The Composition of Kepler’s Astronomia nova.

315 Pages·2001·10.82 MB·English

by  James R. Voelkel

THE COMPOSITION
OF KEPLER’S
ASTRONOM1A NOVA
James R. Voelkel
X
PRINCETON UNIVERSITY PRESS
PRINCETON AND OXFORD
COPYRIGHT • ¿001 HY WINCETON UNIVERSITY PRESS
PUBLISHED BY PRINCETON UNIVERSITY PRESS, -I I WILLIAM STREET,
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LIBRARl OF CONGRESS CATAIOCINCIN PUBLICATION DATA
VOELKEU JAMES R. (JAMES ROBERT), 19iS2-
THE COMPOSITION OF KEPLER S AHUONOMIA NOVA / JAMES R VOELKEL.
P. CM.
INCLUDES BIRUOGRAPHICA1. REFERENCES AND INDEX.
ISBN 0-691-00738-1 lAODFREE PAPER)
I, KEPLER. JOHANNES. 1571-1630. ASTRONOMIA NOVA. 2. KEPLER'S LAWS. I. TITLE.
QB355.3.V64 2001
$21*. 3—dc21 2001036296
THIS BOOK HAS BEEN COMPOSED IN SABON
PRINTED ON ACID FREE PAPER. -
WWW.PUP.PRINCETON.EDU
PRINTED IN THE UNITED STATES OF AMERICA
1 3 J 7 9 10 8 6 4 2
IN MKMOKIAM AMANTI5SIMAM
Robert T. Voelkel (1933-1987)
Victor E. Thoren (1935-1991)
Richard S. Wcstfall (1924-1996)
Herr, lehre doch mich,
daß ein Ende mit mir haben muß,
und mein Leben ein Ziel hat,
und ich davon muß,
und ich davon muß.
—Brahms, Ein deutsches Requiem
Si CONTENTS x
List of Illustrations ix
Acknowledgments xi
Preface xiii
Introduction 1
PART 1: THE MYSTERIUM COSMOCRAPHICUM 11
CHAPTER ONE
The Copernican Context 13
CHAPTER TWO
The Development of the Mysterium cosmographicum 26
CHAPTER THREE
The Mysterium cosmographicum 46
CHAPTER FOUR
Responses to the Mysterium cosmographicum 60
PART 2: THE ASTRONOMIA NOVA 93
CHAPTER FIVE
Kepler and Tycho 97
CHAPTER SIX
Kepler’s Work after Tycho’s Death 130
CHAPTER SEVEN
The Tychonics 142
CHAPTER EIGHT
David Fabricius 170
CHAPTER NINE
The Rhetorical Character of the Astronomia nora 21
CONCLUSION 247
Notes 25S
Bibliography 295
Index 301
Index of Correspondence 307
* ILLUSTRATIONS *
Figure 1.1: A simple eccentric 15
Figure 1.2: The epicycle and deferent 16
Figure 1.3: A Ptolemaic planetary theory 18
Figure 1.4: A Copernican eccentric epicyclet 19
Plate 2.1: The polyhedral hypothesis from the Mysterium
cosmographicum 35
Figure 2.1: Kepler’s sine model 36
Figure 2.2: The greatest and least distances of a planet’s orb in
Copernican theory 43
Figure 3.1: Kepler’s motive force hypothesis from the Mysterium
cosmographicum, chapter 22 57
Figure 5.1: Kepler’s triangulation from observations of Mars to
the earth’s orbit 105
Figure 5.2: The derivation of the vicarious hypothesis 106
Figure 5.3: Kepler’s use of Martian latitudes 116
Figure 6.1: Another test of the division of Mars’s eccentricity 131
Figure 8.1: The epicyclic distance model 190
Figure 8.2: The conchoid 192
Figure 8.3: The via buccosa 194
Figure 8.4: Comparison of anomalies 197
Xli ACKNOWI EDCMENTS
^ralu. mj to rhe ladies, Carla Chrisficld, Rira Dempsey, and Trudy Kon-
(ofl Mv fellow fellow's, especially David McGee and Noah Efron, also
Jrw t my great thanks. The last srages of work on rhis book were sup­
ported hv a postdoctoral fellowship at rhe Department of History of Sci­
ence. Medicine, and Technology at the Johns Hopkins University.
Finally, to Kathryn Fogle, who continues to be a source of inspiration,
aftccnon, consolation, and exasperation, I give my love.
* PREFACE k
In 1964, Mill early m the computer age, Owen Gingerich set out to
demonstrate the power of the mainframe computer by programming
one to perform Kepler's laborious iterative derivation of the elements
of the vicarious hypothesis.1 Kepler complained he had repeated this te­
dious procedure seventy times. In addition to the great speed with which
the computer sailed through the calculation, Gingerich discovered that
it required the computer the minimum number of iterations—nine—to
converge on the solution. From this, he could conclude only that Kepler’s
huge number of trials were due to his being horribly plagued by numerical
errors.
Gingerich returned to this problem several years later, after he had suc­
ceeded in securing a microfilm of Kepler’s Mars manuscripts, designated
Pulkova XIV, in what was then I.eningrad. He was surprised to discover
that, contrary to the logical systematic approach of the Astronomia nova,
the manuscripts contained a variety of approaches to the orbits of the
earth and Mars almost indiscriminately mixed together. In addition to
reassessing his conclusions regarding Kepler’s large number of trials, he
announced:
Most commentators have assumed, because of Kepler’s sequential and at
times autobiographical style, that Kepler has spared no detail in the chronicle
of his researches. Examination of the manuscript material... shows, on the
contrary, that the book evolved through several stages and represents a much
more coherent plan of organization than a mere serial recital of his investiga­
tions would allow.2
In retrospect, it is clear that some earlier scholars were fully aware that
the Astronomia nova did not represent a straightforward chronicle of
Kepler’s researches. Max Caspar, the last century's leading Kepler scholar,
declared in the 1937 Johannes Kepler Gesammelte Werke edition of the
Astronomia nova, “Regardless of all its wrong paths and detours, the
internal structure of the work which unveils itself upon deeper consider­
ation is dictated by strict logic, and is accomplished clearly in a dramatic
step-by-step process. A prelude and an epilogue in Parts I and V frame
the mam plot in Parts II-IV.’’3 Reading between the lines, we see that
Caspar understood the purpose of Kepler's dramatic narrative. And it is
obvious from Caspar’s account of the progress of Kepler's research from
both the notes to the 1937 edition of the Astronomia nova and his biogra­
phy, Kepler (1948; English ed., 1959), that he drew upon his knowledge
of Kepler’s correspondence and manuscripts to establish a sequence ot
xiv PREFACE
events different from that described in the Astronomia nova However,
the biography was misteriocvb published without notes, and it takes a
vers good familiarity with tht supporting material to recognize how faith-
fulls Caspar captured Kepltt's life Similarly, when editing the 1937 edi-
non of the Asrrouomu notsi, Casp-ir had his eye on this remarkable book.
He knew and described thr surf'omiig manuscripts, including Pulkova
>dY. but the sananee of thr manuscripts from the book, rather than being
addressed as an issue of intrinsic interest, itself became the reason for
ignoring them:
This brief «umnary c* the consents (nf the Kepler Mars manuscriptsj must
suffice at this stage. Most of it. as the summary of contents shosvs, does not
come into queitxm for tb.- publication [of the Astronomia nova]. The mate-
nal that solum; XIV contains is all used up, so to speak. Because in his work,
as was already noted. Kepler himself does not present finished results but
rather the store of the discovery of his results, and in fact on the broadest
hasis. it would not do to draw the work out even further by taking up drafts.
For this reprint only that can be considered which senes for the correction
of the printed text, which perhaps illuminates certain trains of thought from
another side, or which further clears up the srorv of discovery of the present
work.*
Caspar's failure to press the distinction between the Astronomia nova as
history and as argument can be seen to belong to a historiographical tradi­
tion that treated the great book as a singular achievement without regard
to its audience.
The first major biographer of Kepler in English w'as Arthur Koestler,
who drew upon Caspar’s Kepler for his own The Sleepwalkers (1959).
For Koestler, who was wont to treat the genius as psychopath,* Kepler’s
narrative became a valuable example of the irrationality of scientific dis­
covery:
Fortunately, [Kepler) did not cover up his tracks, as Copernicus, Galileo and
Newton did. who confront us with the result of their labours, and keep us
guessing bow rrirv armed at it Ktjlet was incapable of exposing his ideas
methodically, text-book fashion; he had to describe them In the order they
came to him, including all the errors, detours, and the traps into which he
i-- ialien IVe .Vca is written in an unacademic, bubbling ba­
roque style, personal, intimate, and r,tten emavpetating. But it is a unique
revelation of the ways in which the creative mind works.*
A* such a reirljtion, the truth of the account offered in the Astronomia
not j had to he assumed. The fact that the book was written for an audi­
ence and that there was a rhetorical purpose to Kepler’s account would
PREFACE XV
have fitted only awkwardly with Kocstlcr’s assertion that Kepler was “in­
capable" of describing his discoveries methodically.
Elegantly edited excerpts of much of Kepler's correspondence had been
published in Christian Frisch's nineteenth-century edition of Kepler’s
complete works, but the complete correspondence was not published in
the Johannes Kepler Gesammelte Werke until 1959 (although all the cor­
respondence through the composition of the Astronomia nova was pub­
lished by 1954). Alexandre Koyre, in The Astronomical Revolution
(1961; English ed. 1973), integrated correspondence more fully into his
account of Kepler’s discoveries, but more as a matter of expanding on
Kepler’s account in the Astronomia nova than of probing the dissimilari­
ties He also better understood the relation of the book’s structure to
Kepler’s context and the intentionality of its narrative, but he too ulti­
mately used the narrative of the Astronomia nova as a reflection of the
nature of Kepler’s mind rather than his audience:
Whilst he assigned Kepler the task of studying the motion of this planet,
Tycho Brahe, nevertheless, did not give him a free hand. He asked—and he
renewed the request on his deathbed—that the motion should be treated ac­
cording to his (Tycho Brahe’s) principles, and not according to those of
Kepler, or of Copernicus. Kepler fulfilled this request, without conforming to
it exactly.
This partly explains the unusual character and extreme difficulty of the
Astronomia nova, which are responsible for the excepnonal interest o* the
work. Indeed, in this book, which is unique among the great classics of sci­
ence, and in wht.h all astronomical problems are treated three, anJ eten
four, times after the manner of Ptolemy, Tycho Brahe, Copernicus and finally
Kepler himself, Kepler does not rrvtritt himself to setting teeth the result*, is
did Copernicus and Newton: he relates at the time, intennonally as he did in
the Wystrnum cosmogrjfJitcum—the development of his thought, has ef­
forts, and his setbacks, Kepler's mind was so constituted that he was unable
to find the way to truth without fitst having explored all the paths leading
into error—but perhaps the mind of man m general is naturally framed in
this manner [sentence structure src].
Thus again, the structure of the Astronomia nova came to be created
largely as an innate production of Kepler's mind rather than as a purpose­
ful device.
Seminal articles on Kepler’s methodology, such as Curtis Wilson s
“Kepler’s Derivation of the Elliptical Path” (1968) and Erie Alton's
“Kepler’s Second Law of Planetary Motion” (1969), although continuing
to cite letters occasionally, came to tel* even more heavilt on the
Astronomia nova as a true account of Kepler’s work.' In his article
XVI PREFACE
"Keplcrian Planerarş Eggs. Laid and Unlaid” (1974), D. T. Whiteside ac­
knowledged Gingerich's recent announcement of the confused state of
the Kepler Mars manusenpes hut continued to treat the correspondence
similarly.' As in the other artk Its. when correspondence is incorporated at
all.it is to elucidate the methodology of the Astronomia nova. In addition,
much of this work can he faulted for focusing rather too narrowly on
those aspects of Kepler's work that today arc considered to be signifi­
cant—the ellipse and the area law—anJ not. as in Koyre, the idea of a
physical astronomy, or Kepler’s purpose in writing the Astronomia nova.
The hreakthrough for modern historiography of Kepler's work came
with the publication of Bruce Stephenson’s Kepler's Physical Astronomy
(1987). Stephenson rightly understood physical astronomy to be the cen­
tral feature of Kepler s work. He described its development in the Myste-
num irvjmug'jphicutn 11 through the Epitome astronomiae Coper-
ntcanae (I618-1A71, And. although he masterfully described the
argument of the not j, he showed how the ellipse and the
area law were ol significance only to the extent that they supported
Kepltr's physical ideas.
Stephenson was also the first to make an explicit statement of the rhe­
torical character of the Astronomia nova:
This profoundly original work has been portrayed as a straightforsvard ac­
count of converging approximations, and it has been portrayed as an account
ol gropings in the dark. Because of the book's almost confessional style, re­
counting failures and false trails along with successes, it has in most cases
been accepted as a straightforward record of Kepler's work. It is none of
these things. The hook was written and (I shall argue) rewritten carefully, to
persuade a very select audience of trained astronomers that all the planetary
theory they knew was wrong, and that Kepler’s new theory was right. The
whole of the Astronomia nova is one sustained argument, and I shall make
what I believe is the first attempt to trace that argument in derail.'0
However, having raised the issue of the Astronomia nova’s being rhetori­
cal. Stephenson then followed its argument almost exclusively While his
work is an extremely valuable reading of the book, Stephenson failed to
convince many readers of the validity of his claims.11
The evidence that the Astronomia nova was “written and rewritten,”
which Stephenson failed to provide, was swiftly produced in a spectacular
way in William H, Donahue’s “Kepler's Fabricated Figures: Covering up
the Mess in the Astronomia nova” 119X81. Donahue’s intricate analysis
revealed that Kepler had worked over ar least one chapter of the
Astronomia nova so many times prior to publication that it scarcely hung
together, and that ultimately Kepler resorted in calculating positions with
his final finished theory and passing them off as the results of an earlier.