JOHANNES KEPLER NEW ASTRONOMY Translated by WILLIAM H. DONAHUE Cambridge UNIVERSITY PRESS Published by the Press Syndicate of the University of Cambridge The Pitt Building, Trumpington Street. Cambridge CB2 IRP 40 West 20th Street. New York. NY 10011-4211. USA 10 Stamford Road, Oakleigh, Victoria 3166. Australia © Cambridge University Press 1992 First published 1992 Printed in Great Britain at the University Press. Cambridge British Library cataloguing in publication data Kepler, Johannes 1571-1630 Johannes Kepler. New astronomy. 1. Astronomy I. Title 11. Donahue, William H. (William Halsted) 1943- III. New astronomy IV. [Astronomia Nova. English] 520 Library of Congress cataloguing in publication data Kepler. Johannes. 1571-1630. [Astronomia nova. English] New astronomy/Johannes Kepler; translated and edited by William H. Donahue, p. cm. Translation of: Astronomia nova. Includes index. ISBN 0-521-30131-9 (hardback) 1. Astronomy. I. Donahue, William H. II. Title. QB3.K3313 ' 1992 520—dc20 90-25494 CIP ISBN 0 521 30131 9 hardback Contents Foreword by Owen Gingerich XI Acknowledgements XV Translator’s introduction 1 Glossary 20 Original title page 26 Dedicatory letter 30 Epigrams 36 Author's introduction 45 Synoptic table 70 Summaries of the individual chapters 78 Author's index 108 Part I: On the relationships of hypotheses 113 1: On the distinction between the first motion and the second or proper motions; and in the proper motions, between the first and the second inequality 115 2: On the first and simple equivalence, that of the eccentric and the concentric with an epicycle, and their physical causes 122 3: On the equivalence and unanimity of different points of observation, and of quantitatively different hypotheses, for laying out one and the same planetary path 130 4; On the imperfect equivalence between a double epicycle on a concentric, or eccentric-epicycle, and an eccentric with an equant 133 5: The extent to which this arrangement of orbs, using either an equant or second epicycle, while remaining entirely one and the same (or very nearly one and the same), can present different phenomena at one and the same Contents instant, according to whether the planets are observed at mean opposition to the sun. or at apparent opposition 140 6: On the equivalence of the hypotheses of Ptolemy, Copernicus, and Brahe, by which they demonstrated the second inequality of the planets, and how each changes when accommodated to the Sun’s apparent motion instead of its mean motion 155 Part 11: On the star Mars’s first inequality, in imitation of the ancients 181 7: The circumstances under which I happened upon the theory of Mars 183 8: Tycho Brahe’s table of observed and computed oppositions of Mars to the line of the Sun’s mean motion, and an examination thereof 186 9: On referring the ecliptic position to the circle of Mars 192 10; Consideration of the observations themselves, through which Tycho Brahe hunted for the moment of opposition to the mean Sun 198 11; On the diurnal parallax of the star Mars 202 12; Investigation of Mars’s nodes 216 13; Investigation of the inclination of the planes of the ecliptic and of the orbit of Mars 221 14; The planes of the eccentrics do not librate 232 15: Reduction of observed positions at either end of the night to the line of the Sun’s apparent motion 235 16; A method of finding a hypothesis to account for the first inequality 249 17; A preliminary investigation of the motion of the apogee and nodes 271 18; Examination of the twelve acronychal positions using the hypothesis we have found 276 19: A refutation, using acronychal latitudes, of this hypothesis constructed according to the opinion of the authorities and confirmed by all the acronychal positions 281 20: Refutation of the same hypothesis through observations in positions other than acronychal 287 21: Why, and to what extent, may a false hypothesis yield the truth? 294 Part 111: Investigation of the second inequality, that is, of the motions of the sun or earth, or the key to a deeper astronomy, wherein there is much on the physical causes of the motions 303 22: The epicycle, or annual orb, is not equally situated about the point of equality of motion 305 23; From the knowledge of two distances of the Sun from the Earth and of the zodiacal positions and the Sun’s apogee, to find the eccentricity of the Sun’s path (or the Earth’s, for Copernicus) 313 24; A more evident proof that the epicycle or annual orb is eccentric with respect to the point of uniformity 316 Contents vu 25: From three distances of the Sun from the centre of the world, with known zodiacal positions, to find the apogee and eccentricity of the Sun or Earth 322 26: Demonstration from the same observations that the epicycle is eccentric with respect to the point of attachment or axis, and that the annual orb (and so also the Earth’s path around the Sun, or the Sun’s around the Earth) is eccentric with respect to the body of the Sun or Earth, with an eccentricity just half that which Tycho Brahe found through equations of the Sun's motion 325 27: From four other observations of the star Mars outside the acronychal situation but still in the same eccentric position, to demonstrate the eccentricity of the Earth’s orb, with its aphelion and the ratio of the orbs at that place, together with the eccentric position of Mars on the zodiac 341 28: Assuming not only the zodiacal positions of the Sun, but also the Sun’s distances from the Earth found using an eccentricity of 1800; through a number of observations of Mars at the same eccentric position, to see whether by unanimous consent the same distance of Mars from the Sun. and the same eccentric position, are elicited. By which argument it will be confirmed that the solar eccentricity of 1800 is correct, and was properly assumed 345 29: A method of deducing the distances of the Sun and Earth from the known eccentricity 358 30: Table of the distance of the Sun from the Earth and its use 363 31: That the bisection of the Sun’s eccentricity does not perceptibly alter the equations of the Sun set out by Tycho: and concerning four ways of computing them 369 32: The power that moves the planet in a circle diminishes with removal from its source 372 33: The power that moves the planets resides in the body of the Sun 376 34: The Sun is a magnetic body, and rotates in its space 385 35: "Whether the motion from the Sun, like its light, is subject to privation in the planets through occultations 392 36: By what measure the motive power from the Sun is attenuated as it spreads through the world 394 37: How the power moving the moon functions 400 38: Besides the common motive force of the Sun. the planets are endowed with an inherent force [vis insita], and the motion of each of them is compounded of the two causes 404 39: By what path and by what means do the powers seated in the planets need to move them in order to produce a planetary orbit through the aethereal air that is circular, as it is commonly thought to be . 407 40: An imperfect method for computing the equations from the physical hypothesis, which nonetheless suffices for the theory of the Sun or Earth 417 vill Contents Part IV: Investigation of the true measure of the first inequality from physical causes and the author’s own ideas 429 41: A tentative examination of the apsides and eccentricity, and of the ratio of the orbs, using the observations recently employed, made at locations other than opposition with the Sun, with, however, a false assumption 431 42: Through several observations at places other than the acronychal position, with Mars near aphelion, and again several others with Mars near perihelion, to find the exact location of the aphelion, the correction of the mean motion, the true eccentricity, and the ratio of the orbs 435 43: On the defect in the equations accumulated by bisection of the eccentricity and the use of triangular areas, on the supposition that the planet s orbit is perfectly circular 446 44: The path of the planet through the ethereal air is not a circle, not even with respect to the first inequality alone, even if you mentally remove the Brahean and Ptolemaic complex of spirals resulting from the second inequality in those two authors 451 45: On the natural causes of this deflection of the planet from the circle: first opinion examined 455 46: How the line of the planet’s motion can be described from the opinion of Chapter 45, and what its properties are 459 47: An attempt is made to find the quadrature of the oval-shaped plane which Chapter 45 brought forth, and which we have been busying ourselves to describe in Chapter 46; and through the quadrature a method of finding equations 468 48: A method of computing the eccentric equations by a numerical measure and division of the circumference of the ovoid described in Ch. 46 479 49: A critical examination of the previous method for the equations, and a more concise method, based upon the principles constituting the oval in the opinion of Chapter 45 489 50: On six other ways by which an attempt was made to construct the eccentric equations 495 51: Distances of Mars from the Sun are explored and compared, at an equal distance from aphelion on either semicircle; and at the same time the trustworthiness of the vicarious hypothesis is explored 508 52; Demonstration from the observations of Chapter 51 that the planet's eccentric is set up, not about the centre of the Sun’s epicycle, or the point of the Sun’s mean position, but about the actual body of the Sun; and that the line of apsides goes through the latter rather than the former 526 53: Another method of exploring the distances of Mars from the Sun, using several contiguous observations before and after acronychal position: wherein the eccentric positions are also explored at the same time 529 54: A more accurate examination of the ratio of the orbs 538 55: From the observations of Chapters 51 and 53, and the ratio of the orbs of Contents IX Chapter 54, it is demonstrated that the hypothesis seized upon in Chapter 45 is in error, and makes the distances at the middle longitudes shorter than they should be 541 56: Demonstration from the observations already introduced, that the distances of Mars from the Sun are to be chosen as if from the diameter of the epicycle 543 57; By what natural principles the planet may be made to reciprocate as if on the diameter of an epicycle 547 58: In what manner the reciprocation discovered and demonstrated in Chapter 56 may be accepted, and nevertheless an error may be introduced in a wrongheaded application of the reciprocation, whereby the path of the planet is made puff-cheeked 573 59: Demonstration that when Mars reciprocates on the diameter of an epicycle, its orbit becomes a perfect ellipse; and that the area of the circle measures the sum of the distances of points on the circumference of the ellipse 577 60; A method, using this physical—that is, authentic and perfectly true— hypothesis, of constructing the two parts of the equation and the authentic distances, the simultaneous construction of both of which was hitherto impossible using the vicarious hypothesis. An argument using a false hypothesis 592 Part V: On the latitude 603 61; An examination of the position of the nodes 605 62: An examination of the inclination of the planes 607 63; Physical hypothesis of the latitudes 612 64: Examination of the parallax of Mars through the latitudes 620 65: Investigation of the maximum latitude at both conjunction with the Sun, and opposition to it 622 66: The maximum excursions in latitude do not always occur at opposition to the Sun 625 67: From the positions of the nodes and the inclination of the planes of Mars and the ecliptic, it is demonstrated that the eccentricity of Mars takes its origin, not from the point of the Sun's mean position (or. for Brahe, the centre of the Sun's epicycle), but from the very centre of the Sun 629 68; Whether the inclinations of the planes of Mars and the ecliptic are the same in our time and in Ptolemy's. Also, on the latitudes of the ecliptic and on the nonuniform circuit of the nodes 633 69; A consideration of three Ptolemaic observations, and the correction of the mean motion and of the motion of the aphelion and nodes 641 70; Consideration of the remaining two Ptolemaic observations, in order to investigate the latitude and ratio of the orbs at the time of Ptolemy 660 Foreword Owen Gingerich Kepler’s Astronomia nova, together with Copernicus’s De revolutio- nibus and Newton’s Principia, belongs in the select group of the most important books of the Scientific Revolution. 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. The Astronomia nova also contains a powerful, but flawed, statement of the law of areas. But perhaps more important, it is the first published account wherein a scientist documents how he has coped with the multiplicity of imperfect data to forge a theory of surpassing accuracy. For centuries, Kepler and his extraordinary creative genius have been overshadowed by his contemporary, Galileo. Like the Astrono­ mia nova, both the Sidereus nuncius and the Dialogo sopra i due massimi sistemi del mondo played major roles in bringing about the acceptance of the heliocentric world view. Galileo's works are eminently readable and have long been accessible in English trans­ lation. Not so for Kepler’s pioneering study. Unlike Galileo’s Dialogo, which was written in the vernacular and aimed at a general intellectual audience that extended far beyond academia, Kepler’s book is a technical treatise written for the specialist in celestial mechanics. Nevertheless, like Galileo's Dialogo. the Astronomia nova is a polemical work; it is crafted to convince Kepler’s readers that his revolutionary solution to the ancient prob­ lem of planetary motions is the only viable alternative. He apologizes at the outset for being too prolix, but its expansive presentation serves his purpose. In fact, 80% of the book was drafted - including the .XI Foreword introduction, the title page, and dedicatory poem-before he had even arrived at the elliptical shape of the Martian orbit. Kepler touched up the introduction with a marginal reference to the ellipse, and tried, with only partial success, to make the new final chapters seamless with what had gone before. If he stumbled and left out an essential paragraph here or there, as D. T. Whiteside has assured me is so, no one seemed to notice - the rhetoric, planned or unwitting, had the desired effect. When Kepler plaintively sought the reader's pity because one wearying iterative procedure was carried out more than 70 times, Delambre remarked that the complaint was its own reward. Kepler's Astronomia nova is more a book to be mined than to be read. Nevertheless it abounds with Kepler's sly humor. ‘I am going to give you a clown show,’ he says as he explains his fumbling attempt to make an observation at a geometrical configuration of Mars that his mentor, Tycho Brahe, had neglected. Elsewhere he writes, ‘Who would believe it! The hypothesis . . . goes up in smoke.’ Chapter 7, entitled 'How I First Came to Work on Mars,’ contains one of Kepler's most important biographical statements, recounting the events that led to his working in Prague for Tycho. The introduction to Kepler’s treatise, salvaged and reworked from his earlier Mysteriiim cosmographicum where it had been censored out by the Tubingen University Senate, is one of the most interesting defenses of the Copernican theory in the entire seventeenth century. In fact, for over three centuries, the introduction to the Astronomia nova was the only significant piece of Keplerian writing turned into English - it was partially translated by Thomas Salusbury in his Mathematical Collections and Translations of 1661. In those decades when the heliocentric arrangement was still problematic, Kepler's discussion of the relation of Holy Scripture to the Copernican doctrine, found in this introduction, was an influential statement. In its Latin original, it was reprinted over and over with Galileo’s Dialogo. Undoubtedly Galileo profited from it, though it would have been suicidal for the Italian Catholic to have acknowledged such a Lutheran source. As long as Latin remained a working language for astronomers, it was unnecessary to translate the Astronomia nova. On the other hand, after the seventeenth century, astronomers had little reason to read Kepler’s original text except as a historical curiosity. Its style was not easy to grasp - Kepler in a hurry is not a notably clear writer - and his allusions and puns and occasionally idiosyncratic punctua­