Astronomia Nova Research Articles

Kepler’s struggle with the problem of force obstruction

The paper examines how the scarcely discussed problem of force obstruction contributed to shaping Kepler’s concept of force, that is, the question whether corporeal forces are blocked when an intermediate body is interposed between the force source and the target body. We explore the role played by this problem in Kepler’s works, focusing on his Optics, Foundations of Astrology, Astronomia Nova and Epitome. While the problem is instrumental in abandoning an initially physicalistic framework for astrology, Kepler attempts at different solutions when discussing the forces responsible for planetary motion. These forces are first modelled upon light, and then magnetism (and gravity). However, after considering several ways to get rid of the problem, he is eventually unable to decide why observable effects of obstruction are usually absent. So he accepts this absence at face value, similarly to Newton in his most relevant passages, allowing for a new ontological category that is physical on the one hand, but non-material on the other.

François Viète's method for calculating the eccentricity in a bisected model and its possible application to Kepler's Vicarious Hypothesis

According to Kepler's own words in Astronomia Nova, he invested five years trying to find the values for the eccentricities for his “vicarious” hypothesis. At some point, he asked Herwart von Hohenburg, to ask François Viète's help to solve his problem, but there is no evidence that Viète received this request. At that time, Viète was working on his unpublished Ad harmonicon coeleste. In it, he proposes a new method for bisected models, which can easily be extended to non-bisected models. In this paper, I describe Viète's method, analyze its accuracy, and show how to extend it to non-bisected models, making it suitable for solving Kepler's problem.

The Earth's eccentricity in Kepler's refutation of the Tychonic approach to the problem of Mars

In this paper I explain Kepler's procedure for refuting the Ptolemaic-Tychonic approach to the problem of Mars, by using latitudinal observations at Mars's opposition, from Chapter 19 of the Astronomia Nova. This critique is fundamental to his reformation of the foundations of astronomy with his first two laws. Moreover, as I argue, the strategy he follows is deeply rooted in certain rhetorical considerations that he employed during the composition of his work.

Kepler’s derivation of the bisection of the earth’s orbit in Astronomia Nova

Chapter 22 of Astronomia Nova is focused on the calculation of the Earth’s eccentricity. This is carried out by observing the effect of the Earth’s motion on the apparent position of Mars. Kepler’s method to derive the exact eccentricity, however, requires as data a set of longitudes of Mars while that planet and the Earth are in a very particular and restricted number of possible configurations. This paper explains how Kepler understood and tackled the Earth problem in theoretical terms, and also how he drew information from Tycho’s observational registers in a methodical way in order to obtain the necessary data to calculate the desired parameter, i.e. the eccentricity of the Earth’s orbit. In doing so, I will analyze not only Astronomia Nova’s relevant passages, but also Kepler’s preliminary annotations, as published in the Gesammelte Werke.

The Tychonic Method for Calculating the Ratio between the Eccentricities of Mars

In Chapter 16 of Astronomia nova, Kepler describes and applies a method for finding the parameters of what he will call the vicarious hypothesis: a model that still assumes circular orbits and an equant point, but does not assume the bisection of the eccentricity, that is, that the center of the orbit is halfway between the equant point and the Sun. The method allows Kepler to find independently both centers in a very elegant way, but its application is tedious. He confesses that he had to apply it seventy times over a period of 5 years to obtain trustable results. Years earlier, when Kepler arrived to work with Tycho, he found that Tycho and Longomontanus had rejected bisection and somehow had obtained a ratio between eccentricities that, as Kepler himself highlights, happened to be very close to the one Kepler would later find after so much effort. Kepler does not say how Tycho and Longomontanus obtained their parameters and, to the best of my knowledge, there is no single published work that attempts to answer this question. Still, it is a very interesting question to ask how they arrived at values so close to those that took so much pain for Kepler to obtain. Recently, I published a paper describing a method Tycho used for finding Saturn’s parameters. In this paper, I show that by applying this method to the data of Tychonic observations of oppositions, it is possible to arrive at parameters very close to those that we know Tycho found. In this way, I argue that this is the method Tycho applied for obtaining Mars’s parameters. The simplicity of the Tychonic method contrasts with the complexity of Kepler’s.

Longomontanus’ Model for the Longitudes of Mars

When at the beginning of 1600, Kepler arrived to work with Tycho Brahe, Longomontanus, Tycho’s principal assistant, who was working with a model for Mars that predicted with remarkable accuracy its longitudes at oppositions. According to Kepler, this hypothesis “represented all these oppositions within a distance of two minutes in longitude.” The model, however, was unsuccessful in predicting longitudes at other elongations from the Sun, and latitudes even at opposition. Much has been said on how Kepler developed his model after this meeting, arriving finally at the so-called first two laws published in his Astronomia Nova in 1609. By contrast, Longomontanus’ attempt, published as a final model in his Astronomia Danica, has received little scholarly attention. In this paper, I will systematically analyse and explain this model. Even if Longomontanus’ solution is not as elegant as Kepler’s, it deserves scholarly attention, both because it solves the problems posed by the model that he and Tycho were working on when Kepler arrived and because it offers an interesting though heterodox solution that, by contrast, helps to highlight the elegance and simplicity of Kepler’s own solution.

Accurata delineatio motuum stellae Martis: How Accurate Is Kepler’s Pretzel Diagram?

AbstractIn the first chapter of his Astronomia Nova, Kepler introduced a diagram that, he claimed, represents the path of Mars between 1580 and 1596, assuming a resting Earth. In the words of Willi...

Newton’s Parabola Observed from Pappus’ Directrix, Apollonius’ Pedal Curve (Line), Newton’s Evolute, Leibniz’s Subtangent and Subnormal, Castillon’s Cardioid, and Ptolemy’s Circle (Hodograph) (09.02.2019)

Johannes Kepler and Isaac Newton inspired generations of researchers to study properties of elliptic, hyperbolic, and parabolic paths of planets and other astronomical objects orbiting around the Sun. The books of these two Old Masters “Astronomia Nova” and “Principia…” were originally written in the geometrical language. However, the following generations of researchers translated the geometrical language of these Old Masters into the infinitesimal calculus independently discovered by Newton and Leibniz. In our attempt we will try to return back to the original geometrical language and to present several figures with possible hidden properties of parabolic orbits. For the description of events on parabolic orbits we will employ the interplay of the directrix of parabola discovered by Pappus of Alexandria, the pedal curve with the pedal point in the focus discovered by Apollonius of Perga (The Great Geometer), and the focus occupied by our Sun discovered in several stages by Aristarchus, Copernicus, Kepler and Isaac Newton (The Great Mathematician). We will study properties of this PAN Parabola with the aim to extract some hidden parameters behind that visible parabolic orbit in the Aristotelian World. In the Plato’s Realm some curves carrying hidden information might be waiting for our research. One such curve - the evolute of parabola - discovered Newton behind his famous gravitational law. We have used the Castillon’s cardioid as the curve describing the tangent velocity of objects on the parabolic orbit. In the PAN Parabola we have newly used six parameters introduced by Gottfried Wilhelm Leibniz - abscissa, ordinate, length of tangent, subtangent, length of normal, and subnormal. We have obtained formulae both for the tangent and normal velocities for objects on the parabolic orbit. We have also obtained the moment of tangent momentum and the moment of normal momentum. Both moments are constant on the whole parabolic orbit and that is why we should not observe the precession of parabolic orbit. We have discovered the Ptolemy’s Circle with the diameter a (distance between the vertex of parabola and its focus) where we see both the tangent and normal velocities of orbiting objects. In this case the Ptolemy’s Circle plays a role of the hodograph rotating on the parabolic orbit without sliding. In the Plato’s Realm some other curves might be hidden and have been waiting for our future research. Have we found the Arriadne’s Thread leading out of the Labyrinth or are we still lost in the Labyrinth?

Panorama geral da obra astronômica de Kepler

Nesse trabalho apresentamos uma visão panorâmica da obra astronômica de Johannes Kepler. Tratamos, em ordem cronológica, dos quatro principais livros relacionados ao tema por ele escritos, a saber, Mistério Cosmográfico, Astronomia Nova, Harmonia dos Mundos e Epitome de Astronomia Copernicana, a fim de evidenciar as etapas históricas do desenvolvimento do pensamento científico do autor. Procuramos ressaltar a presença nesse pensamento de um elemento filosófico-teológico e de uma concepção física fortemente determinantes, paralelamente a um orientação metodológica já significativamente típica da ciência moderna, então nascente.

The Geometrical Root of the Area-Measure of Time (From Kepler’s Astronomia nova)

In Astronomia nova (1609), Kepler quantified a geometrically exact measure of time. His innovative approach was to consider intervals (discrete but) so small that in his terms the results became exact. He divided the orbit (initially circular) into 360 equal arcs from its centre to establish uniformity of time, and combined these arcs with 360 distances drawn from the Sun, to represent variable increments of time in orbit. Those increments did not accurately measure areas; but subsequently Kepler discovered a sound geometrical reformulation of the increment which produced an area-representation that he was able straightforwardly to sum. (He wrongly described his method as ‘distance-summation’). Then the time in orbit was measured by a sector of the exact ellipse he had concurrently constructed, founded on the work of Archimedes. Essential diagrams, and the notable justification, from Euclid’s Elements, of the reformulation of the increment, have been added on Kepler’s behalf.

Baroque Science by Ofer Gal and Raz Chen-Morris (review)

Reviewed by: Baroque Science by Ofer Gal and Raz Chen-Morris Mary Henninger-Voss (bio) Baroque Science. By Ofer Gal and Raz Chen-Morris. Chicago: University of Chicago Press, 2013. Pp. xiv+ 333. $45. Baroque Science is an ambitious attempt to re-cast our notions of seventeenth-century science entirely. The authors, Ofer Gal and Raz Chen-Morris, specifically eschew the grand narratives of the “scientific revolution.” Instead, they root that revolution’s main protagonists—Kepler, Galileo, Descartes, Newton—within a particular vision of baroque culture, one fraught with paradox and the tensions of the natural/artificial divide. In doing so, they re-inscribe the “revolution” they specifically mention only in passing. Baroque Science is a work of impressive scholarship, enjoyable to read, and an important interpretation for anyone in dialogue with the historiography of seventeenth-century science. The great originality of this book is that Gal and Chen-Morris look at the emergence of an observation-based mathematical natural philosophy with new eyes. They do not fall under the spell of the promoters of this new science, or take as obvious Galileo’s famous dictum that nature is written “in the language of mathematics.” Rather, they unveil seventeenth-century justifications of the new science as “feigning” the pathways between the imputed mathematical structures of nature, new scientific apparatus, and rationality itself. Their fascination is for the ways in which baroque science enforced, rather than uncovered, a mathematical order of physical experience. In Baroque Science, the key to new attitudes toward empirical observation and the mathematization of nature is found in seventeenth-century optics. The authors show that theoretical and practical advances in baroque optics changed what it meant to observe, affected what it meant to imagine, and offered a bridge between the mathematical and physical more immediate and universal than did other “mixed sciences.” Here, both the astronomical revolution and the mechanization of nature are extensions of the new optical sciences and technologies of the century. [End Page 533] In Gal and Chen-Morris’s narrative, Kepler—with his writings on optics and his announcement in Astronomia Nova that mathematicians will invade the territory of physicists—is the central founding father of baroque science. The book covers all the main characters one might find in any standard scientific revolution textbook, but rarely resists overturning conventional interpretations of their work. Gal and Chen-Morris redefine Kepler’s discursive optics against his scholastic forebears and his Aristotelian contemporaries; they re-cast the comet controversy between Galileo and Orazio Grassi as one over optical instrumentation and re-examine Galileo’s distinction between primary and secondary qualities; they invert wisdom on Descartes’ method of doubt; they reexamine the correspondence between Hooke and Newton on the inverse square law as it pertains to commonplaces of optics, and recast Newton as not so much a unifier of seventeenth-century physics as a discursive thinker. In a final chapter, they examine the key role of imagination in the new conceptions of seventeenth-century knowledge, with special attention to the correspondence between Descartes and Princess Elisabeth on the passions. In fact, it is in the imagination, “this most Baroque of the faculties,” that Gal and Chen-Morris claim the real power of the new science lies. As the authors point out, few historians of science have attempted to locate seventeenth-century science on the same canvas with baroque art and culture. Their book is framed by references to art and literature—by Vermeer and Rubens on the art of seeing and Shakespeare on the art of the imagination—and is peppered with the techniques of cultural history. However, these discussions have an illustrative rather than structural role in the argument. Indeed, the interest in capturing motion, in the play of art and nature, in blurring the line between the fantastic and the real, all characterize works of baroque art. Yet we are not really meant to focus on any bleeding between the creative arts and scientific practice, but brought to a better understanding of a broad tapestry that might have grounded the epistemological issues that are the real core of Gal and Chen-Morris’s discourse. This is a rich and ambitious book, but it should not...

Underdetermination and decomposition in Kepler's Astronomia Nova

This paper examines the underdetermination between the Ptolemaic, Copernican, and the Tychonic theories of planetary motions and its attempted resolution by Kepler. I argue that past philosophical analyses of the problem of the planetary motions have not adequately grasped a method through which the underdetermination might have been resolved. This method involves a procedure of what I characterize as decomposition and identification. I show that this procedure is used by Kepler in the first half of the Astronomia Nova, where he ultimately claims to have refuted the Ptolemaic theory, thus partially overcoming the underdetermination. Finally, I compare this method with other views of scientific inference such as bootstrapping.

Kepler = Koestler: On Empathy and Genre in the History of the Sciences

This essay looks at the roles in the history of the sciences of empathetic approaches to past authors. It focuses on the ways in which Arthur Koestler and other historians have engaged with Kepler and his works, and in particular with his Astronomia nova. I argue that here, as with many other historical sources, close attention to the process of composition and conventions of genre is crucial for adequate interpretation.

Book Review: Insights into Astronomia Nova: Kepler: La Physique Celeste, Autour de l'Astronomia Nova (1609)

INSIGHTS INTO ASTRONOMIA NOVA Kepler: La Physique Celeste, Autour de /'Astronomia Nova (1609). Edited by Edouard Mehl with collaboration of Nicolas Roudet (Les Belles Lettres, Paris, 2011). Pp. 358. euro39. ISBN 978-2-251-42046-2.This collection includes thirteen diverse papers, in German, French, and English, presented at a December 2008 Strasbourg conference celebrating (just in the nick of time) the 400th anniversary of Johannes Kepler' s great Astronomia nova of 1 609 . It begins with a poignant appreciation by Nick Jardine of the late Alain Segonds, who among his many other accomplishments wrote knowledgeably and incisively on Kepler.Edouard Mehl's introduction to the volume lays out some of the paradoxes surrounding the Astronomia nova. The first and most personal work of Kepler's maturity, it is frequently obscured by the youthful Mysterium cosmographicum, whose charming foreshadowing of what we now regard as Kepler's most important discoveries suffers hardly at all from its lack of astronomical sophistication. The Mysterium offers students a lot of Kepler per page, without the lengthy, torturous, repetitive, and highly technical obstacles of the Astronomia nova . Yet the Astronomia nova had far more impact on professional astronomers in the period we think of as the Astronomical Revolution.The conference that generated the papers in this volume tried to restore balance to our appreciation of Kepler by focusing on the Astronomia nova, assuredly Kepler's most important contribution to astronomy. The Mysterium had tried to convince its readers that the recently proposed heliocentric arrangement of planets was an attractive idea; the Astronomia nova dragged its readers through a detailed analysis that demolished all the models that astronomers had ever used, only to build a new astronomy from the observations of Tycho Brahe, but also from celestial physics - to use the phrase Kepler defiantly employed in his title and that Mehl has picked up in the title of this volume.Isabelle Pantin's essay looks at the Astronomia nova as a significant moment in the history of the book. Kepler had a precise, and rather demanding, idea of how the pages of his book should appear. Pantin builds much of her argument around the work of James Voelkel. She discusses the material constraints of printing and points out how Kepler exploited these constraints for his own purposes. Under legal pressure from Tycho's son-in-law, Franz Tengnagel, Kepler included an introductory note in which Tengnagel warns readers not to heed Kepler's physical arguments; but Kepler buried the note amidst a sheaf of front matter to such an extent that it effectively lost its intended function as the introduction to the work (p. …

Michael Maestlin's Mystery: Theory Building with Diagrams

BEGINNINGS, QUESTIONS AND APPENDICESIn his 1973 article, Anthony Grafton described the intensive collaborative work undertaken between Johannes Kepler and his former university professor, Michael Maestlin, during the writing of Kepler's Mysterium cosmographicum. Kepler had left the University of Tubingen, Germany, to work as a mathematics teacher in Graz, Austria, where he had immediately begun to conduct his first independent research in astronomy. The book took the form of a collection of works by contributors: besides Kepler's main contribution, it contains the Narrano prima of Rheticus, which consisted of a comprehensive representation of the doctrine of Nicolaus Copernicus, with corrections and additions, followed by an appendix by Maestlin in which the latter presented an advanced version of Copernican planetary theory, the improved parameters of which he had reconstructed from Erasmus Reinhold's Prutenic tables. Grafton writes:For in the Mysterium Kepler began the work which led to his discovery of the true nature of planetary motion; it was there that he first posed the questions to which his three laws were the answers. Yet no one seems to have discussed the treatise which Kepler's teacher, Michael Maestlin, added to the Mysterium when he edited his student's work for publication - namely, Maestlin's appendix On the Dimensions of the Heavenly Circles and Spheres, according to the Prutenic Tables, after the theory of Nicolaus Copernicus.1Clearly, praise is due to Kepler as the author of the Mysterium, but were Maestlin's contributions confined to the appendix, leaving it ambiguous to what extent Maestlin 'edited' Kepler's text? Kepler was able to answer his own questions only in his later works, Astronomia nova and Harmonics. And were the research questions, whose pursuit led later to the so-called 'Kepler's laws', perhaps answered differently in the Mysterium!The intense exchange of letters between Kepler and Maestlin in fact tells us more about Kepler's ignorance of astronomy than of his knowledge, and highlights the indispensable role that Maestlin played in Kepler's research. Maestlin is more than just the author of an appendix: he was responsible for working out the underlying astronomical theory of Kepler's first major work. Maestlin can, therefore, be rightly regarded as the co-author of the Mysterium, a fact that Kepler himself acknowledged in one of his letters to his former teacher.DIMENSIONS OF THE COSMOSThe fact that the Copernican Revolution changed the astronomical and physical conception of the world in many different ways is often overlooked. Displacing the Earth from the centre of the universe was only a minor change; it involved no more than a small geometrical reconfiguration, the consequences of which had been discussed in Antiquity. The consequences, of course, were crucial. Of dynamical importance is the fact that, from a geometrical viewpoint, the Earth rotates around its own axis every 24 hours. Kepler, as well as Maestlin, indicated that this alternative theory of a daily rotating celestial sphere implied that the rotating bodies would have far greater velocities. Grave difficulties then arose when it came to laying the foundations of classical mechanics, which had to describe and explain the movement of heavy bodies on the Earth's rotating surface under the influence of the Earth's heaviness. Copernicus recognized these consequences in De revolutionibus orbium coelestium (1543); however, he stressed that it was up to future researchers to deal with them. Neither Kepler nor Maestlin addressed these issues as such in the Mysterium; they examined the consequences, which were astronomically far more radical.The idea - that one can obtain much more empirical data on the positions of the planets on their way around the Sun from the movement of the Earth and from observers on the Earth - was clear to all mathematical astronomers of the time. It was impossible to deduce the sizes of the planetary orbits on the basis of empirical astronomical observations using the Ptolemaic view of the world, as the projected positions of the planets moving around the Earth (with an observer at the centre of the universe) were independent of the presumed distances of the planets from the Earth. …

„Nicolaus Ficke … der sich mit Physiognomie, Astrologie etc. abgab, übrigens ein schlechter Mann war“

This arcticle summarizes what could be learned from newly discovered documents about the biography of Nicolas von Vicken, first known reader of Kepler’s „Astronomia Nova“ and Kepler’s partner in an exchange of more than a dozen letters over several years. Von Vicken stems from a rich and influential family of merchants in Riga, made noble by the Polish King (who ruled Riga at the time) in 1580. His education included legal studies at the universities of Konigsberg, Leipzig and Rostock, partially overlapping with a stay of ten years at the Polish court. There von Vicken pursued family business but also served in an official court role. In 1600/1 von Vicken switched sides and started to serve the Swedish ruler (and later king) Duke Carl IX, who was at war with Poland to gain control over Riga and Livonia. In 1602 a mission for Sweden to Northern Germany brought him in conflict with Francis II, Duke of Saxe-Lauenburg, who accused von Vicken of withholding money from him, which was supposed to be used for hiring troops. Von Vicken, together with his brother Heinrich, was imprisoned, but could flee. During a mission to Maximilian III, Archduke of Austria, in 1599/1600 von Vicken had been initiated as an alchemist and astrologer through reading the works of Paracelsus and his future stations in life were influenced by this. These include an attempt to get employed at the Saxon court in Dresden, and stays in Wolfenbuttel and Halberstadt, both ruled by Duke Henry Julius of Brunswick-Luneburg. Von Vicken offered various astrological and alchemical services to the Duke and private investors. With one of them he got into a serious conflict over the alleged non-fillment of a contract to produce steel in an alchemical way. During that vonVicken got imprisoned twice, in 1609 and between 1611 and 1614. A subsequent attempt to get employed by Ernst of Schaumburg left us with several letters that detail von Vicken’s alchemical and astrological thinking, two of these are published here in the appendix. Since 1603 von Vicken was also in the service of Emperor Rudolf II; again he got imprisoned in Prague at least once. An interesting speculation based on some hints in the documents is that after reading Paracelsus and during his time in Leipzig von Vicken authored a book on mining, that was later to become part of the works of the alleged medevial monk Basilius Valentinus.

The great Martian catastrophe and how Kepler fixed it

For a few weeks every 32 years, both the Ptolemaic and Copernican predictions for the position of Mars are off by close to 5 degrees—a problem first noticed by Tycho Brahe.

The Allegory of War in Johannes Kepler's Astronomia Nova

AbstractIn the dedicatory letter to Rudolf II that opens his work Astronomia Nova Kepler presents an allegory of war. Taking as its premise that the Habsburg emperor was his specific audience and that the rhetorical guidelines were provided by Melanchthon's Elementorum rhetorices and Crusius' Scholia and Quaestiones, this paper will offer an interpretation of the allegory and discuss the thesis that Kepler's aim, in representing astronomy as war, was to explain his vision of the role of the court astronomer, setting it apart from the traditional roles of the court astrologer and the court artist. This will be explored beginning with an analysis of Kepler's use of rhetoric, based on his training in the methods of Philipp Melanchthon, and will go on to discuss Kepler's allegory in its cultural and political context, and finally examine it from the rhetorical and conceptual points of view.

La recensión de las leyes de Kepler en Inglaterra

El objetivo del presente artículo consiste en la reconstrucción racional que se llevó a cabo durante los años 1609-1630 y 1630-1666, i.e, el año de la publicación de la Astronomia Nova y el año del fallecimiento del astrónomo alemán Johannes Kepler; y el posterior intervalo desde su deceso hasta el conocimiento de dichas leyes del movimiento planetario, por parte del sabio inglés Sir Isaac Newton.

Text, Context, and Conflict in Early Modern CosmologyNicholas Jardine;, Alain Philippe Segonds. La guerre des astronomes: La querelle au sujet de l'origine du système géo‐hèliocentrique à la fin du XVIe siècle. (Science and Humanisme.) 2 volumes. xix + 852 pp. Paris: Les Belles Lettres, 2008. €85 (cloth).

This book is a major contribution to the history of science in the late Renaissance. Thematically, it focuses on cosmology, but because of the importance of the sources here researched and their excellent treatment, it is highly recommended to anyone interested in this key period in the history of ideas. Cosmological theories and disputes belong to the core of the history of philosophy and science in the late Renaissance, particularly in the period from the second half of the sixteenth century—Copernicus’s De revolutionibus appeared in 1543—through the first decade of the seventeenth century—which saw the publication of Kepler’s Astronomia nova in 1609 and Galileo’s Sidereus nuncius in 1610. During this period of expansion and deepening of knowledge, astronomy was the scientific discipline that dominated the scene and provided the background for debates, polemics, quarrels, and, yes, intellectual “wars.” It is important to note that during this period not only were particular technical questions under discussion; in fact, the systema mundi itself was under revision. To a great extent, the “guerre” regarding the correct world system was motivated by the emergence of Copernicanism. While Rheticus’s Narratio prima (1540) gave a first (but incomplete) presentation of the new system, the publication of De revolutionibus three years later hardly escaped misunderstanding and polemics; the furor began, of course, with the foreword by Andreas Osiander (then anonymously published), and the so-called Wittenberg interpretation of Copernicus shortly ensued. Combining philosophical issues from both the Platonic and the Aristotelian tradition, Johannes Kepler first succeeded in