Editing Johannes Kepler (section)

== Astronomy ==
=== ''Mysterium Cosmographicum'' ===
[[File:Kepler-solar-system-1.png|thumb|Kepler's [[Platonic solid]] model of the [[Solar System]], from ''[[Mysterium Cosmographicum]]'' (1596)]]

Kepler's first major astronomical work was ''[[Mysterium Cosmographicum]]'' (''The Cosmographic Mystery'', 1596). Kepler claimed to have had an [[epiphany (feeling)|epiphany]] on 19 July 1595, while teaching in [[Graz]], demonstrating the periodic [[Conjunction (astronomy and astrology)|conjunction]] of [[Saturn]] and [[Jupiter]] in the [[zodiac]]: he realized that [[regular polygon]]s bound one inscribed and one circumscribed circle at definite ratios, which, he reasoned, might be the geometrical basis of the universe. After failing to find a unique arrangement of polygons that fit known astronomical observations (even with extra planets added to the system), Kepler began experimenting with 3-dimensional [[polyhedron|polyhedra]]. He found that each of the five [[Platonic solid]]s could be inscribed and circumscribed by spherical [[orb (astronomy)|orbs]]; nesting these solids, each encased in a sphere, within one another would produce six layers, corresponding to the six known planets—[[Mercury (planet)|Mercury]], [[Venus]], [[Earth]], [[Mars]], Jupiter, and Saturn. By ordering the solids selectively—[[octahedron]], [[icosahedron]], [[dodecahedron]], [[tetrahedron]], [[cube]]—Kepler found that the spheres could be placed at intervals corresponding to the relative sizes of each planet's path, assuming the planets circle the Sun. Kepler also found a formula relating the size of each planet's orb to the length of its [[orbital period]]: from inner to outer planets, the ratio of increase in orbital period is twice the difference in orb radius. 

Kepler thought the ''Mysterium'' had revealed God's geometrical plan for the universe. Much of Kepler's enthusiasm for the Copernican system stemmed from his [[theological]] convictions about the connection between the physical and the [[Spirituality|spiritual]]; the universe itself was an image of God, with the Sun corresponding to the Father, the stellar sphere to the [[Jesus|Son]], and the intervening space between them to the [[Holy Spirit in Christianity|Holy Spirit]]. His first manuscript of ''Mysterium'' contained an extensive chapter reconciling heliocentrism with biblical passages that seemed to support geocentrism.<ref>Barker and Goldstein. "Theological Foundations of Kepler's Astronomy," pp.&nbsp;99–103, 112–113.</ref> With the support of his mentor Michael Maestlin, Kepler received permission from the Tübingen university senate to publish his manuscript, pending removal of the Bible [[exegesis]] and the addition of a simpler, more understandable, description of the Copernican system as well as Kepler's new ideas. ''Mysterium'' was published late in 1596, and Kepler received his copies and began sending them to prominent astronomers and patrons early in 1597; it was not widely read, but it established Kepler's reputation as a highly skilled astronomer. The effusive dedication, to powerful patrons as well as to the men who controlled his position in Graz, also provided a crucial doorway into the [[Patronage|patronage system]].<ref>Caspar. ''Kepler'', pp.&nbsp;65–71.</ref>

In 1621, Kepler published an expanded second edition of ''Mysterium'', half as long again as the first, detailing in footnotes the corrections and improvements he had achieved in the 25 years since its first publication.<ref>Field. ''Kepler's Geometrical Cosmology'', Chapter IV, pp. 73ff.</ref> In terms of impact, the ''Mysterium'' can be seen as an important first step in modernizing the theory proposed by [[Nicolaus Copernicus|Copernicus]] in his ''[[De revolutionibus orbium coelestium]]''. While Copernicus sought to advance a heliocentric system in this book, he resorted to [[Ptolemy|Ptolemaic]] devices (viz., epicycles and eccentric circles) in order to explain the change in planets' orbital speed, and also continued to use as a point of reference the center of the Earth's orbit rather than that of the Sun "as an aid to calculation and in order not to confuse the reader by diverging too much from Ptolemy." Modern astronomy owes much to ''Mysterium Cosmographicum'', despite flaws in its main thesis, "since it represents the first step in cleansing the Copernican system of the remnants of the Ptolemaic theory still clinging to it."<ref>Dreyer, J.L.E. ''A History of Astronomy from [[Thales]] to Kepler'', Dover Publications, 1953, pp.&nbsp;331, 377–379.</ref> Kepler never abandoned his five solids theory, publishing the second edition of ''Mysterium'' in 1621 and affirming his continued belief in the validity of the model. Although he noted that there were discrepancies between the observational data and his model's predictions, he did not think they were large enough to invalidate the theory.<ref>{{Cite book |last=Field |first=Judith Veronica |title=Kepler's geometrical cosmology |date=2013 |publisher=Bloomsbury |isbn=978-1-4725-0703-7 |series=Bloomsbury academic collections. Philosophy |location=London |pages=94}}</ref>

=== ''Astronomia Nova'' ===
[[File:Kepler Mars retrograde.jpg|thumb|upright=.9|Diagram of the [[geocentric]] trajectory of Mars through several periods of [[apparent retrograde motion]] in ''Astronomia Nova'' (1609)]]
The extended line of research that culminated in ''[[Astronomia Nova]]'' (''A New Astronomy'')—including the first two [[Kepler's laws of planetary motion|laws of planetary motion]]—began with the analysis, under Tycho's direction, of the orbit of Mars. In this work Kepler introduced the revolutionary concept of planetary orbit, a path of a planet in space resulting from the action of physical causes, distinct from previously held notion of planetary orb (a spherical shell to which planet is attached). As a result of this breakthrough astronomical phenomena came to be seen as being governed by physical laws.<ref>{{Cite journal|last1=Goldstein|first1=Bernard|last2=Hon|first2=Giora|date=2005|title=Kepler's Move from Orbs to Orbits: Documenting a Revolutionary Scientific Concept|url=https://www.researchgate.net/publication/246602496|journal=Perspectives on Science|volume=13|pages=74–111|doi=10.1162/1063614053714126 |s2cid=57559843 }}</ref> Kepler calculated and recalculated various approximations of Mars's orbit using an [[equant]] (the mathematical tool that Copernicus had eliminated with his system), eventually creating a model that generally agreed with Tycho's observations to within two [[arcminute]]s (the average measurement error). But he was not satisfied with the complex and still slightly inaccurate result; at certain points the model differed from the data by up to eight arcminutes. The wide array of traditional mathematical astronomy methods having failed him, Kepler set about trying to fit an [[Oval|ovoid]] orbit to the data.<ref>Caspar, ''Kepler'', pp.&nbsp;123–128</ref>

In Kepler's religious view of the cosmos, the Sun (a symbol of [[God the Father]]) was the source of motive force in the Solar System. As a physical basis, Kepler drew by analogy on [[William Gilbert (physician)|William Gilbert]]'s theory of the magnetic soul of the Earth from ''[[De Magnete]]'' (1600) and on his own work on optics. Kepler supposed that the motive power (or motive ''species'')<ref>On motive species, see Lindberg, "The Genesis of Kepler's Theory of Light," pp.&nbsp;38–40.</ref> radiated by the Sun weakens with distance, causing faster or slower motion as planets move closer or farther from it.<ref>Koyré, ''The Astronomical Revolution'', pp.&nbsp;199–202.</ref>{{NoteTag|"Kepler's decision to base his causal explanation of planetary motion on a distance-velocity law, rather than on uniform circular motions of compounded spheres, marks a major shift from ancient to modern conceptions of science&nbsp;... [Kepler] had begun with physical principles and had then derived a trajectory from it, rather than simply constructing new models. In other words, even before discovering the area law, Kepler had abandoned uniform circular motion as a physical principle."<ref>Peter Barker and Bernard R. Goldstein, "Distance and Velocity in Kepler's Astronomy", ''Annals of Science,'' 51 (1994): 59–73, at p.&nbsp;60.</ref>}} Perhaps this assumption entailed a mathematical relationship that would restore astronomical order. Based on measurements of the [[aphelion]] and [[perihelion]] of the Earth and Mars, he created a formula in which a planet's rate of motion is inversely proportional to its distance from the Sun. Verifying this relationship throughout the orbital cycle required very extensive calculation; to simplify this task, by late 1602 Kepler reformulated the proportion in terms of geometry: ''planets sweep out equal areas in equal times''—his second law of planetary motion.<ref>Caspar, ''Kepler'', pp.&nbsp;129–132</ref>

He then set about calculating the entire orbit of Mars, using the geometrical rate law and assuming an egg-shaped [[ovoid]] orbit. After approximately 40 failed attempts, in late 1604 he at last hit upon the idea of an [[ellipse]],<ref>{{cite book |last = Dreyer |first = John Louis Emil |url = https://books.google.com/books?id=OgRAAQAAIAAJ&pg=PA402 |title = History of the Planetary Systems from Thales to Kepler |publisher = Cambridge University Press |year = 1906 |location = Cambridge, England |page = 402 |author-link = John Louis Emil Dreyer }}</ref> which he had previously assumed to be too simple a solution for earlier astronomers to have overlooked.<ref>Caspar, ''Kepler'', p.&nbsp;133</ref> Finding that an elliptical orbit fit the Mars data (the [[Vicarious Hypothesis]]), Kepler immediately concluded that ''all planets move in ellipses, with the Sun at one focus''—his first law of planetary motion. Because he employed no calculating assistants, he did not extend the mathematical analysis beyond Mars. 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.<ref>Caspar, ''Kepler'', pp.&nbsp;131–140; Koyré, ''The Astronomical Revolution'', pp.&nbsp;277–279</ref>

=== ''Epitome of Copernican Astronomy'' ===
{{further|Epitome Astronomiae Copernicanae}}

Since completing the ''Astronomia Nova'', Kepler had intended to compose an astronomy textbook that would cover all the fundamentals of [[Heliocentrism|heliocentric astronomy]].<ref>Caspar, ''Kepler'', pp.&nbsp;239–240, 293–300</ref> Kepler spent the next several years working on what would become ''Epitome Astronomiae Copernicanae'' (''Epitome of Copernican Astronomy''). Despite its title, which merely hints at heliocentrism, the ''Epitome'' is less about Copernicus's work and more about Kepler's own astronomical system. The ''Epitome'' contained all three laws of planetary motion and attempted to explain heavenly motions through physical causes.<ref name="Gingerich pp 302">Gingerich, "Kepler, Johannes" from ''Dictionary of Scientific Biography'', pp.&nbsp;302–304</ref> Although it explicitly extended the first two laws of planetary motion (applied to Mars in ''Astronomia nova'') to all the planets as well as the Moon and the [[Galilean moons|Medicean satellites of Jupiter]],{{NoteTag|By 1621 or earlier, Kepler recognized that Jupiter's moons obey his third law. Kepler contended that rotating massive bodies communicate their rotation to their satellites, so that the satellites are swept around the central body; thus the rotation of the Sun drives the revolutions of the planets and the rotation of the Earth drives the revolution of the Moon. In Kepler's era, no one had any evidence of Jupiter's rotation. However, Kepler argued that the force by which a central body causes its satellites to revolve around it, weakens with distance; consequently, satellites that are farther from the central body revolve slower. Kepler noted that Jupiter's moons obeyed this pattern and he inferred that a similar force was responsible. He also noted that the orbital periods and semi-major axes of Jupiter's satellites were roughly related by a 3/2 power law, as are the orbits of the six (then known) planets. However, this relation was approximate: the periods of Jupiter's moons were known within a few percent of their modern values, but the moons' semi-major axes were determined less accurately. Kepler discussed Jupiter's moons in his ''[[Epitome Astronomiae Copernicanae|Summary of Copernican Astronomy]]'':<ref>Linz ("Lentiis ad Danubium"), (Austria): Johann Planck, 1622, book 4, part 2, [https://books.google.com/books?id=wa2SE_6ZL7YC&pg=PA554 p. 554]</ref><ref>Christian Frisch, ed., ''Joannis Kepleri Astronomi Opera Omnia'', vol. 6 (Frankfurt-am-Main, (Germany): Heyder & Zimmer, 1866), [https://books.google.com/books?id=xjMAAAAAQAAJ&pg=PA361 p. 361].)</ref><!--Original : ''4) Confirmatur vero fides hujus rei comparatione quatuor Jovialium et Jovis cum sex planetis et Sole. Etsi enim de corpore Jovis, an et ipsum circa suum axem convertatur, non-ea documenta habemus, quae nobis suppetunt in corporibus Terrae et praecipue Solis, quippe a sensu ipso: at illud sensus testatur, plane ut est cum sex planetis circa Solem, sic etiam se rem habere cum quatuor Jovialibus, ut circa corpus Jovis quilibet, quo longius ab illo potest excurrere, hoc tardius redeat, et id quidem proportione non eadem, sed majore, hoc est sescupla proportionis intervallorum cujusque a Jove: quae plane ipsissima est, qua utebantur supra sex planetae. Intervalla enim quatuor Jovialium a Jove prodit Marius in suo Mundo Joviali ista: 3, 5, 8, 13 (vel 14 Galilaeo)&nbsp;... Periodica vero tempora prodit idem Marius ista: dies 1. h. 18 1/2, dies 3 h. 13 1/3, dies 7 h. 3, dies 16 h. 18: ubique proportio est major quam dupla, major igitur quam intervallorum 3, 5, 8, 13 vel 14, minor tamen quam quadratorum, qui duplicant proportiones intervallorum, sc. 9, 25, 64, 169 vel 196, sicut etiam sescupla sunt majora simplis, minora vero duplis.''-->{{blockquote|(4) However, the credibility of this [argument] is proved by the comparison of the four [moons] of Jupiter and Jupiter with the six planets and the Sun. Because, regarding the body of Jupiter, whether it turns around its axis, we don't have proofs for what suffices for us [regarding the rotation of ] the body of the Earth and especially of the Sun, certainly [as reason proves to us]: but reason attests that, just as it is clearly [true] among the six planets around the Sun, so also it is among the four [moons] of Jupiter, because around the body of Jupiter any [satellite] that can go farther from it orbits slower, and even that [orbit's period] is not in the same proportion, but greater [than the distance from Jupiter]; that is, 3/2 (''sescupla'' ) of the proportion of each of the distances from Jupiter, which is clearly the very [proportion] as [is used for] the six planets above. In his [book] ''The World of Jupiter'' [''Mundus Jovialis'', 1614], [[Simon Marius|[Simon] Mayr]] [1573–1624] presents these distances, from Jupiter, of the four [moons] of Jupiter: 3, 5, 8, 13 (or 14 [according to] Galileo)&nbsp;... Mayr presents their time periods: 1 day 18 1/2 hours, 3 days 13 1/3 hours, 7 days 3 hours, 16 days 18 hours: for all [of these data] the proportion is greater than double, thus greater than [the proportion] of the distances 3, 5, 8, 13 or 14, although less than [the proportion] of the squares, which double the proportions of the distances, namely 9, 25, 64, 169 or 196, just as [a power of] 3/2 is also greater than 1 but less than 2.}}}} it did not explain how elliptical orbits could be derived from observational data.<ref>Wolf, ''A History of Science, Technology and Philosophy'', pp.&nbsp;140–141; Pannekoek, ''A History of Astronomy'', p. 252</ref>

Originally intended as an introduction for the uninitiated, Kepler sought to model his ''Epitome'' after that of his master [[Michael Maestlin]], who published a well-regarded book explaining the basics of [[Geocentric model|geocentric astronomy]] to non-experts.<ref name=":1">{{Cite journal|last=Rothman|first=A.|date=2021|title=Kepler's Epitome of Copernican Astronomy in context|url=https://onlinelibrary.wiley.com/doi/epdf/10.1111/1600-0498.12356|journal=Centaurus|volume=63|pages=171–191|doi=10.1111/1600-0498.12356|issn=0008-8994|s2cid=230613099}}</ref> Kepler completed the first of three volumes, consisting of Books I–III, by 1615 in the same question-answer format of Maestlin's and have it printed in 1617.<ref>{{Cite journal|last=Gingerich|first=Owen|date=1990|title=Five Centuries of Astronomical Textbooks and Their Role in Teaching|url=http://adsabs.harvard.edu/abs/1990teas.conf..189G|journal=The Teaching of Astronomy, Proceedings of IAU Colloq. 105, Held in Williamstown, MA, 27–30 July 1988|pages=189|bibcode=1990teas.conf..189G}}</ref> However, the [[Index Librorum Prohibitorum|banning of Copernican books]] by the Catholic Church, as well as the start of the [[Thirty Years' War]], meant that publication of the next two volumes would be delayed. In the interim, and to avoid being subject to the ban, Kepler switched the audience of the ''Epitome'' from beginners to that of expert astronomers and mathematicians, as the arguments became more and more sophisticated and required advanced mathematics to be understood.<ref name=":1" /> The second volume, consisting of Book IV, was published in 1620, followed by the third volume, consisting of Books V–VII, in 1621.

=== ''Rudolphine Tables'' ===
[[File:Rudolphine tables.jpg|thumb|upright=1.2|Two pages from Kepler's ''Rudolphine Tables'' showing eclipses of the Sun and Moon]]
In the years following the completion of ''Astronomia Nova'', most of Kepler's research was focused on preparations for the ''Rudolphine Tables'' and a comprehensive set of [[ephemerides]] (specific predictions of planet and star positions) based on the table, though neither would be completed for many years.<ref>Caspar, ''Kepler''. pp. 178–179.</ref>

Kepler, at last, completed the ''[[Rudolphine Tables]]'' in 1623, 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.<ref>Robert J. King, “Johannes Kepler and Australia”, ''The Globe,'' no. 90, 2021, pp. 15–24.</ref>