kepler and the New Astronomy, Ch IX Astronomy with the Ellipse, p277-8 of 1973 Hermann Paris edition of The Astronomical Revolution]


 * And according to Pannekoek in his A History of Astronomy, it was not until his 1618 Epitome that Kepler first gave the orbits of Mercury and Venus with their eccentricities and aphelions as completely regular ellipses. But Pannekoek comments:
 * "How Kepler derived them from the observations is nowhere explained [in the Epitome]. In a letter of May 5 1616 to his former teacher Maestlin he merely says "In the summer of 1614 the theory of Venus followed, in the winter of 1615 that of Mercury: they are in no way peculiar as compared with Saturn, Jupiter and Mars;... " " [p242 A History of Astronomy]


 * This raises at least two questions. First, did Kepler claim the orbits of Saturn and Jupiter were also elliptical and provide their parameters, and secondly, where if anywhere between 1607 and 1616(?) did he get the observational data to confirm the orbits of all the other five planets were regular ellipses, if indeed he did ? Or did he simply blag it ? Does anybody know ?


 * This information also provides an interesting light on Ragesoss’s misquotation of Caspar as claiming Epitome was "the first systematic [complete] presentation of astronomy to introduce the idea of modern celestial mechanics founded by Kepler." that omitted the word 'complete'. For it may be that Caspar was implicitly acknowledging that Astronomia Nova was radically incomplete in respect of not establishing its planetary theory empirically for any other planet but Mars. Logicus 15:31, 6 January 2007 (UTC)
 * Thanks for catching that missing word. I think that's right that Caspar was acknowledging that Astronomia Nova was incomplete.--ragesoss 17:11, 6 January 2007 (UTC)

When and where did Kepler first publish his complete elliptical astronomy ?


 * When and where did Kepler first present an 'ellipse-based astronomy' with the relevant parameters for all the planets, after only allegedly presenting these for Mars in AN ?

The article currently claims

"Since completing the Astronomia nova, Kepler had intended to compose an astronomy textbook.[28] In 1615, he completed the first of three volumes of Epitome astronomia Copernicanae (Epitome of Copernican Astronomy); the first volume (books I-III) was printed in 1617, the second (book IV)in 1620, and the third (books V-VII) in 1621. Despite the title, which referred simply to heliocentrism, Kepler's textbook culminated in his own ellipse-based system. Epitome became Kepler's most influential work. It contained all three laws of planetary motion and attempted to explain heavenly motions through physical causes, and it was widely read by astronomers througout Europe between 1630 and 1650.[29]"

Ragesoss claims this information is from Gingerich. But a perusal of Book IV in the Great Western Books English translations hows no trace of relevant parameters such as eccentricities and aphelions for all the planets, and nor are these apparent in a quick scan of Book V. So where were they presented ? In Books VI or VII, and hence not until 1621 ?

And both Pannekoek and Wolf claim no adequate data proof of the orbits was given. Logicus 15:44, 14 January 2007 (UTC)


 * Wolf says that in Epitome "Kepler's two laws of planetary motion are explicitly extended (though without adequate proof) to the remaining planets, to the Moon, and to the Medicean satellites of Jupiter." p140-41 Wolf 1950 Logicus 19:06, 17 January 2007 (UTC)

GA nomination
Well, I read this article and found it to be exemplary, but let's go through the motions anyway
 * 1) Well written -pass
 * 2) factually accurate and verifiable - pass
 * 3) broad in coverage - pass
 * 4) neutral - pass
 * 5) stable - pass
 * 6) images - pass

Overall, I'm very happy to make this a Good Article. Deyyaz [ Talk 18:31, 6 January 2007 (UTC)
 * I wouldn't be so sure about the stable part, as it just went through a complete re-write and there are there are lots of bugs to work out, but thanks.--ragesoss 18:40, 6 January 2007 (UTC)


 * As yet Logicus cannot give passes at least for 2, 3 and 4, but works towards improvements to that end. Logicus 19:08, 10 January 2007 (UTC)

Kepler's laws falsified by transits of Mercury and Venus
NB This discussion continues the above discussion "Was Kepler's first law a rash conclusion ?". Check it out first as an orientating introduction.

From the above discussion it seemed from Pannekoek's critical comments that Kepler never provided any evidential proof that his first two laws of planetary motion proclaimed in his 1609 Astronomia Nova squared with the observational data for any planet other than Mars, if indeed he even did that. But at least in a letter to Maestlin in 1616 Kepler seemed to claim he had established this at least for Venus and Mercury in 1614 and 1615 respectively, that is at least 5 years after he had published Astronomia Nova. However, other commentaries from historians of science suggests the 1631 and 1638 transits of Mercury and Venus respectively falsified Kepler's laws and his 1627 Rudolphine Tables on Kepler's own criterion of falsifying discrepancies between theoretical prediction and observation, as follows:

- The 1631 transit of Mercury

According to Owen Gingerich's account of the episode [in his book The Eye of Heaven published by The American Institute of Physics in 1993], it seems that the 1631 transit of Mercury falsified Kepler's elliptical laws and Rudolphine Tables on Kepler's own criterion of a sufficient degree of observational error to falsify Ptolemaic astronomy and a circular or ovoid orbit for Mars. For by the same token that Kepler regarded a divergence between theoretical prediction and data of as little as 8' of arc as having falsified a circular orbit for Mars (and also an ovoid orbit), eventually in favour of an elliptical orbit, on just as strict a Keplerian criterion of an unacceptable degree of observational error it seems the transit of Mercury falsified an elliptical orbit or the second law, since it diverged from the Rudolphine Tables by even more than 8', namely by 10' of arc according to Gingerich. [See p342, Gingerich 1993.]

Thus from a logical point of view as opposed that of historians of science, Gingerich's conclusion that "Kepler did not live to see his prediction fulfilled" should rather have been "Kepler did not live to see his prediction refuted on his own criterion of a falsifying degree of observational error."

And his conclusion that "the evidence for the new system was overwhelming" overlooks the glaring question of why a discrepancy of 8' of arc refuted circular and ovoid orbits for Mars, but an even greater discrepancy of 10' of arc was overwhelming evidence that Mercury's orbit was elliptical or obeyed Kepler's laws, rather than evidence that however good, they were also false. Some astronomers might well have been underwhelmed.

Kepler himself had written on the 8' Martian discrepancy's falsification of Ptolemaic astronomy as follows: "God's goodness has granted us such a diligent observer in Tycho Brahe that his observations convicted the Ptolemaic calculation of an error of 8' of arc. It is therefore right that we should with a grateful mind make use of this gift to find the true celestial motions." [p178, Kepler's 1609 AN, quoted by Gingerich on p312]

The logically analogous Keplerian conclusion from the 10' discrepancy in Mercury's 1631 transit would have been:

'God's goodness has granted us such a diligent observer in Gassendi that his 7 November 1631 observations in Paris of the transit of Mercury have convicted Kepler's planetary laws of an error of 10' of arc. It is therefore right that we should with a grateful mind make use of this gift to find the true celestial motions.'

Whether this is yet another example of the inability of historians of science to achieve logically joined up thinking and proof-read their works for logical consistency, or there is some absolving but unstated technical explanation, is at least a question that should be posed here. Whilst the fact reported by Gingerich that other Ptolemaic and Copernican tables were 5 degrees out on this transit and thus worse than the Rudolphine Tables in this prediction does not absolve the latter from falsification by 10' of arc on Kepler's own criterion. Moreover, any mention of the maximum discrepancy between Kepler's elliptical Martian orbit and Tycho's data is hardly readily forthcoming in the literature. Did Kepler's elliptical Martian orbit improve on the maximum 8' of arc discrepancy for circular and ovoid Martian orbits ? We are not told what maximum discrepancy Kepler himself identified or reported, if any, for his proposed elliptical orbit, and thus what amount of discrepancy less than 8' he regarded as acceptable. Ferguson claims the Rudolphine Tables got the Martian orbit to within 3 arcminutes, but does not mention whether Astronomia Nova did also.

-The 1639 transit of Venus

In discussing the reception of Kepler's planetary laws and his Rudolphine Tables based on them, Dreyer reports that the Copernican astronomer Philip Lansberg (1561-1632), who rejected Kepler's planetary theories. published planetary tables in 1632 founded on an epicyclical theory that were used by many astronomers. And Dreyer says of them "They probably owed a great deal of the good repute they enjoyed for some time to the circumstance that they by a fluke represented the transit of Venus in 1639 fairly well, while the Rudolphine Tables threw Venus quite off the Sun's disc." [p420, Dreyer.] But Dreyer does not explain why this comparative success for Lansberg's tables was no more than a fluke. So it seems the 1639 transit of Venus was regarded as refuting the Rudolphine Tables' prediction, but corroborated Lansberg's tables in something of a crucial experiment against Kepler that made Lansberg's epicyclical heliocentric tables more popular than the elliptical heliocentric Rudolphine Tables with scientists who valued greater observational accuracy.

Did Kepler fit elliptical orbits for every planet to within less than 8' of arc observational error for Tycho's data ? There is much mindless and glaringly illogical celebratory hagiography on Kepler in the positivist religious literature, but little critical scientific analysis of the most elementary questions such as this that the reader of an Encyclopedia might wish to know. Even the proclaimed 'great American detective' of the history of astronomy, the Harvard academic Gingerich, much concerned with proclaiming Kepler's alleged improvement of astronomical accuracy, never claims improvements over rivals for any planet other than Mercury in his cited 1993. In fact Gingerich's silence tends to confirm Pannekoek's analysis that nowhere did Kepler ever demonstrate how his laws squared with the data or not. And he at least reveals the elliptical orbit for Mars was no better than its circular and ovoid rivals with respect to maximum discrepancies with Tycho's data. But if the answer to our question is that Kepler did not even fit an elliptical orbit for Mars to less than 8' error, what horrors might be revealed by his curve-fitting ventures for other planets. The 10' error for the Mercury transit may only be the thin end of the wedge. Logicus 19:12, 10 January 2007 (UTC)

Gassendi, Horrocks and the transits
The interaction of the observations of the transits of Venus and Mercury with Keplerian theory raises important issues in the reception of scientific theories. The only historian cited as describing the event, Owen Gingerich, saw the transit of Mercury as a fulfillment of Kepler's prediction. The article's current claim that these observations showed Kepler's elliptical orbit laws were false implies that this was recognized by the observers, when in fact this is not the case.


 * In the case of the transit of Mercury in 1631, Kepler had been extremely uncertain of the parameters for Mercury, and advised observers to look for the transit the days before and after the predicted date. Pierre Gassendi observed the transit on the date predicted, a confirmation of Kepler's prediction.  Gassendi himself was less concerned with planetary theory than with the size of Mercury, which he found to be much smaller than expected.  Planetary astronomers, when considering his observation, used it to improve the values of the inclination of Mercury's orbit to the ecliptic and the location of the orbit's nodes, rather than to reject any astronomical theory. (Albert van Helden, "The Importance of the Transit of Mercury of 1631," Journal for the History of Astronomy, 7 (1976): 1-10.)


 * Jeremaiah Horrocks, who observed the 1638 Venus transit, had used his own observations of Venus to adjust the parameters of the Keplerian model, predicted the transit, and then built apparatus to observe the transit. He remained a firm advocate of the Keplerian model. ("A Monument to Jeremaiah Horrocks," Nature, July 9, 1874, p. 190; Wilbur Applebaum and Robert Hatch,"Boulliau, Mercator, and Horrock's Venus in sole visa: Three Unpublished Letters," Journal for the History of Astronomy, 14(1983): 166-179)

What we're looking at here is an interesting case study of the reception of a scientific theory – of Kepler's laws. Perhaps the best way to deal with this is by removing the paragraph on the transit observations and adding a new section on the reception of Kepler's astronomy in the course of the Seventeenth century. There are two recent articles, which I haven't seen, that should have more to say about this matter:


 * Allan Chapman, "Jeremiah Horrocks, the transit of Venus, and the 'New Astronomy' in early seventeenth-century England", Quarterly Journal of the Royal Astronomical Society, 31 (1996): 333-357.


 * Wilbur Applebaum, "Keplerian astronomy after Kepler: Researches and problems," History of Science, 34 (1996): 451-504.

--SteveMcCluskey 16:13, 29 January 2007 (UTC)

Logicus's case study:Logicus welcomes McCluskey's (M's) recognition that Logicus's anti-positivist case study in the history of the reception of Kepler's astronomy is interesting, if not his misinterpretations of it and of the current article. Thus first Logicus corrects McCluskey's misinterpretations. He will subsequently offer some research suggestions for its further development.


 * Contrary to M's claim that Gingerich is the only historian cited by the article as describing observations of the transits of Venus and Mercury, Dreyer is (was?) also cited as describing the total failure of Kepler's Rudolphine Tables to predict the 1639 transit of Venus, which was successfully predicted by Lansberg's epicyclical tables published in 1632. See footnote 41 as was.


 * The article does not currently claim these transits showed Kepler's orbital laws were false, nor that observers concluded they did. It only makes the corrective logical point that if circular orbits were falsified by 8 arcminutes error as Kepler claimed they were by the case of Mars and as positivist commentators endorse in trumpeting the alleged general much greater accuracy of Keplerian astronomy over circularist astronomy, then by the same token an elliptical orbit for Mercury in the Rudolphine Tables was also falsified by the even greater 10 arcminutes error in the 1631 transit of Mercury prediction. Thus to claim as Gingerich does that it was a dramatic success for Kepler's astronomy would seem to be a paradigm case of illogically employing double standards of falsification. To turn the tables around logically, if a 10' error is a dramatic success for elliptical orbits, rather than falsifying them then it would seem the lesser 8' error for circular and ovoid Martian orbits was an even greater dramatic success for them.


 * The two quotations from the Journal for the History of Astronomy to show some observers did not conclude the 1631 and 1639 transits of Mercury and of Venus showed Kepler's elliptical laws were false are logically irrelevant, since the article does not currently claim they did. However, as a matter of fact both passages clearly attest the specific Keplerian orbital models for Mercury and Venus were falsified by the 1631 and 1639 transit observations, and regarded to be so by astronomers, because both passages attest they replaced their false parameters.

Moreover Wolf's 1950 (p143) gives an interestingly different account of Horrocks on the transit of Venus to that of Applebaum and Hatch reported by McCluskey, including of its date: "He studied the astronomical tables of Lansberg and Kepler, which he corrected from the results of his own observations, and he satisfied himself that a transit of Venus, unpredicted by Kepler, would take place on November 24, 1639." The implication here, also in line with Dreyer's reportage, is that Lansberg's circularist tables predicted the transit, whereas Kepler's did not, with the same clear implication that Kepler's elliptical tables therefore did not logically supersede circularist tables.


 * The 1607 non-transit of Mercury: In the context of inner planet transits or not falsifying Keplerian astronomy or not, it should also be noted that Kepler wrongly predicted a 1607 transit of Mercury. There was no such transit.

Research points to follow. Logicus 19:13, 30 January 2007 (UTC)


 * The article on transits of Venus says: "Johannes Kepler was the first to predict a transit of Venus in 1631, but no one observed it, because Kepler's predictions were not sufficiently accurate to predict that the transit would not be visible in most of Europe. " This contradicts the assertion that Gassendi observed it. Does anyone know how these can be reconciled? Rjm at sleepers 10:43, 15 July 2007 (UTC)
 * Apparently Gassendi observed the transit of Mercury, but not Venus. I have edited the article to this effect. Rjm at sleepers 07:24, 19 July 2007 (UTC)

Carl Sagan and "astrophysics"
I find myself agreeing with Logicus's proposal to remove this quotation from Sagan, although for a different reason. Sagan's use of the modern term "astrophysics" is profoundly misleading. "Astrophysics" is primarily concerned with the physical processes taking place in stars and the interstellar media. If we were to describe what Kepler (and later Newton) were doing in modern terms, we would call it "celestial mechanics" or perhaps "dynamical astronomy."

Before Kepler, astronomers built geometrical kinematic models to predict planetary phenomena based on combinations of uniform circular motions. (To some of them, motions around equants and eccentrics were troubling and called for special justification or rejection.) Natural philosophers, on the other hand, demonstrated the physical causes of those motions but paid little attention to their mathematical details. Kepler changed this by bringing the philosophers' concern with causes into astronomy and using forces that varied with distance to produce varying motions. Although the nature of the assumed forces and the laws of motion has changed since Kepler, this new approach has remained the method of celestial mechanics.

Sagan's point, that Kepler was the first to derive particular planetary motions from assumed forces, is well taken and should be preserved in some way; his description of it as astrophysics is misleading and so the quotation should be replaced. --SteveMcCluskey 01:31, 23 January 2007 (UTC)


 * Alas, since you both agree, I've removed it. I hope we can come up with an alternative clincher to the intro that sums up Kepler's historical significance concisely and uncontroversially.--ragesoss 04:01, 23 January 2007 (UTC)


 * Logicus is preparing something on Kepler's achievements in astronomy, but it is difficult and needs research, on the secondary literature of course. His celestial mechnics, kinematical laws and Rudolphine Tables need seperate assessment, but then there is his maths, optics etc. Perhaps a final evaluation section is required ? Logicus 19:13, 24 January 2007 (UTC)
 * Yes, I think a section on Kepler's legacy would be a good addition.--ragesoss 01:20, 25 January 2007 (UTC)
 * Nice idea Logicus. I think you'll find some historically informed comments on how Kepler made astronomy part of physics in Bruce Stephenson's Kepler's Physical Astronomy.  There are some quotable passages in the introduction (pp. 1-2) and the conclusion (pp. 204-5).  SteveMcCluskey 15:31, 25 January 2007 (UTC)

Logicus's Assessment
Logicus's proposed assessment of the role of Kepler's ellipse law, that "it is a fallacy to say, as some commentators and other encyclopedias have, that planetary orbits were held to be circular before Kepler but elliptical thereafter." is both ambiguous and inadequate. It is ambiguous as it seems to propose (here I follow the talk page) each of the following negative statements:


 * Before Kepler it was not held that planetary orbits were circular.


 * After Kepler many people held that planetary orbits were circular.


 * After Kepler, no one adopted elliptical orbits, because the orbits weren't really elliptical

But negative statements are inadequate for an encyclopedia. We are trying to tell our readers the general consensus among historians of the significance of Kepler's work.

As I see it the historians' consensus involves at least two points:


 * A shift from a geometrical to a physical mode of analysis. (I won't deal with that issue here).


 * A shift from the use of circles to the use of ellipses as the ruling geometrical/philosophical model.

The final point does not imply either that the paths of the planets were actually circular or elliptical, but only that circles or ellipses formed the reigning paradigm.
 * As to circles, the consensus is consistent with the fact that in the medieval model the planets followed compound circular motions, both
 * in the more qualitative discussions in the theorica planetarum literature and.
 * in the mathematical geometrical models used to compute astronomical tables
 * As to ellipses: the consensus is consistent with the fact that after Kepler
 * ellipses did not immediately replace the circular paradigm since
 * some philosophers (Galileo, Descartes, Huygens) continued to advocate circles and
 * some astronomers used circular mechanisms as a way to mathematically approximate Kepler's ellipses.
 * Newton and subsequent astronomers used ellipses even while they recognized that the elliptical orbits were perturbed and only approximated ellipses. For continued use at the present see Osculating orbit.

The cutting point here is that Logicus maintains that if a planet's motion isn't exactly a circle, circularity is irrelevant; if an orbit isn't exactly an ellipse, we can't speak of an orbit as elliptical. An analogous approach is found in Logicus's earlier assertion that the observation of the 1631 transit of Mercury, which Gingerich described as a fulfillment of Kepler's theory, is seen by Logicus as a falsification of Kepler's elliptical laws and Rudolphine Tables.

Logicus seems to maintain that any discrepancy, no matter how small, leads to falsification, while most historians of science – and many philosophers – see such anomalies as a normal part of scientific activity. Imre Lakatos pointed out the problems of such strict falsifcationism in a 1973 exchange with Alex Bellamy (M. Motterlini, ed., For and Against Method, p. 90):


 * According to the Logic of Scientific Discovery (and, Alex, I think you will find it very difficult to refute this), the rationality of the scientific enterprise... depends on cutting the propositions into two: basic statements and theoretical statements; falsifiable statements and unfalsifiable statements....
 * Moreover, I pointed out—and this is a matter of historical fact, not logic—that all theories are anomaly-laden. That means that there are always problems in any theory which have to be shelved.  If all theories are born refuted, then it is perfectly clear that all theories are falsified right at the beginning....

Since all theories are born anomaly-laden, historical discussion involves describing how scientists actually deal with these anomalies rather than how they should deal with them if they were following a particular philosophical model. As an example, consider that while Newton fully recognized the imperfection of Kepler's ellipses, he still opened his demonstration of planetary motion and its perturbations with the statement: "The planets move in ellipses which have their common focus in the centre of the sun; and by radii drawn to that centre, they describe areas proportional to the times of description" (Principia, Book III, Proposition XIII, Theorem XIII).

History is a subtle study and does not employ philosophy's simple logical dichotomies, since they are seldom found in science as it is actually practiced. Perhaps this explains why Logicus heaps abuse on so many historians. I will revert Logicus's proposed assessment and hope we can come to a new one that reflects the complexity of history. --SteveMcCluskey 23:07, 26 January 2007 (UTC)

Logicus to McCluskey: I have reverted your revert and edited in the improvements I had drafted before I read this. I regard your criticisms as mistaken, and hope what I have put reflects the complexity of history more to your taste. Later on I suggest the issues in the long footnote must be discussed in the article itself. I may explain why your criticisms are mistaken later. Logicus 15:47, 27 January 2007 (UTC)


 * Since Ragesoss has restored my version to this disputed introduction, I've added a few references and a citation to Stephenson on Kepler, astronomy, and physics, replacing the troubling quotation from Sagan discussed above. --SteveMcCluskey 14:07, 28 January 2007 (UTC)

Logicus on McCluskey's mistaken criticisms: McCluskey's above 26 January criticisms of Logicus edits are all variously mistaken, logically confused and misrepresentative of Newton, Lakatos, Logicus and historians' consensus. And his conclusion in the last paragraph seems to have entirely lost the plot here, as follows: 'History is a subtle study and Logicus's edits contravene the fact that it does not employ simple logical dichotomies because they do not reflect the complexity of history'. But let us remind McCluskey and the reader of the plot and contextual rationale of Logicus's edits by quoting them here, whereby the ironic utter absurdity of McCluskey's complaint and conclusion may be appreciated. For Logicus's edit was precisely concerned to replace both the previous edit that added the historically seriously false simplistic logical dichotomy: "Before Kepler's laws, planets' orbits were believed to be circular. Kepler's laws of planetary motion proved that the planets' orbits were actually elliptical.", and also to replace McCluskey's almost as simplistic and confused historically false logical dichotomy he added in response to Logicus's deletion of that false claim, namely "Before Kepler, planets' paths were computed by combinations of the circular motions of the celestial orbs; after Kepler astronomers shifted their attention from orbs to orbits - paths that could be represented mathematically as an ellipse".

In response Logicus replaced McCluskey's claim with a denial of its alleged dichotomy that, when read together with its accompanying footnote that McCluskey apparently completely overlooked, was not ambiguous and inadequately negative as McCluskey claims, but rather added important historical information about the complexity of the historical situation, as follows:

"He is best known for his three kinematical laws of planetary motion, based on his works Epitome of Copernican Astronomy and Harmonices Mundi. Kepler's third law eventually led to the important discovery that the gravitational attraction between two bodies is inversely proportional to the square of the distance between them. However with respect to his first law that the planets move in ellipses, it is a fallacy to say, as some commentators and encyclopedias have, that planetary orbits were generally held to be circular before Kepler but elliptical thereafter, since neither is true.1 [Footnote 1: This was part pointed out by the Cambridge historian Herbert Butterfield in 1949 in his book The Origins of Modern Science p64. In fact planetary orbits were thought to be non-circular since antiquity with Apollonius's introduction of the epicycle in the 3rd century BC, but rather epitrochoidal or even oval as in Peuerbach's astronomy, as depicted for Mercury's orbit in the 1558 Rheinhold edition of it, as featured on p341 of Gingerich's 1993 The Eye of Heaven. And also in the immediately historically preceding geocentric Tychonic astronomy planetary orbits were epitrochoidal. Kepler himself portrayed elliptical orbits as only magnetic perturbations from essentially circular motion. On the other hand, immediately after Kepler in 1632 Galileo published his pro-heliocentric Dialogue concerning the two chief world systems, which posited helio-concentric circular orbits rather than ellipses. And also that same year Lansberg published non-elliptical epicyclical heliocentric astronomical tables that outperformed Kepler's Rudolphine Tables in some respects, such as in predicting the 1639 transit of Venus which the latter entirely failed to predict, but which was predicted from Lansberg's Tables by the English Kepler admirer Jeremiah Horrocks. Then in the Cartesian vortex cosmology that rose to prominence in the second half of the 17th century and later, the planets were swept around in compounded systems of material circular vortices or whirlpools within whirlpools, analogous to the compounded circular systems of Ptolemaic astronomy. (See p147-8 of Butterfield's Origins and also the diagram of Cartesian vortices from Descartes' 1644 Le Monde on p241 of Kuhn's 1957 The Copernican Revolution.) It seems Cartesians denied elliptical orbits, and reportedly Huygens rejected Kepler's first two laws. In fact Newton argued at the end of Book 2 of his Principia that elliptical orbits were impossible in Cartesian vortices. The historical question of whether, and if so when, astronomers ever accepted planetary orbits really are elliptical, or at least that ellipses are the best possible simplifying approximation for some practical purpose, is complex, (and to which the history of science literature gives no clear reliable answer).]"

From this quotation readers may judge for themselves WHO is most attempting to deny the real complexities of history: Logicus or McCluskey ? And they may also judge whether McCluskey is simplifying history in order to try and preserve the simplistic logical dichotomy asserted by the naive positivist interpretation of Kepler - 'circles ante Kepler - ellipses post Kepler'.

McCluskey's claim, now restored by Ragesoss, that "after Kepler astronomers shifted their attention from orbs to orbits - paths that could be represented mathematically as an ellipse" is blatantly false, at least both for the reasons given above and also because of its logically invalid comparison in mislocating a shift from the pre-Tychonic focus of attention in astro-dynamics on rotating solid orbs such as in Copernicus's celestial mechanics, which was the focus on the underlying mechanical cause of planetary orbits, to a focus on kinematical orbits. Rather the focus on the underlying physical causes of the kinematical orbits shifted from orbs to the rotating solar anima motrix, inertia and magnetism (Kepler), to impetus (Galileo), then to vortices (Descartes) and finally to the twin forces of gravity and of inertia (Newton), rather than to the kinematical orbits these various physical causes were alleged to produce. It is also false because, as McCluskey himself variously admits, orbits cannot be truthfully represented by a mathematical ellipse, but at best only approximately. And here we come to the crucial questions of (1) why, out of the infinitely many recurrent closed curves (including circles, epitrichoids and ovals) that could provide good approximative fits to ever changing planetary orbits, should they be represented as deviations from recurrent ellipses ? and (2) when and in which astronomical tables did they come to be represented as ellipses or as deviations from ellipses ?

Re Newton's Principia Bk 3 Theorem 13 mentioned by McCluskey, in its commentary Newton says Saturn Jupiter and the Earth sensibly deviate from elliptical orbits, and oif course in the Scholium he says planetary orbits are helioconcentric circles, as quoted above by Logicus. Logicus 19:14, 29 January 2007 (UTC)

Homosexual
In the article it says: "Kepler broke off his friendship with Paulin shotly after finding out he was in fact a homosexual" I couldn't find any sources verifying this. --129.13.186.2 17:58, 27 January 2007 (UTC)

RfC on Logicus's editing
A Request for Comment (RfC) has been opened at Requests for comment/Logicus on Logicus's editing on this article and its associated talk page.

Anyone is welcome to add comments by certifying the dispute, by endorsing either the posted summary or responses to it, or by submitting their own perspective on the events described.

--SteveMcCluskey 02:01, 6 February 2007 (UTC)

Copyright?
At 19:06, 2 March 2007 added the following passage to the article's Trivia section:
 * Almost everything in the above article was cut and pasted from another website (whose content is copyrighted).

I have moved that passage to this place on the talk page. As someone who has participated recently in the writing of this article, I can say that this claim is totally false. Anyone who wishes may try to verify this claim with specific web citations. --SteveMcCluskey 01:23, 3 March 2007 (UTC)


 * GaylordBumBum 23:56, 4 March 2007 (UTC)Well someone's either copied copyright material here, or the website in question is trying to pass off Wikipedia content as its own.


 * It's probably the latter; Wikipedia material is "copyrighted (automatically under the Berne Convention) by Wikipedia contributors and licensed to the public under the GNU Free Documentation License (GFDL)" and is widely copied by a number of other clones of Wikipedia. For details see Copyrights.
 * I Googled a sentence I had written recently and found it had been copied in GoUpstate.com,a web site run by the Spartanburg (S.C.) Herald. They gave appropriate citation of Wikipedia as their source so all is well.  If someone else is claiming copyright on Wikipedia material, that is a problem.  --SteveMcCluskey 01:22, 5 March 2007 (UTC)

Outline for a new section: Kepler in the philosophy and historiography of science
In addition to the section on the acceptance of Kepler's work and its role in the wider history of science, which probably has some room for expansion, I think this article should have a discussion of Kepler as an object of historical and philosophical discourse.--ragesoss 02:30, 14 March 2007 (UTC)

Beyond his role in the historical development of astronomy and natural philosophy, Kepler has loomed large in the philosophy and historiography science. Kepler and his laws of motion were central to early histories of astronomy such as as Jean Etienne Montucla’s 1758 Histoire des mathématiques and Jean-Baptiste Delambre's 1821 Histoire de l’astronomie moderne. These and other histories written from an Enlightenment perspective treated Kepler's metaphysical and religious arguments with skepticism and disapproval, but later Romantic-era natural philosophers viewed these elements as central to his success. William Whewell, in his influential History of the Inductive Sciences of 1837, found Kepler to be the archetype of the inductive scientific genius, and in his Philosophy of the Inductive Sciences of 1840, an exemplar of the most advanced forms of scientific method. Similarly, Ernst Friedrich Apelt&mdash;the first to extensively study Kepler's manuscripts, after their purchase by Catherine the Great&mdash;identified Kepler as a key to the "Revolution of the sciences". Apelt, who saw Kepler's mathematics, aesthetic sensibility, physical ideas, and theology as part of a unified system of thought, produced the first extended analysis of Kepler's life and work.

Modern translations of a number of Kepler's books appeared in the late-nineteenth and early-twentieth centuries, the systematic publication of his collected works began in 1937 (and is nearing completion in the early twenty-first century), and Max Caspar's seminal Kepler biography was published in 1948. However, Alexander Koyré's work with Kepler was, after Apelt, the first major milestone in historical interpretations of Kepler's cosmology and its influence. In the 1930s and 1940s Koyré, and a number of others in the first generation of professional historians of science, described the "Scientific Revolution" as the central event in the history of science, and Kepler as a (perhaps the) central figure in the revolution. Koyré placed Kepler's theorization, rather than his empirical work, at the center of the intellectual transformation from ancient to modern world-views. Since the 1960s, the volume of historical Kepler scholarship has expanded greatly, including studies of his astrology and meteorology, his geometrical methods, the role of his religious views in his work, his literary and rhetorical methods, his interaction with the broader cultural and philosophical currents of his time, and even his role as an historian of science.

Kepler's place in Scientific Revolution historiography also spawned a wide variety of philosophical and popular treatments. One of the most influential is Arthur Koestler's 1959 The Sleepwalkers, in which Kepler is unambiguously the hero (morally and theologically as well as intellectually) of the revolution. Influential philosophers of science&mdash;such as Charles Sanders Peirce, Norwood Russell Hanson, Stephen Toulmin, and Karl Popper&mdash;have repeatedly turned to Kepler : examples of incommensurability, analogical reasoning, falsification, and many other philosophical concepts have been found in Kepler's life. Physicist Wolfgang Pauli even used Kepler's priority dispute with Robert Fludd to explore the implications of analytical psychology on scientific investigation. A well-received, if fanciful, historical novel by John Banville, Kepler (1981), explored many of the themes developed in Koestler's non-fiction narrative and in the philosophy of science. Kepler has acquired a popular image as an icon of scientific modernity; science popularizer Carl Sagan described him as "the first astrophysicist and the last scientific astrologer"


 * Nice way to put Kepler in a larger context. As I read your proposal, you plan to integrate this into the section on the acceptance of Kepler's work.  A good transition would be from that discussion (which probably could be trimmed down a little) to your proposed discussion of the influence of Kepler's laws on Newton.  --SteveMcCluskey 02:44, 14 March 2007 (UTC)
 * I'm not sure whether it would work best as a separate section or integrated with the acceptance. My feeling is the former would be better, to set off the historical issues (including Kepler's influence on Newton) from the historiographical issues.  I hope you'll contribute for the Newton aspects, as I don't really know where to begin source-wise.  Did you notice that this is currently an Featured Article nominee?  It slipped under my radar, but I'm going to try to deal with as many of the issues it brings up as possible, even if it seems a little premature to me.  I'm finally done with qualifiers and on spring break, so I have some time to work on this.--ragesoss 03:01, 14 March 2007 (UTC)
 * OK, a separate section would work fine. Congratulations on the qualifiers.
 * Given the FA nomination, do you want to start working on the draft on a User Page, rather than clutter up what seems a good FA candidate? Post where you're working on it, and we can all chip in. --SteveMcCluskey 19:26, 15 March 2007 (UTC)

Images
One issue brought up at FAC is images, and the uneven spacing of them. Anyone have access to images related to Harmonices Mundi, Epitome, or witch trials, or anything else for the unillustrated sections?--ragesoss 03:09, 14 March 2007 (UTC)

Lutheran education system
The term "lutheran" is confusing here, because the seminary Kepler joined was state-run. The dukes of Wuerttemberg were very famous for their advanced education system which the "Maulbronn seminary" was part of, as well as the Tübingen Stift.

To qualify for this elite school system, one had to qualify by passing a state-wide exam, the so-called "Landexamen". Only talent and knowledge was decisive to be recruited, not noble or rich ancestry.

The aim of that school system was to educate the eventual Wuerttemberg civil servants (higher ranks) and the priests of the Wuerttemberg State Church.

Other famous students of that education system were, i.a., the german poets and writers Friedrich Hölderlin and Hermann Hesse.

Therefore, I will change "Lutheran" to Württemberg state-run". —The preceding unsigned comment was added by Pfg (talk • contribs) 15:42, 19 March 2007 (UTC).
 * It's true that it was a state-run school, but it is relevant that it was a Lutheran seminary; after all, the religious aspect is fundamental to being a seminary, and the Württemberg State Church was a Lutheran one. I'm adding "Lutheran" back in after "state-run"--ragesoss 15:50, 19 March 2007 (UTC)

Bad Dates and Ages
Despite his desire to become a minister, near the end of his studies Kepler was recommended for a position as teacher of mathematics and astronomy at the Protestant school in Graz, Austria (later the University of Graz). He accepted the position in April 1594, at the age of 23.

It is impossible that Kepler was 23 when he took up the position at Graz, as he was born in December and he arrived in austria in April.

1594 - 1571 = 23 But as he arrived in April and not after his birthday Kepler was only 22. Maybe the other dates and corresponding ages should be checked over

Mike 220.235.175.166 14:42, 2 April 2007 (UTC)

Kepler
I have read some of your posts and the homosexual topic was interesting because it's not true. I am related to Johannes Kepler. I found this out from my grandmother and I'd never even heard of him. Bye.

Kristina —The preceding unsigned comment was added by 66.185.6.93 (talk) 15:39, 10 April 2007 (UTC).

Do you know what was Johannes Kepler's full name?

WB

Planets in continual free fall?
“Planets sweep out equal areas in equal times.” Why would the planet care??? I mean, this is so abstract and mathematical. (And I know a planet doesn’t actually care, but why would an inanimate object act in this fashion?)

What I’m asking for is to explain the whole idea more conceptually. For example, “A planet is in continuous free fall, and goes faster as it nears the Sun and then moderately sling-shots out, and slows due to the Sun’s continuous gravitation pull, thusly beginning its return trip at a certain point. The result is an equilibrium with a modest elliptical orbit.”

And if I’m mistaken, please correct me. And if Kepler didn’t quite take it this far, then maybe we can tell how his theories developed over the next hundred years, for he was a highly influential figure in the history of science. (And as our article says, he was also a mystical guy, but an honest experimentalist, he really did compare his theories to the available data.)  FriendlyRiverOtter 06:22, 11 June 2007 (UTC)

Retina
Kepler is the first scientist who determined that human sight results from image projected onto the retina. So should we add it into the article? KyleRGiggs 09:21, 12 July 2007 (UTC)

Holy Roman Empire
I think the Holy Roman Empire part of "Regensburg, Bavaria, Holy Roman Empire" (where Kepler died) is inappropriate. As Peter Hamish Wilson remarks (in The Holy Roman Empire, 1495-1806, Palgrave Macmillan, 1999) "many scholars dispute whether [the Holy Roman Empire] was indeed a state at all." Besides, the article adds only a simple "Germany" to "Stuttgart." I propose to change Kepler's place of death to "Regensburg, Germany" - second choice: "Regensburg, Bavaria, Germany." Iterator12n  Talk 04:12, 15 July 2007 (UTC)

Lutheran
The first line reads: Johannes Kepler was a German Lutheran mathematician, astronomer and astrologer, and a key figure in the 17th century astronomical revolution.

I don't see that his religious affiliation should be given such prominence. If it is important to his work, or his outlook, or his personality, then it should be referred to elsewhere and explained there. However, to define him by his religion seems bizarre. Would we say "JFK was an American Catholic politician", "Carl Sagan was an American atheist astronomer", "Katherine the Great was a Russian Orthodox ruler" etc? Kitty Davis 08:12, 15 July 2007 (UTC)


 * I noticed that on the front page and was going to remove it for precisely the reasons you cite, but somebody beat me to it. &#0149;Jim 62 sch&#0149;  11:48, 15 July 2007 (UTC)


 * His opinions on religion and his troubles with Lutheran orthodoxy are mostly absent in the article. Also the background of Counter-Reformation shaping his stays at Graz and Linz is barely mentioned. --Pjacobi 17:07, 15 July 2007 (UTC)

Danke, i was thinking the same thing.Arthurian Legend 23:00, 15 July 2007 (UTC)

Stereometrica doliorum and contributions to mathematics
Good article. I was hoping to find some mention of to Kepler's contributions early ideas of the calculus - in particular Stereometrica doliorum ("Volume-measurement of Barrels"). Just a thought if anyone wants to add new material. Rob Burbidge 13:43, 18 July 2007 (UTC)

Kepler's Magnetic Astronomical Theory
Only a brief mention is made concerning one of Kepler's most important scientific ideas. This was the magnetic theory of planetary orbits. He was the first to hypothesise some kind of motive force that caused the revolution of the planets. This is only briefly mentioned. It is the foundational idea for the later theory of gravity invented by Newton. It is an important forward step. Yet its importance is neglected. I realise that in this article, Kepler's scientific work is not the main focus. However, at the very least, I would like to see the following included as one of the external links so that this important aspect of Kepler's work will not be further neglected. 

— Preceding unsigned comment added by 72.64.37.102 (talk) 16:27, 19 July 2007 (UTC)

xkcd Bookstore Joke
http://www.xkcd.org/21/

Does Johannes Kepler have anything to do with this joke?

67.53.145.48 14:24, 1 September 2007 (UTC)

So far as I can tell, the joke references Kepler's 2nd law of planetary motion (see http://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion). So I'd answer in the affirmative. --smoo222

Well, since I noticed there is no "In popular culture" section, do you think it would be a good idea to add one, and perhaps insert this? I mean, everyone loves xkcd references. Rfts (talk) 06:25, 10 January 2008 (UTC)

No absolute epicyclical v elliptical historical dichotomy
In its Introduction the article currently claims:

"Before Kepler planets' paths were computed by combinations of the circular motions of the celestial orbs. After Kepler astronomers shifted their attention from orbs to orbits - paths that could be represented mathematically as an ellipse.[1][2]"

But the historical contrast depicted by these two sentences is an untenable falsification of the history of astronomy and so they should be deleted. Certainly neither of their two footnoted justifying references to [1] Gingerich's Preface to Donahue's Astronomia Nova translation and to [2] Koyre's 1973 Astronomical Revolution for the second claim support this contrast. These two footnotes should therefore be deleted. And so should the second sentence itself because its claim is historically false, as the history of science literature reported below attests. And since the first claim then becomes pointless because the claimed contrast fails, it should also be deleted.

On footnote [1], the nearest Gingerich remotely comes to any such claim on his page xi quoted is in his claim that "Kepler's formidable treatise contains the first statement of elliptical orbits - a radical departure from the previous exclusive pre-eminence of the circle in astronomical hypotheses.". But no claim whatever is made here about what astronomers did after Kepler. Moreover, Gingerich's claim of a "previous exclusive pre-eminence of the circle in astronomical hypotheses" is clearly refuted, for example, by Gingerich's very own evidence of oval orbits for Mercury before Kepler both in Alfonsine and also Peuerbach's Ptolemaic astronomy on pp121 & 341 of Gingerich's 1993 The Eye of Heaven. Thus, even as Gingerich's own evidence attests in refuting his own claim, elliptical orbits were not a radical departure from the previous epicyclical astronomy, both because it had anyway produced near elliptical oval orbits for Mercury, as Gingerich reveals, and also because it could anyway also easily reproduce elliptical orbits if required, as Fabricius did for Mars as he told Kepler in 1605 and Ismael Boulliau's 1645 and 1657 Astronomia Philolaica epicyclical astronomy did more generally for all planets. Because it could reproduce both ellipses and non-elliptical ovals, epicyclical astronomy was obviously more flexible than purely elliptical astronomy, and given that planetary orbits are anyway not recurrent ellipses, was thereby presumably therefore capable of being more accurate. Indeed in his 1989 Predictive Astronomy after Kepler, Curtis Wilson, the American doyen of the history of astronomy, claims the ellipse caught on because it was "a simple curve that could be produced by a combination of circular motions." (p161), which at least testifies to the falsity of the 'ellipse vs circle' dichotomy currently asserted by the article, if not explaining why anybody should wish to represent all orbits as ellipses anyway.

Moreover Wilson reports only Mars and Mercury observably deviated from circular orbits (p161), and also that even Mars deviated from a simple ellipse by some 8' in the octants (p183).). And also according to Gingerich's 1989 Johannes Kepler article in the same volume (p58), only the orbit of Mars was detectably non-circular by Tychonic levels of observational accuracy. So it seems Tychonic data could not confirm Kepler's ellipse hypothesis for at least 10 of all the 11 known planets and their satellites it claimed had elliptical orbits, and it was even refuted for its paradigm case of Mars on Wilson's account. These testimonies apparently dispose of the notion that Kepler's laws of elliptical planetary orbits were based on, derived from or justified by Tycho's astronomical data.

On the issue of the comparative accuracy of Boulliau's epicyclical astronomy, Wilson's Table 10.1 of the comparative accuracy of three different planetary orbital parameters of 5 different astronomers, including Kepler and Boulliau, compared against the yardstick of Newcomb's values for 1600, reveals that contrary to the 1666 founding judgment of the Paris Academy that Kepler's Rudolphine Tables had not yet been improved upon and that Boulliau's epicyclical Astronomia Philolaica tables were so inaccurate he was excluded from membership (see p175), in fact Boulliau's values for the three orbital parameters listed were at least as 'Newcomb-accurate' as Kepler's in half of the 18 cases and even more accurate in 7 cases. And Isaac Newton also cited Kepler and Boulliau as the two most accurate astronomers in his Principia Bk 4 Phenomenon 4 discussion, and its table of the mean distances of the planets and earth from the sun shows that in the 4 out of 6 cases in which they differed, Boulliau was more accurate in two cases and Kepler more accurate in a different two cases on Newton's yardstick, thus being on a par for their accuracy. (This remained the case in all three editions of the Principia in spite of the changing mean distance values in this table.) Thus even by 1726 Newton was still claiming Kepler and Boulliau were the two most accurate published mean distances, although Wilson's Table 10.2 suggests Newton's yardstick values were taken from Halley, whose tables printed in 1705 were only eventually published in 1749.

Turning now to footnote [2], nor does its quoted Koyre 1961/1973 Astronomical Revolution p362-4 make any such claim that after Kepler astronomy adopted elliptical orbits, but if anything the very contrary, namely that virtually nobody accepted Kepler's elliptical orbit astronomy, citing only three exceptions who did, namely Horrocks, Ward and Borelli.

The historical truth of the matter seems to be that 'circularist' epicyclical astronomy continued to thrive long after Kepler in the astronomies of such as Longomontanus, Lansberge, Boulliau and others. And it seems even Newton and Halley both employed epicycles in their lunar theories, Halley's Tabulae astronomicae being published in 1749. Perhaps most notably Ole Roemer, arguably the greatest exact observer of the 17th century who also had access to Tycho's observations, remained an adherent of Tycho's geoheliocentric epicyclical astronomy even until his death in 1710.

There might perhaps have been some small historical period in the 18th century in which some wholly non-epicyclical elliptical geometrico-kinematical astronomy based on curve-fitting with no other curve than an ellipse pre-dominated astronomy before it was replaced by dynamical astronomy in the 1780s. But it is unclear from the literature when this might possibly have been, if ever, and whose non-epicyclical tables were ever exclusively used by astronomers, if ever. Indeed insofar as Halley employed an ellipse on an epicycle in his lunar theory, it seems most likely there never was such a period before the end of curve-fitting kinematical astronomy itself as opposed to Newtonian dynamical astronomy.

But the fundamental fallacy of this falsely alleged historical contrast is its presumption that epicyclical and elliptical astronomy were somehow mathematically and/or historically exclusive, for they were not.

Moreover it sems the main 17th century astronomy post 1610 was geoheliocentric, with its non-elliptical epicyclical model with planets orbiting the Earth on Sun-centred epicycles with the solar orbit as deferent, although Morin combined it with its planetary orbits around the Sun being elliptical.

The two sentences in question should therefore be deleted.

--Logicus (talk) 19:16, 31 January 2008 (UTC)

Further comment on the revision of 31 January
After this discussion was posted, yesterday there was then a one word revision of the second sentence discussed here to now become

"After Kepler astronomers gradually shifted their attention from orbs to orbits - paths that could be represented mathematically as an ellipse.[1][2]" [My emboldening]

But at best this revision of this second sentence by inserting the adverb 'gradually' only perpetuates a serious ontological confusion it expresses that was not commented upon in this discussion above on the nature of orbits, but which is yet another reason why it should be deleted.

This sentence is fundamentally misleading because it confuses two different and distinct levels of analysis in astronomy, confusing the actual orbits of planets with the mechanisms or entities posited as transporting them in their orbital paths, as required by the core principle of Aristotelian dynamics and its Newtonian development that 'all motion requires a conjoined mover'. In Aristotelian and Copernican celestial physics non-circular and ovoid or elliptical orbits are caused by nested rotating orbs, and in some versions these were physically solid orbs and in others fluid orbs. In the late 16th century it seems the belief by some in solid orbs was challenged by the conclusion that transits of comets are superlunary and would be sphere-busting, whereby solid orbs would be impossible, and also by geoheliocentric astronomical models with intersecting planetary orbits posited by such as Ursus, Roslin and Tycho Brahe. It seems this initiated a conversion to a belief in fluid orbs, and then in the form of (Cartesian) vortices or aether that carried the planets around in their orbits instead of solid orbs. And even in the 19th century an aetherial cause of the perturbation of Neptune was put forward by the English Astronomer Royal, George Airy. And the next conversion was to the belief that the planets are carried around not by any kind of material whatever, but rather by the twin incorporeal forces of a transverse inherent impetus or inertia and of centripetal gravity.

Thus rather than it being the case as claimed that 'After Kepler astronomers [gradually] shifted their attention from orbs to orbits', gradually or otherwise, instead it would be radically less false and misleading to say 'After Tycho astronomers posited fluid orbs or vortices rather than solid orbs as the physical causes of planetary or orbits, but eventually came to the view that the planets are transported purely by incorporeal forces.'

But it seems nobody claimed the motions of fluid orbs or vortices were elliptical, and it seems they were thought to be essentially circular. Thus in essence the dominant later 17th century Cartesian astronomy, for example, retained the Aristotelian plenum of rotating (fluid) orbs, before Newton's full restoration of Aristotelian dynamics against the Cartesian relativist anti-Aristotelian geometrico-kinematical science of motion.

However, this correction of the first clause of the second sentence simply reveals that Kepler's celestial physics in which the rotating sun propells the planets was essentially irrelevant to these developments.

It is of course an historically interesting question of whether the major astronomical conversion from solid to fluid orbs or vortices was gradual or relatively sudden, compared with the approximately two century two stage transition from geocentrism to heliocentrism via geoheliocentrism (itself at most only a revolution in the model of a specific kind of motion in the Aristotelian science of motion, rather than a scientific revolution).

But this is not anyway the issue the sentence is concerned to establish, which is rather that there was a conversion from believing orbits to be non-elliptical to the belief that they are elliptical, whether gradual or otherwise. But was there ever any such conversion to the belief that orbits are actually specifically elliptical, as opposed to infinitely many other possible closed curves, for example ? The literature seems to suggest not, and that Kepler's laws may have never been generally accepted as actually true of planetary orbits in reality, any more than circles. For example, Newton's 1713/1726 concluding General Scholium in the Principia summarised planetary orbits as circles. It seems what may have happened is that not only did Newton prove 'fixed-sun single-planet' planetary orbits WOULD be elliptical under some false specific dynamic conditions in an early stage of his serial multi-stage celestial modelling in a series of ever more complicated false models, but perturbation theory in Newtonian dynamical astronomy that reportedly superceded kinematical curve-fitting astronomy in the late 18th century may have been based on perturbation from ellipses at some time. But whilst it may be interesting whether this was ever so, and thus interesting to see some evidence that it was, of course it still does not establish orbits were ever seriously thought to be specifically elliptical.

Hence in conclusion the whole second sentence as well as the first should also be deleted as historically and analytically misleading or irrelevant to Kepler.

But further, if evidence can be found that astronomers generally ever claimed all orbits are elliptical, or even just those 11 planet and satellite orbits Kepler claimed were elliptical but without evidence, then a sentence establishing this should be introduced.

Also if it can be established that Newtonian perturbation theory in astronomy and the preparation of astronomical tables and ephemerides was ever exclusively based on perturbations from ellipses as opposed to any other orbital path, then this would also be worthy of mention as arguably of relevant interest to Kepler's ellipse hypothesis.--Logicus (talk) 20:01, 1 February 2008 (UTC)


 * On the specific point of ellipses, Curtis Wilson points out the general acceptance of Keplerian ellipses, asking "why the Keplerian ellipse was so widely accepted by post-Keplerian astronomers, while the area law was frequently replaced by a punctum aequans in the superior focus (the so-called 'simple elliptic hypothesis')." ("Kepler's Derivation of the Elliptical Path, " Isis, 59, 1, (Spring, 1968): 4-25, at p. 22). --SteveMcCluskey (talk) 21:14, 7 February 2008 (UTC)


 * Logicus: What specific point about ellipses does this McCluskey note refer to ? Ellipses don’t have points (-: ? Its quotation from Wilson does not itself demonstrate the GENERAL acceptance of Keplerian ellipses by post-Keplerian astronomers, but rather merely poses the question of why it was as widely accepted as it was, however wide that might have been and which it does not itself say, as nor does the next quotation from Wilson McCluskey gives below. But is the point at issue here that of how widely it was accepted that all of the 11 celestial orbits Kepler claimed to be elliptical were indeed actually elliptical rather than any of the infinitely many other shapes that could fit them, or is it how widely the ellipse came to be used as a calculating device rather than circles, whatever the actual non-elliptical shapes of orbits might be, so that there was a shift from explaining orbits as perturbations from circles in terms of compounded circles made by rotating orbs to explaining orbits as perturbations from ellipses in terms of compounded ellipses or perturbing forces ?


 * It should be born in mind that Kepler himself explained elliptical orbits as perturbations from circular orbits, perturbations caused by magnetic attraction & repulsion. The simple fact of the matter is that orbits are not elliptical and were never accepted to be, and indeed the fact that Mercury’s orbit is not a recurrent ellipse but an evolving rosetta is one of the most important accepted facts in the history of astronomy by virtue of the explanation of its anomalous perihelion being the first astronomical fact to be explained by Einstein’s theory of gravitation. As I have already suggested, the main issue to be determined here is when, if ever, there was a period when the ellipse became the sole calculating device used in astronomy for plotting orbits kinematically. Did Newtonian astronomers ever restrict themselves to plotting celestial orbits as dynamical perturbations exclusively from ellipses, as opposed to any other conic section, such as parabolas or circles ?


 * The main question here is what is the point, if any, that Logicus has made pertaining to the proposed deletion that McClusky is contesting here ?--Logicus (talk) 18:56, 2 March 2008 (UTC)


 * The citation of Wilson's "Predictive astronomy in the century after Kepler" misses the author's intent. He states that:
 * In the century following the publication of Johannes Kepler's Rudolphine Tables (1627) improvement in the accuracy of astronomical theories and tables depended in large measure on the adoption, gradual and successive in some instances, abrupt and wholesale in others, of six Keplerian innovations:
 * (1) Replacement of the Mean Sun ... by the true Sun....
 * (2) Adoption, as a corollary to this, of the postulate that each orbital plane shall pass through the true Sun....
 * (3) Bisection of the eccentricity of the Earth's orbit....
 * (4) Replacement of the eccentric circle of each planet by an elliptical orbit, with the Sun at one focus....
 * (5) Determination of the motion of the planet on its orbit by the rule of constant areal velocity: the areas swept out by the radius vector from Sun to planet are proportional to the times....
 * (6) Adoption of Kepler's 'third law', the rule according to which the periods of the planets are as the 3/2 powers of their mean distances from the Sun.
 * Wilson clearly sees the adoption of Kepler's elliptical model as part of this gradual change. --SteveMcCluskey (talk) 21:44, 7 February 2008 (UTC)


 * Please explain the logical relevance of these two points by McCluskey --Logicus (talk) 15:46, 24 February 2008 (UTC) What citation of Wilson's article by Logicus does the second McCluskey note here refer to ? And why should it be concerned with expressing the author's intent, rather than just reporting claims made ? And again, what is the overall point being made here ? Is it that Wilson claims that it gradually became generally accepted that the 11 orbits Kepler claimed to be elliptical really actually were elliptical ? Or just that the ellipse came to generally and exclusively adopted as a calculating device rather than circles, notwithstanding Wilson's bizarre claim that elliptical orbits caught on because the ellipse was "a simple curve that could be produced by a combination of circular motions.", bizarre because it equally applies to infinitely many other curves that can also be modelled by epicyclical astronomy (and notwithstanding Newton and Halley still using an epicycle in the 18th century)? --Logicus (talk) 18:56, 2 March 2008 (UTC)


 * Logicus deletes 3 invalid citations: In addition to deleting the two footnotes for the reasons given above as to why they do not support the claim made, I have also deleted the third footnote, which was:


 * "On the change from orbs moving with circular motion to orbits derived from physical principles see Peter Barker and Bernard R. Goldstein, "Distance and Velocity in Kepler's Astronomy", Annals of Science, 51 (1994): 59-73"


 * But this is not the claim made here, which is rather the historical falsehood that the concern with orbs changed to a concern with orbits, when in fact that concern changed from a 16th century(?) concern with solid orbs to a concern with fluid orbs and Cartesian vortices first and then to incorporeal forces of inertia and gravity. Moreover the contrast depicted in this note is obviously confused and mistaken, since the very purpose of the celestial mechanics of rotating orbs was to explain the actual planetary orbits from physical principles, the physics of rotating orbs made of the quintessence. Astronomers were concerned both with orbits and also with the physical orbs that caused them. See the Wikipedia article on Celestial spheres. It is surely utter nonsense to claim that Kepler invented celestial physics and the principle of explaining orbits from physical principles, since they always were. —Preceding unsigned comment added by Logicus (talk • contribs) 17:45, 2 March 2008 (UTC)


 * Sorry, I've been away on other things and have not been paying much attention to this article. Looking at Logicus's recent changes I'm intrigued by the process.  Logicus deleted three references because, as he understood them, they did not agree with his original research on the history of astronomy.  He then deleted the statement that had been supported by those references because it was unreferenced.
 * In following up on these changes, I found two further references supporting this point of which I was unaware, one a recent study by David Miller in Journal for the History of Astronomy, 39(2008): 43-63 and even more to the point, a study by Bernard R. Goldstein and Giora Hon, "Kepler’s Move from Orbs to Orbits: Documenting a Revolutionary Scientific Concept," Perspectives on Science, 13 (2005): 74-111.
 * I am reverting these two changes and replacing the citation of Barker and Goldstein to the Goldstein and Hon article, which pretty well closes the issue on the scholarly consensus among historians of science. --SteveMcCluskey (talk) 17:11, 29 March 2008 (UTC)


 * These comments by McCluskey completely fail to rebutt the point that neither of the first two references justify the claim made, as pointed out in Logicus's contribution of 1 February above, and so they should be deleted until such time as it can be shown otherwise. McCluskey needs to state what the point is he imagines he is contesting, and notably fails to do so when challenged. Certainly these references do not support the point made in the text.--Logicus (talk) 14:48, 13 April 2008 (UTC)


 * I had thought that Logicus had made it quite clear a few paragraphs up that he was arguing against "the historical falsehood that the concern with orbs changed to a concern with orbits". It seemed to me that since Goldstein and Hon had written an entire article dealing with the sequence and nature of that change from orbs to orbits, we now have very good evidence for the existence of such a change and that the change was not, as Logicus has repeatedly claimed, a "historical falsehood".  --SteveMcCluskey (talk) 21:08, 13 April 2008 (UTC)
 * Logicus: From an admittedly very quick glance at this reference, I could see no justification in it for the perspicuously false claim made that "After Kepler, astronomers gradually shifted their attention from orbs to orbits." In the first instance I would therefore be grateful for the provision of a quotation from it that reliably establishes the claim, in compliance with the Verifiability courtesy requirement stated in its footnote 2. Meanwhile I shall citation flag the claim for a citation that provides such a quotation. --Logicus (talk) 16:05, 11 July 2008 (UTC)

Kepler did not inherit Tycho's observations, but misappropriated them
The article is currently in flagrant contradiction between its following two conflicting claims in two different passages as italicised and capitalised here:

'Work for Tycho Brahe' section

"Two days after Tycho's unexpected death on October 24, 1601, Kepler was appointed his successor as imperial mathematician; he INHERITED Tycho's observations as well as the responsibility to complete his unfinished work."

'Astronomia nova' section

"By the end of the year, he completed the manuscript for Astronomia nova, though it would not be published until 1609 due to legal disputes over the use of Tycho's observations, the PROPERTY OF HIS HEIRS."

Also

"In 1623, Kepler at last completed the Rudolphine Tables, which at the time was considered his major work. However, due to the publishing requirements of the emperor and negotiations with Tycho Brahe's HEIR, it would not be printed until 1627."

I provisionally propose the following replacement from the word Kepler:

'...Kepler was appointed his successor as imperial mathematician with the responsibility to complete his unfinished work. He illegally appropriated [some of] Tycho's observations, the property of his heirs, which subsequently led to 4 year delays each to the publications of two of his works whilst he negotiated copyright permissions.'

However, it is unclear from the literature (i) what exactly this formal responsibility, if any, consisted of, and whether or not it was fulfilled more faithfully by Longomontanus in his 1622 Astronomia Danae and (ii) whether Kepler appropriated and secreted all of Tycho's observations, or only some of them, such as those for Mars especially.

The question of what happened to Tycho's observations and who had access to them in the 17th century, and especially Longomontanus, is crucial to determining the issue of such as whether Kepler's proposed three ellipse laws were confirmed or refuted by them.

--Logicus (talk) 15:46, 24 February 2008 (UTC)

Is it really correct to mention 'copyright permissions' here? Copyright didn't really exist for over a hundred years after this date.. 206.248.152.244 (talk) 17:07, 20 August 2008 (UTC)

Mistake
The word "polygons" in a box in the main article seems to be a mistake for "polyhedra" or "polyhedrons". —Preceding unsigned comment added by 81.135.224.70 (talk) 15:18, 14 July 2008 (UTC)
 * thanks i'll change to perfect solids per image description page, tpbradbury (talk) 21:43, 23 November 2008 (UTC)

Named after
Another thing named after Johannes Kepler is the Kepler Track. http://en.wikipedia.org/wiki/Kepler_Track 58.3.78.89 (talk) 10:27, 21 December 2008 (UTC), Karla.

Kepler grew up in the Alps. He enjoyed many things. —Preceding unsigned comment added by Jamesbjj (talk • contribs) 16:49, 5 March 2009 (UTC)

Greater detail
The way Kepler came across the three laws is mentioned in http://www.wlym.com/~animations/ part4/47/index.html —Preceding unsigned comment added by 87.194.34.71 (talk) 10:32, 28 April 2009 (UTC)

Epitome
There should be a Wikipedia article on Kepler's Epitome. It is free from the tedious matter in his other books. —Preceding unsigned comment added by 86.137.170.8 (talk) 10:13, 21 May 2009 (UTC)

Epitaph
All the learned contributors to this article are invited to the fact that Kepler had written his own epitaph : Skybound was the mind, I measured the skies the earthbound body, the body rests  now.

2.It is very intresting and heart moving point in the life of the scientific giant who was very modest, not known to show any attitude in his life marred with struggle, poverty and controvery. So if he ever claimed any prowess of his capabilities even in the shape of an epitaph, it is our duty to pay tribute to him by recording the modest couplet in the light of the fact that Kepler indeed measured the skies.The couplet in itself is a poetic marvel.It is left to the makers of the articles as to where this couplet should be incorporated in the main articles. But incorporated it should be for it is too beautiful to be wasted.And our Wikipedia can't leave out such facts.

Regards SubzbhartiSubzbharti (talk) 09:35, 17 June 2009 (UTC)

Epitaph
I have found some more information on the epitaph which is from the book, 100 GREAT SCIENTISTS, American Library,in the biography of Kepler. The exact lines of the couplet are as under as per this book: ''' measured the skies, now the shadows I measure, Sky-bound was the mind, earth-bound the body rests.''' subzbharti 22 Dec 2009

All the learned contributors to this article are invited to the fact that Kepler had written his own epitaph : Skybound was the mind, I measured the skies the earthbound body, the body rests  now.

2.It is very intresting and heart moving point in the life of the scientific giant who was very modest, not known to show any attitude in his life marred with struggle, poverty and controvery. So if he ever claimed any prowess of his capabilities even in the shape of an epitaph, it is our duty to pay tribute to him by recording the modest couplet in the light of the fact that Kepler indeed measured the skies.The couplet in itself is a poetic marvel.It is left to the makers of the articles as to where this couplet should be incorporated in the main article. But incorporated it should be for it is too beautiful to be wasted.And our Wikipedia can't leave out such facts.

Regards SubzbhartiSubzbharti (talk) 09:36, 17 June 2009 (UTC) 10:39, 22 December 2009 (UTC)Subzbharti (talk)

Vague
The word "legitimize" appears in the second paragraph. I am not sure how exactly the legitimising took place. Any activity of Kepler's in this respect was hardly unique to Kepler. Many others made much the same remarks about Galileo's observations. —Preceding unsigned comment added by 86.180.182.155 (talk) 12:37, 2 December 2009 (UTC) Helping the legitimising is even vaguer. —Preceding unsigned comment added by 86.180.182.155 (talk) 11:29, 3 December 2009 (UTC)

Not clear
It is not stated clearly in the article whether Kepler's mother was actually tortured or not. —Preceding unsigned comment added by 86.180.182.155 (talk) 12:29, 3 December 2009 (UTC)

Assessment comment
Substituted at 20:36, 3 May 2016 (UTC)