Johannes Kepler

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.[61] In terms of impact, the Mysterium can be seen as an important first step in modernizing the theory proposed by Copernicus in his De revolutionibus orbium coelestium. While Copernicus sought to advance a heliocentric system in this book, he resorted to 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."^[62] 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.^[63]

In Kepler's religious view of the cosmos, the Sun (a symbol of

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.^[69]

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,^[70] which he had previously assumed to be too simple a solution for earlier astronomers to have overlooked.^[71] 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.^[72]

Epitome of Copernican Astronomy

Further information: Epitome Astronomiae Copernicanae

Since completing the Astronomia Nova, Kepler had intended to compose an astronomy textbook that would cover all the fundamentals of heliocentric astronomy.^[73] 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.^[74] 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 Medicean satellites of Jupiter,^{[note 2]} it did not explain how elliptical orbits could be derived from observational data.^[77]

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 astronomy to non-experts.^[78] 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.^[79] However, the 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.^[78] 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

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.^[80]

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.^[81]

Astrology

General Wallenstein

Like Ptolemy, Kepler considered astrology as the counterpart to astronomy, and as being of equal interest and value. However, in the following years, the two subjects drifted apart until astrology was no longer practiced among professional astronomers.^[82]

Sir Oliver Lodge observed that Kepler was somewhat disdainful of astrology in his own day, as he was "continually attacking and throwing sarcasm at astrology, but it was the only thing for which people would pay him, and on it after a fashion he lived.^[83] Nonetheless, Kepler spent a huge amount of time trying to restore astrology on a firmer philosophical footing, composing numerous astrological calendars, more than 800 nativities, and a number of treaties dealing with the subject of astrology proper.^[84]

De Fundamentis

In his bid to become imperial astronomer, Kepler wrote De Fundamentis (1601), whose full title can be translated as "On Giving Astrology Sounder Foundations", as a short foreword to one of his yearly almanacs.[85]

In this work, Kepler describes the effects of the Sun, Moon, and the planets in terms of their light and their influences upon humors, concluding with Kepler's view that the Earth possesses a soul with some sense of geometry. Stimulated by the geometric convergence of rays formed around it, the world-soul is sentient but not conscious. As a shepherd is pleased by the piping of a flute without understanding the theory of musical harmony, so likewise Earth responds to the angles and aspects made by the heavens but not in a conscious manner. Eclipses are important as omens because the animal faculty of the Earth is violently disturbed by the sudden intermission of light, experiencing something like emotion and persisting in it for some time.^[82]

Kepler surmises that the Earth has "cycles of humors" as living animals do, and provides as an example: "the highest tides of the sea are said by sailors to return after nineteen years around the same days of the year". (This may refer to the 18.6-year lunar node precession cycle.) Kepler advocates searching for such cycles by gathering observations over a period of many years, "and so far this observation has not been made".^[86]

Tertius Interveniens

Kepler and Helisaeus Roeslin engaged in a series of published attacks and counter-attacks on the importance of astrology after the supernova of 1604; around the same time, physician Philip Feselius published a work dismissing astrology altogether (and Roeslin's work in particular).^[87]

In response to what Kepler saw as the excesses of astrology, on the one hand, and overzealous rejection of it, on the other, Kepler prepared Tertius Interveniens (1610). Nominally this work—presented to the common patron of Roeslin and Feselius—was a neutral mediation between the feuding scholars (the titled meaning "Third-party interventions"), but it also set out Kepler's general views on the value of astrology, including some hypothesized mechanisms of interaction between planets and individual souls. While Kepler considered most traditional rules and methods of astrology to be the "evil-smelling dung" in which "an industrious hen" scrapes, there was an "occasional grain-seed, indeed, even a pearl or a gold nugget" to be found by the conscientious scientific astrologer.^[88]

Music

Harmonice Mundi

Main article: Harmonice Mundi

Kepler was convinced "that the geometrical things have provided the Creator with the model for decorating the whole world".^[89] In Harmonice Mundi (1619), he attempted to explain the proportions of the natural world—particularly the astronomical and astrological aspects—in terms of music.^{[note 3]} The central set of "harmonies" was the musica universalis or "music of the spheres", which had been studied by Pythagoras, Ptolemy and others before Kepler; in fact, soon after publishing Harmonice Mundi, Kepler was embroiled in a priority dispute with Robert Fludd, who had recently published his own harmonic theory.^[90]

Kepler began by exploring regular polygons and

Kepler's solids. From there, he extended his harmonic analysis to music, meteorology, and astrology; harmony resulted from the tones made by the souls of heavenly bodies—and in the case of astrology, the interaction between those tones and human souls. In the final portion of the work (Book V), Kepler dealt with planetary motions, especially relationships between orbital velocity and orbital distance from the Sun. Similar relationships had been used by other astronomers, but Kepler—with Tycho's data and his own astronomical theories—treated them much more precisely and attached new physical significance to them.^[91]

Among many other harmonies, Kepler articulated what came to be known as the third law of planetary motion. He tried many combinations until he discovered that (approximately) "The square of the periodic times are to each other as the cubes of the mean distances." Although he gives the date of this epiphany (8 March 1618), he does not give any details about how he arrived at this conclusion.

Edmund Halley, and perhaps Christopher Wren and Robert Hooke to demonstrate independently that the presumed gravitational attraction between the Sun and its planets decreased with the square of the distance between them.^[93] This refuted the traditional assumption of scholastic physics that the power of gravitational attraction remained constant with distance whenever it applied between two bodies, such as was assumed by Kepler and also by Galileo in his mistaken universal law that gravitational fall is uniformly accelerated, and also by Galileo's student Borrelli in his 1666 celestial mechanics.^[94]

Optics

Astronomiae Pars Optica

As Kepler slowly continued analyzing Tycho's Mars observations—now available to him in their entirety—and began the slow process of tabulating the

eye's lens onto the retina. The solution to this dilemma was not of particular importance to Kepler as he did not see it as pertaining to optics, although he did suggest that the image was later corrected "in the hollows of the brain" due to the "activity of the Soul."^[95]

Today, Astronomiae Pars Optica is generally recognized as the foundation of modern optics (though the

law of refraction is conspicuously absent).^[96] With respect to the beginnings of projective geometry, Kepler introduced the idea of continuous change of a mathematical entity in this work. He argued that if a focus of a conic section were allowed to move along the line joining the foci, the geometric form would morph or degenerate, one into another. In this way, an ellipse becomes a parabola when a focus moves toward infinity, and when two foci of an ellipse merge into one another, a circle is formed. As the foci of a hyperbola merge into one another, the hyperbola becomes a pair of straight lines. He also assumed that if a straight line is extended to infinity it will meet itself at a single point at infinity, thus having the properties of a large circle.^[97]

Dioptrice

In the first months of 1610, Galileo Galilei—using his powerful new telescope—discovered four satellites orbiting Jupiter. Upon publishing his account as Sidereus Nuncius [Starry Messenger], Galileo sought the opinion of Kepler, in part to bolster the credibility of his observations. Kepler responded enthusiastically with a short published reply, Dissertatio cum Nuncio Sidereo [Conversation with the Starry Messenger]. He endorsed Galileo's observations and offered a range of speculations about the meaning and implications of Galileo's discoveries and telescopic methods, for astronomy and optics as well as cosmology and astrology. Later that year, Kepler published his own telescopic observations of the moons in Narratio de Jovis Satellitibus, providing further support of Galileo. To Kepler's disappointment, however, Galileo never published his reactions (if any) to Astronomia Nova.^[98]

Kepler also started a theoretical and experimental investigation of telescopic lenses using a telescope borrowed from Duke Ernest of Cologne.

Keplerian telescope—in which two convex lenses can produce higher magnification than Galileo's combination of convex and concave lenses.^[100]

Mathematics and physics

As a New Year's gift that year (1611), he also composed for his friend and some-time patron, Baron Wackher von Wackhenfels, a short pamphlet entitled Strena Seu de Nive Sexangula (A New Year's Gift of Hexagonal Snow). In this treatise, he published the first description of the hexagonal symmetry of snowflakes and, extending the discussion into a hypothetical atomistic physical basis for their symmetry, posed what later became known as the Kepler conjecture, a statement about the most efficient arrangement for packing spheres.^[101][102] This was proved in 1998 by Thomas Callister Hales.^[103]

Kepler wrote the influential mathematical treatise Nova stereometria doliorum vinariorum in 1613, on measuring the volume of containers such as wine barrels, which was published in 1615.

integral calculus, is known in German as Keplersche Fassregel (Kepler's barrel rule).^[108]

Legacy

Reception of his astronomy

Seth Ward used an elliptical orbit with motions defined by an equant.^{[109][110][111]}

Several astronomers tested Kepler's theory, and its various modifications, against astronomical observations. Two transits of Venus and Mercury across the face of the sun provided sensitive tests of the theory, under circumstances when these planets could not normally be observed. 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 day before and after the predicted date.

1639 Venus transit, had used his own observations 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.^{[114][115][116]}

Epitome of Copernican Astronomy was read by astronomers throughout Europe, and following Kepler's death, it was the main vehicle for spreading Kepler's ideas. In the period 1630–1650, this book was the most widely used astronomy textbook, winning many converts to ellipse-based astronomy.

Beyond his role in the historical development of astronomy and natural philosophy, Kepler has loomed large in the

Alexandre Koyré's work on 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.^[121]

Philosophers of science—such as

A new edition was planned beginning in 1914 by Walther von Dyck (1856–1934). Dyck compiled copies of Kepler's unedited manuscripts, using international diplomatic contacts to convince the Soviet authorities to lend him the manuscripts kept in Leningrad for photographic reproduction. These manuscripts contained several works by Kepler that had not been available to Frisch. Dyck's photographs remain the basis for the modern editions of Kepler's unpublished manuscripts.

Max Caspar (1880–1956) published his German translation of Kepler's Mysterium Cosmographicum in 1923. Both Dyck and Caspar were influenced in their interest in Kepler by mathematician Alexander von Brill (1842–1935). Caspar became Dyck's collaborator, succeeding him as project leader in 1934, establishing the Kepler-Kommission in the following year. Assisted by Martha List (1908–1992) and Franz Hammer (1898–1969), Caspar continued editorial work during World War II. Max Caspar also published a biography of Kepler in 1948.^[123] The commission was later chaired by Volker Bialas (during 1976–2003) and Ulrich Grigull (during 1984–1999) and Roland Bulirsch (1998–2014).^[124][125]

Kepler has acquired a popular image as an icon of scientific modernity and a man before his time; science popularizer

A well-received 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.^[128] A 2004 nonfiction book, Heavenly Intrigue, suggested that Kepler murdered Tycho Brahe to gain access to his data.^[129]

In Austria, a silver collector's

The German composer Paul Hindemith wrote an opera about Kepler titled Die Harmonie der Welt (1957), and during the prolonged process of its creation he concurrently wrote a symphony of the same name based on the musical ideas he had developed for the opera.^[131] Hindemith's work inspired John Rodgers and Willie Ruff of Yale University to create a synthesizer composition based on Kepler's scheme for representing planetary motion with music.^[132] Philip Glass wrote an opera called Kepler (2009) based on Kepler's life, with a libretto in German and Latin by Martina Winkel.^[133]

Directly named for Kepler's contribution to science are:

The Kepler space telescope has observed 530,506 stars and detected 2,778 confirmed planets (as of 16 June 2023^[update]), many of them named after the telescope and Kepler himself.^[134][135]

• Mysterium Cosmographicum (The Sacred Mystery of the Cosmos) (1596)
• De Fundamentis Astrologiae Certioribus (On Firmer Fundaments of Astrology) (1601)
• Astronomiae pars optica (in Latin). Frankfurt am Main: Claude de Marne. 1604.
• De Stella nova in pede Serpentarii (On the New Star in Ophiuchus's Foot) (1606)
• Astronomia nova (New Astronomy) (1609)
• Tertius Interveniens (Third-party Interventions) (1610)
• Dissertatio cum Nuncio Sidereo (Conversation with the Starry Messenger) (1610)
• Dioptrice (1611)
• De nive sexangula (On the Six-Cornered Snowflake) (1611)
• De vero Anno, quo aeternus Dei Filius humanam naturam in Utero benedictae Virginis Mariae assumpsit (1614)^[136]
• Eclogae Chronicae (1615, published with Dissertatio cum Nuncio Sidereo)
• Nova stereometria doliorum vinariorum (New Stereometry of Wine Barrels) (1615)
• Ephemerides nouae motuum coelestium (1617–30)
• Epitome astronomiae copernicanae (in Latin). Linz: Johann Planck. 1618.
• Epitome astronomiae Copernicanae. 1–3, De doctrina sphaerica (in Latin). Vol. 44199. Linz: Johann Planck. 1618.
  • Epitome astronomiae Copernicanae. 4, Doctrina theorica. 1, Physica coelestis (in Latin). Vol. 4. Linz: Gottfried Tambach. 1622.
  • Epitome astronomiae Copernicanae. 5–7, Doctrina theorica (in Latin). Vol. 44323. Linz: Gottfried Tambach. 1621.
• De cometis (in Latin). Augsburg: Sebastian Müller. 1619.
• Harmonice Mundi (Harmony of the Worlds) (1619)
• Mysterium cosmographicum
  (The Sacred Mystery of the Cosmos), 2nd edition (1621)
• Tabulae Rudolphinae (Rudolphine Tables) (1627)
• Somnium (The Dream) (1634) (English translation on Google Books preview)
• [Opere] (in Latin). Vol. 1. Frankfurt am Main: Heyder & Zimmer. 1858.
  • [Opere] (in Latin). Vol. 2. Frankfurt am Main: Heyder & Zimmer. 1859.
  • [Opere] (in Latin). Vol. 3. Frankfurt am Main: Heyder & Zimmer. 1860.
  • [Opere] (in Latin). Vol. 4. Frankfurt am Main: Heyder & Zimmer. 1863.
  • [Opere] (in Latin). Vol. 5. Frankfurt am Main: Heyder & Zimmer. 1864.
  • [Opere] (in Latin). Vol. 6. Frankfurt am Main: Heyder & Zimmer. 1866.
  • [Opere] (in Latin). Vol. 7. Frankfurt am Main: Heyder & Zimmer. 1868.
  • [Opere] (in Latin). Vol. 8. Frankfurt am Main: Heyder & Zimmer. 1870.
  • [Opere] (in Latin). Vol. 9. Frankfurt am Main: Heyder & Zimmer. 1871.

A critical edition of Kepler's collected works (Johannes Kepler Gesammelte Werke, KGW) in 22 volumes is being edited by the Kepler-Kommission (founded 1935) on behalf of the

Vol. 1: Mysterium Cosmographicum. De Stella Nova. Ed. M. Caspar. 1938, 2nd ed. 1993. Paperback

ISBN 3-406-01639-1

.

Vol. 2: Astronomiae pars optica. Ed. F. Hammer. 1939, Paperback

ISBN 3-406-01641-3

.

Vol. 3: Astronomia Nova. Ed. M. Caspar. 1937. IV, 487 p. 2. ed. 1990. Paperback

ISBN 3-406-01642-1

.

Vol. 4: Kleinere Schriften 1602–1611. Dioptrice. Ed. M. Caspar, F. Hammer. 1941.

ISBN 3-406-01644-8

.

Vol. 5: Chronologische Schriften. Ed. F. Hammer. 1953. Out-of-print.

Vol. 6: Harmonice Mundi. Ed. M. Caspar. 1940, 2nd ed. 1981,

ISBN 3-406-01648-0

.

Vol. 7: Epitome Astronomiae Copernicanae. Ed. M. Caspar. 1953, 2nd ed. 1991.

ISBN 3-406-01651-0

.

Vol. 8: Mysterium Cosmographicum. Editio altera cum notis. De Cometis. Hyperaspistes. Commentary F. Hammer. 1955. Paperback

ISBN 3-406-01653-7

.

Vol 9: Mathematische Schriften. Ed. F. Hammer. 1955, 2nd ed. 1999. Out-of-print.

Vol. 10: Tabulae Rudolphinae. Ed. F. Hammer. 1969.

ISBN 3-406-01656-1

.

Vol. 11,1: Ephemerides novae motuum coelestium. Commentary V. Bialas. 1983.

ISBN 3-406-01659-6

.

Vol. 11,2: Calendaria et Prognostica. Astronomica minora. Somnium. Commentary V. Bialas, H. Grössing. 1993.

ISBN 3-406-37511-1

.

Vol. 12: Theologica. Hexenprozeß. Tacitus-Übersetzung. Gedichte. Commentary J. Hübner, H. Grössing, F. Boockmann, F. Seck. Directed by V. Bialas. 1990.

ISBN 3-406-01661-8

.

Vol. 13: Briefe 1590–1599. Ed. M. Caspar. 1945. 432 p.

ISBN 3-406-01663-4

.

Vol. 14: Briefe 1599–1603. Ed. M. Caspar. 1949. Out-of-print. 2nd ed. in preparation.

Vol 15: Briefe 1604–1607. Ed. M. Caspar. 1951. 2nd ed. 1995.

ISBN 3-406-01667-7

.

Vol. 16: Briefe 1607–1611. Ed. M. Caspar. 1954.

ISBN 3-406-01668-5

.

Vol. 17: Briefe 1612–1620. Ed. M. Caspar. 1955.

ISBN 3-406-01671-5

.

Vol. 18: Briefe 1620–1630. Ed. M. Caspar. 1959.

ISBN 3-406-01672-3

.

Vol. 19: Dokumente zu Leben und Werk. Commentary M. List. 1975.

ISBN 978-3-406-01674-5

.

Vols. 20–21: manuscripts

Vol. 20, 1: Manuscripta astronomica (I). Apologia, De motu Terrae, Hipparchus etc. Commentary V. Bialas. 1988.

ISBN 3-406-31502-X

.

Vol. 20, 2: Manuscripta astronomica (II). Commentaria in Theoriam Martis. Commentary V. Bialas. 1998. Paperback

ISBN 3-406-40593-2

.

Vol. 21, 1: Manuscripta astronomica (III) et mathematica. De Calendario Gregoriano. In preparation.

Vol. 21, 2: Manuscripta varia. In preparation.

Vol. 22: General index, in preparation.