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Who was Kepler to go against the wisdom of millennia? Kepler's new law finally made sense of the astronomical data. His second law, which he actually discovered first, contributed to the demolition of the ancient assumptions. It stated that the planets swept out equal areas of their orbits in equal times.

He was forced to dispose of the idea of circular planetary orbits, and had to reject the ancient belief that the planets traveled their orbits with a consistent speed. Instead, he tweaked the notion of uniform motion. Kepler discovered that the planets' speeds varied as they circled the sun — they went faster when they were at a point on their orbit closer to the sun than they did when they were farther away from it. But the area of the elliptical orbit that was covered in a certain amount of time always remained the same.

Kepler's first two laws were important for a number of reasons. They made sense of the universe's structure — astronomers could finally throw out the epicycles and the equant, and construct a simplified version of the Copernican universe. The epicycles had never been intended to model the actual motion of the planets; they were only there to preserve the appearance of uniform circular motion.

Now that there was no need for such preservation, astronomy could for the first time describe the physical reality of the universe. Kepler also reiterated his belief that a force emanating from the sun causes the motion of the six planets. He was the first astronomer to fully address the cause of celestial motion, rather than the mere mathematical description of it. The best example of this is perhaps the heptagon. This figure cannot be described outside of the circle, and in the circle its sides have, of course, a determinate magnitude, but this is not knowable.

Kepler himself says that this is important because here he finds the explanation for why God did not use such figures to structure the world.

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Consequently, he devotes many pages to discussing the issue KGW 6, Prop. Certainly for a geometer like Kepler, approximations constitute — as mathematical theory—a painful and precarious way to progress.

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The philosophical background for his rejection of algebra seems to be, at least partially, Aristotelian in some of its basic suppositions: But the difference from the Aristotelian ideal of science remains an important one: A general presentation of Kepler's philosophical attitude and principles is not complete without reference to his link to the world of experience. For, despite his mainly theoretical approach in the natural sciences, Kepler often emphasized the significance of experience and, in general, of empirical data.

In his correspondence there are many remarks about the significance of observation and experience, as for instance in a letter to Herwart von Hohenburg from KGW 13, let. Looking for empirical support for the Copernican system, Kepler compares different astronomical tables in his MC, and in AN he makes extensive use of Tycho's observational treasure trove. In MC chapter 18 he quotes a long passage from Rheticus for the sake of rhetorical support when, as was the case here, the data of the tables he used did not fit perfectly with the calculated values from the polyhedral hypothesis.

In this passage, the reader learns that the great Copernicus, whose world system Kepler defends in MC, said one day to Rheticus that it made no sense to insist on absolute agreement with the data, because these themselves were surely not perfect. After all, it is questionable whether Kepler, using for instance the Prutenic Tables of Erasmus Reinhold — , had access to complete and correct empirical information to confirm the Copernican hypothesis in grand style, as he claimed for an analysis of Reihold's tables and their influence see Gingerich , pp.

The situation changed completely when Kepler came into contact at Prague with Tycho's observations which, as Kepler often reports, were seldom at his disposal. However, a change of attitude is evident in AN, where he used Tycho's observations without restriction which is something he makes clear in the work's title. In part 2 chap.

Johannes Kepler

This hypothesis represents the best result which can be reached within the limits of traditional astronomy. This works with circular orbits and with the supposition that the motion of a planet appears regular from a point on the lines of apsides. Against the traditional method, here, Kepler does not cut the eccentricity into equal parts but leaves the partition open. To check his hypothesis, he needs observations of Mars in opposition, where Mars, the Earth, and the Sun are at midnight on the same line.

In chapters 17—21, Kepler carries out an observational and computational check of his vicarious hypothesis. On the one hand, he points out that this hypothesis is good enough, since the variations of the calculated positions from the observed positions fall within the limits of acceptability 2 minutes of arc. On the other hand, this hypothesis can be falsified if one takes the observations of the latitudes into consideration.

Further calculations with these observations produce a difference of eight minutes, something that cannot be assumed because the observations of Tycho are reliable enough. Kepler's famous sentence runs: There seems to be agreement that Kepler's AN contains the first explicit consideration of the problem of observational error for this question see Hon and Field Kepler also gave an important place to experience in the field of optics.

As a matter of fact, he began his research on optics because of a disagreement between theory and observation, and he made use of scientific instruments he had designed himself see, for instance, KGW Finally, it should be mentioned that a similar significance is assigned to experience and empirical data in Kepler's harmonic-musical and astrological theories, two fields which are subordinated to his greater cosmological project of HM.

For astrology, he uses meteorological data, which he recorded for many years, as confirmation material. This material shows that the Earth, as a whole living being, reacts to the aspects which occur regularly in the heavens. In his musical theory Kepler was a modern thinker, especially because of the role he gave to experience.

As has been noted Walker, , p. Kepler does not accept that this limitation is founded on arithmetical speculations, even if this was already assumed by Plato, whom he often follows, and by the Pythagoreans. On the basis of his experiments, Kepler found that there are other divisions of the string that the ear perceives as consonant, i. Today Kepler is remembered in the history of sciences above all for his three planetary laws, which he produced in very specific contexts and at different times.

Besides this, it should be remarked that the common denominator of all three laws is Kepler's defense of the Copernican worldview, a cosmological system which he was not able to defend without reforming it radically. The first two laws were published initially in AN , although it is known that Kepler had arrived at these results much earlier. His first law establishes that the orbit of a planet is an ellipse with the Sun in one of the foci see Figure 2.

The planet P is therefore faster at perihelion, where it is closer to the Sun, and slower at aphelion, where it is farther from the Sun. In accordance with his dynamical approach, Kepler first found the second law and, then, as a further result because of the effect produced by the supposed force, the elliptical path of the planets for the two first planetary laws see especially Aiton c, Davis a-e, and ; Donahue ; Gingerich , pp. Perhaps the most significant impact of Kepler's two laws can be found by considering their cosmological consequences.

The first law abolishes the old axiom of the circular orbits of the planets, an axiom which was still valid not only for pre-Copernican astronomy and cosmology but also for Copernicus himself, and for Tycho and Galileo. The second law breaks with another axiom of traditional astronomy, according to which the motion of the planets is uniform in swiftness.

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Copernicus, for his own part, insisted on the necessity of the axiom of uniform circular motion. Ptolemy's equant was understood by Copernicus as a technical device based on the violation of this axiom. Kepler, on the contrary, affirms the reality of changes in the velocities of the planetary motions and provides a physical account for them.

After struggling strenuously with established ideas which were located not only in the tradition before him but also in his own thinking, Kepler abandoned the circular path of planetary motion and in this way initiated a more empirical approach to cosmology though see Brackenridge In his Epitome , he provided a more systematic approach to all three laws, their grounds and implications see Davis ; Stephenson In Book 5, chapter 3, as point 8 of 13 KGW 6, p.

A further formulation of this relationship, which is often found in the literature, is: As a consequence of the third law, the time a planet takes to travel around the Sun will significantly increase the farther away it is or the longer the radius of its orbit. Thus, for instance, Saturn's sidereal period is almost 30 years, while Mercury needs fewer than 88 days to go around the Sun.

For the history of cosmology, it is important to make clear that the third law fulfils Kepler's search for a systematic representation and defense of the Copernican worldview, in which planets are not absolutely independent of each other but integrated in a harmonic world system. The background for his investigation into optics was undoubtedly the different particular questions of astronomical optics see Straker In this context he concentrated his efforts on an explanation of the phenomena of eclipses, of the apparent size of the Moon and of atmospheric refraction.

Kepler investigated the theory of the camera obscura very early and recorded its general principles see commentary by M. Hammer in KGW 2, pp. Besides these impressive contributions, Kepler expanded his research program to embrace mathematics as well as anatomy, discussing for instance conic sections and explaining the process of vision see Crombie and especially Lindberg b. Following—but also inverting—the Aristotelian argument for the temporality of motion, he affirms that the motion of light takes place not in time but in an instant in momento.

Light is propagated by straight lines rays , which are not light itself but its motion. It is important to note that although light travels from one body to another, it is not a body but a two-dimensional entity which tends to expand to a curved surface. The two-dimensionality of light is probably the main reason why it is incorporeal. Motion in general plays a significant role in Kepler's philosophy of light.

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For Straker, the supposed link between optics and physics especially in Prop. Two questions are intensively discussed by modern specialists. Firstly, to what extent is the attribution of a mechanistic approach to Kepler justified? Secondly, how should one determine his place in the history of sciences, especially in the field of optics: There are well—grounded arguments for different positions on both questions. For Crombie , and Straker, Kepler develops a mechanical approach, which can be particularly appreciated in his explanation of vision using the model of the camera obscura.

Besides this, Straker stresses that Kepler's basic mechanicism is also powerfully assisted by his conception of light as a non-active, passive entity. In addition, the concept of motion and the explanations using the model of the balance are indicative of a commitment to mechanicism Straker , pp. From a philosophical point of view, Kepler considered the HM to be his main work and the one he most cherished.

Containing his third planetary law, this work represents definitively a seminal contribution to the history of astronomy. Thus, Kepler's third planetary law appears in a context which goes far beyond astronomy and to a great extent takes up again the perspective of his youthful MC. The first is to be found among natural, sensible entities, like sounds in music or rays of light; both could be in proportion to one another and hence in harmony.

He resolves this matter by combining three of the Aristotelian categories: Through the function of the category of relation Kepler passes over to the active function of the mind or soul. It turns out that two things can be characterized as harmonic if they can be compared according to the category of quantity. Furthermore, the relationship between the things cannot be found in the things themselves either; rather, it is produced by the mind: This process takes place through the comparison of different sensible things with an archetype archetypus present in the mind.

The next central question directly concerns gnoseology, for Kepler gives a psychological account of the path followed by sensible things into the mind. He resumes the scholastic species theory: They arrive at the imagination and from there go over to the sensus communis , so that, according to the traditional teaching, the sensible information received is now able to be processed and used in statements.

How do they come into the soul? Kepler accepted Aristotle's criticism of Pythagorean philosophy concerning numbers: Nevertheless, Aristotle's philosophy is insufficient to grasp the essence of mathematics. His discussion lies at the origin of the classical debate between empiricism and rationalism which was to dominate the philosophical scene for generations to come. A connection with idealism is, of course, apparent see, for instance, Caspar , Engl. Historically, however, it seems to be more accurate to link his position with the philosophical tradition of St.

Rather, both the Earth and human beings, ultimately, like all other living entities, are provided with a soul in which the geometrical archetypes are present. By the formation of an aspect in the heavens, symmetry arises and stimulates the soul of the Earth or of human beings. Aristotle Copernicus, Nicolaus cosmology: Emmanuel Bury , where the author was a Prof. The author also wishes to thank David T. McAuliffe, and his colleague Patrick J. Boner for their suggestions as to how to improve the text linguistically. The editors of the SEP wish to thank Sheila Rabin and Jill Kraye, respectively, for their outstanding efforts in refereeing and editing this work.

Life and Works 2. Philosophy, theology, cosmology 3. The five regular solids 4. Epistemology and philosophy of sciences 4. Copernicanism reformed and the three planetary laws 6. Optics and metaphysics of light 7. Harmony and Soul Bibliography A. The five regular solids Philosophical, geometrical and even theological speculations related to the five regular polyhedra, the cube or hexahedron, the tetrahedron, the octahedron, the icosahedron and the dodecahedron, were known at least from the time of the ancient Pythagoreans. Table 3 in Mysterium Cosmographicum , with Kepler's model illustrating the intercalation of the five regular solids between the imaginary spheres of the planets cf.

Epistemology and philosophy of sciences Almost all of Kepler's scientific investigations reflect a philosophical background, and many of his philosophical questions find their final answer, even if they are of scientific interest, in the realm of theology. Copernicanism reformed and the three planetary laws Today Kepler is remembered in the history of sciences above all for his three planetary laws, which he produced in very specific contexts and at different times.

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Kepler's first law of ellipse and second law of areas modern representation with greatly exaggerated eccentricity. Harmony and Soul From a philosophical point of view, Kepler considered the HM to be his main work and the one he most cherished. Duncan, The secret of the universe Translation by A.

Apologia Tychonis contra Ursum: Cambridge University Press, with corrections Green Lion Press, Johnson Reprint Corporation, De fundamentis astrologiae certioribus: Donahue, Santa Fe, NM: Harmonices mundi libri V: Field, The Harmony of the World. Wallis, Epitome of Copernican Astronomy: IV and V , Chicago, London: Strena seu de nive sexangula: Somnium seu de astronomia lunari: University of Wisconsin Press, Life and Letters , New York: Secondary Literature Aiton, E.

Di Liscia, and H. Miscellanea Kepleriana , [Algorismus 47], Augsburg: Astrology, Mechanism and the Soul , Leiden: Kegan Paul; 2nd rev. Doubleday, reprinted , New York: Heffer for the Royal Microscopical Society , pp. Di Liscia, Daniel A.

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Athlone and University of Chicago Press. Gingerich, Owen, , The Eye of Heaven. Ptolemy, Copernicus, Kepler , New York: American Institute of Physics. Conversations with Aristotle , Aldershot: