Isaac newton scientific method

Free ebooks ==> www.Ebook777.com Isaac N ew ton’s Scientific M ethod Isaac Newton’s Scientific Method examines N ew ton’s argument for universal gravity and its application to cosmology William L Harper shows that N ew ton’s inferences from phenomena realize an ideal o f empirical success that is richer than prediction To achieve this rich sort o f empirical success, a theory must more than predict the phenomena it purports to explain; it must also make those phenomena accurately measure the parameters that explain them Harper shows how N ew ton’s method turns theoretical questions into ones that can be answered empirically by measurement from phenomena W ith this method, propositions inferred from phenomena are provision­ ally accepted as guides to further research Informed by its rich ideal of empirical success, N ew ton’s concept o f scientific progress does not require construing it as progress toward Laplace’s ideal Unlit o f a ‘final theory of everything’ and is not threatened by the classic argument against convergent reaUsm Harper argues that New ton’s method supports the revolutionary theoretical transformation from Newtonian theory to Einstein’s general relativity and continues to illuminate work in gravity and cosmo­ logy today W illiam L H arper is a Member the Rotm an Institute for Philosophy and Professor Emeritus at the University o f Western Ontario www.Ebook777.com Free ebooks ==> www.Ebook777.com Isaac Newton’s Scientific Method Turning Data into Evidence about Gravity and Cosmology W illiam L H arp er OXFORD U N IV E R S IT Y PRESS www.Ebook777.com OXFORD UNIVERSITY PRESS Great Clarendon Street, Oxford, X 6DP, United Kingdom Oxford Univenity Press is a department o f the University o f Oxford It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide Oxford is a registered trade mark o f Oxford University Press in the U K and in certain other countries © William L Harper 2011 The moral rights o f the author have been asserted First published 2011 First published in paperback 2014 Impression: All rights reserved No part o f this publication may be reproduced, stored in a retrieval system, or transmitted, in any fonn or by any means, without the prior pennission in writing o f Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization Enquiries concerning reproduction outside the scope o f the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other fonn and you must impose this same condition on any acquirer Published in the United States o f America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States o f America British Library Cataloguing in Publication Data Data available ISBN -0 -1 -9 -9 (Hbk.) ISBN -0 -1 -8 -8 (Pbk.) Printed and bound by CPI Group (UK) Ltd, Croydon, CRO 4YY Links to third party websites are provided by Oxford in good faith and for information only Oxford disclaims any responsibility for the materials contained in any third party website referenced in this work This book is dedicated to the memory of my father, LEO N A R D A N D R E W H A R P E R and to the memory of my mother, SOPHIA RA TO W SK I H A R P E R PREFACE Vll convergent agreeing measurements o f parameters by diverse phenomena that turned Preface dark energy from a wild hypothesis into an accepted background assumption that guides further empirical research into the large-scale structure and development o f our universe This book is directed to philosophers o f science and students studying it It is also The title o f this book uses the modem term “scientific method” to refer to the directed to physical scientists and their students Practicing scientists may well be able methodology for investigating nature argued for and applied in N ew ton’s argument to profit from this book Almost universally, scientists describe the role o f evidence in for universal gravity I use this modem term, rather than N ew ton’s tema “experimental their science as though it were just an application o f hypothetico-deductive confirma­ philosophy” for his method o f doing natural philosophy, to make salient the main tion This is so even when, as I try to show in the context o f General Relativity and its theme I will be arguing for I will argue that N ew ton’s rich method o f turning data into empirical evidence, the practice o f their science exemplifies N ew ton’s richer and more evidence was central to the transformation o f natural philosophy into natural science effective method o f turning data into evidence This book is also directed to historians and continues to inform the practice o f that science today o f science and their students I hope it can suggest how studying the role o f evidence N ew ton’s argument for universal gravity exemplifies a method that adds features which can significantly enrich the basic hypothetico-deductive (H -D ) model that can usefully contribute toward understanding the history o f radical theory change I have found that attention to the details o f calculations and proofs o f theorems informed much o f philosophy of science in the last century On this familiar H -D offered by N ew ton in support o f his inferences helped me understand their role in model, hypothesized principles are tested by experimental verification o f observable affording empirical support for the propositions inferred as outcomes o f theory-mediated consequences drawn from them Empirical success is limited to accurate prediction o f measurements I have also found attention to historical details about data available to observable phenomena Such success is counted as confirmation taken to legitimate New ton instructive I have found historical episodes, such as R om er’s use o f eclipses of increases in probability W e shall see that N ew ton’s inferences from phenomena realize a moon o f Jupiter’s to measure a finite speed o f light and the observation enterprise an ideal o f empirical success that is richer than prediction To achieve this richer sort o f Pound and Bradley initiated by New ton to obtain more precise measurements o f the of empirical success a theory needs, not only to accurately predict the phenomena orbits ofjupiter’s moons, both informative and fascinating I have, however, attempted it purports to explain, but also, to have those phenomena accurately measure the to relegate such details o f proofs, calculations, and specialized historical background to parameters which explain them N ew ton’s method aims to turn theoretical questions appendixes so that readers who not share my fascination for such details can follow into ones which can be empirically answered by measurement from phenomena the main argument without getting bogged down Propositions inferred from phenomena are provisionally accepted as guides to further I have, however, included a fairly detailed account o f data cited by Newton in support research Newton employs theory-mediated measurements to turn data into far more o f his phenomena in chapter and o f his argument in chapters through Readers informative evidence than can be achieved by hypothetico-deductive confirmation interested in N ew ton’s main lessons on scientific method can focus on chapter 1, alone section IV of chapter 3, sections II.2—IV of chapter 4, and chapters 7, 9, and 10 They On his method, deviations from the model developed so far count as new theory- would also profit from the specifically labeled sections on method in the other chapters, mediated phenomena to be exploited as carrying information to aid in developing a without costing them very much extra time and effort to master details The details more accurate successor This methodology, guided by its richer ideal o f empirical offered in the other sections o f these chapters, and the other chapters, strongly success, supports a conception o f scientific progress that does not require construing it reinforce these lessons on method and their historical context I hope they will be of as progress toward Laplace’s ideal limit o f a final theory o f everything This method­ considerable interest to the growing number o f very good philosophers of science, who ology o f progress through successively more accurate revisions is not threatened by are now taking a great interest in the details o f N ew ton’s work on gravity and method Larry Laudan’s argument against convergent realism W e shall see that, contrary to a and in how these details can illuminate scientific method today famous quotation from Thomas Kuhn, N ew ton ’s method endorses the radical In my effort to show how N ew ton’s argument can illuminate scientific method theoretical transformation from his theory to Einstein’s W e shall also see that this today, I have appealed to modem least-squares assessments o f estimates o f parameter rich empirical method o f N ew ton ’s is strikingly realized in the development and values I argue that N ew ton’s moon-test inference holds up by our standards today application o f testing frameworks for relativistic theories o f gravity Finally, we shall Student’s t-95% confidence parameter estimates illustrate the basic agreement achieved see that this rich methodology o f N ew ton’s appears to be at work in cosmology in the moon-test in N ew ton’s initial version, and in the different published editions, of today It appears that it was realizations o f N ew ton’s ideal o f empirical success as his Principia Gauss’s least-squares method o f combining estimates o f differing accuracy affords insight into how the agreement o f the cruder moon-test estimates o f the Vlll PREFACE Free ebooks ==> www.Ebook777.com Strength o f terrestrial gravity adds empirical support to the much sharper estimates from pendulums The cruder agreeing moon-test estimates are irrelevant to small differences from the pendulum estimates, but they afford additional empirical support for resisting Some Acknowledgements large differences This increased resistance to large differences - an increased resiliency - is an important empirical advantage afforded by agreeing measurements from diverse phenomena I want to thank my wife, Susan Pepper W ithout her generous support I would not have been able to finish this long project M y daughter Kathryn May Harper and my sister Vicki Lynn Harper have also provided much appreciated support and encouragement A great many people have contributed to assist my efforts over the more than twenty years I have worked on this project The historian o f science Curtis Wilson and the philosophers o f science Howard Stein and George Smith have been my chief role models and have offered very much appreciated critical comments on early versions o f several chapters I also thank George for his permission to use his very informative phrase “Turning data into evidence” in the title o f this book M y colleague W ayne Myrvold has been responsible for a great many improve­ ments, as his very insightful criticisms over quite a few years have led me to deeper understanding o f important issues I have tried to come to grips with This book is part o f a project supported by a joint research grant awarded to W ayne and me Gordon Fleming and Abner Shimony, both o f whom are physicists as well as philosophers o f science, have offered very much appreciated encouragement and guidance I especially thank Gordon for his careful reading and critical comments on chapters 1, 9, and 10 Gordon’s emphasis on the value o f diagrams was reinforced by my reading o f Simon Singh’s book Big Bang: The Origin o f the Universe as a role model suggested by my lawyer Anthony H Litde I also want to thank North Davis, a physician and a fellow mountain hiker, who kindly read and sent comments on an early version o f my introductory chapter My colleagues Robert Batterman, Chris Smeenk, John Nicholas, and Robert DiSalle have also contributed much appreciated critical comments and important guidance The historical background section in chapter benefited from very much appreciated help by the late James MacLachlan The comments by referees and by Eric Schliesser have led to substantial improvements, for which I thank them This work on N ew ton’s scientific method has benefited from students and colleagues who participated in my graduate seminars on Newton and method These included over the years four two-term interdiscipUnary seminars on gravitation in Newton and Einstein These were jointly listed in and taught by faculty from Physics and Astronomy, Applied Mathematics and Philosophy I want especially to thank Shree R am Valluri, from Applied Mathematics, who convinced me to help initiate these valuable learning experiences He has also helped me understand details o f many o f the calculations and is the developer o f the extension o f New ton’s precession theorem to eccentric orbits I also want to thank R ob Corless, another participant in the gravitation seminars from Applied Mathematics, for checking derivations www.Ebook777.com X SOME AC K N O W L E D G E M E N T S M y treatment o f N ew ton’s method at work in cosmology today owes much to Dylan Gault who, in December 2009, completed his thesis on cosmology as a case study o f scientific method Wayne Myrvold and I were co-supervisors Contents This book has also benefited from questions and comments raised at the many talks I have given over the years on N ew ton’s method I want, particularly, to thank Kent Staley, who presented very insightful comments on my paper at the Henle conference in March 2010 An Introduction to N ew ton’s Scientific Method N ew ton’s Phenomena 50 converted my WordPerfect documents to W ord, acquired permissions, and put the Inferences from Phenomena (Propositions and Book 3) 84 whole thing together W ithout her talent, dedication, effort, and good judgment Unification and the M oon-Test (Propositions and Book 3) I want to thank my research assistant Soumi Ghosh She developed diagrams, this project might never have resulted in this book In the last drive to format the 160 Christiaan Huygens: A Great Natural Philosopher W ho Measured manuscript she was ably assisted by Emerson Doyle Their work was supported by Gravity and an Illuminating Foil for Newton on Method 194 the joint research grant awarded to Wayne Myrvold and me I am grateful to Wayne and the Social Sciences and Humanities Research Council o f Canada for this support Soumi’s work reading page proofs was supported by the Rotm an Institute o f Philoso­ phy at the University o f Western Ontario I am very grateful for their funding support Unification and the M oon-Test: Critical Assessment 220 Generalization by Induction (Propositions and Book 3) 257 Gravity as a Universal Force of Interaction and their much appreciated support in work space, resources help and encouragement in my project for engaging the role o f evidence in science I want to thank Peter M omtchdoff for encouraging me to publish with Oxford (Propositions -1 Book 3) Beyond Hypotheses: N ew ton’s Methodology vs Hypothetico-Deductive M ethodology University Press, selecting the excellent initial readers, guiding me through the initial revisions, and convincing me to turn endnotes into footnotes Daniel Bourner, the 10 N ew ton’s Methodology and the Practice of Science production editor, kept us on track and helped to resolve difficult problems about notation Eleanor Collins was responsible for the excellent cover design Sarah Cheeseman skillfully guided the transformation to page proofs, including the transformation of my long endnotes into footnotes Soumi Ghosh helped me proofread and assemble the corrections for the page proofs Erik Curiel was an excellent, careful proofreader for chapters -3 , 6, and Howard Emmens was the expert proofreader who used all the queries and my responses to produce the final version for printing I am very grageful for all their efforts This book is much better than it would have been without all their help 290 338 372 References 397 Acknowledgements fo r use o f Images and Text 411 Index 415 DETAILED C O N T E N T S Detailed Contents III The orbits o f the primary planets encompass the sun 57 IV Kepler’s Harmonic Rule 60 V The Area Rule for the primary planets 62 VI The moon Chapter 1: An Introduction to N ew to n ’s Scientific M ethod I Some historical background Astronomy Mechanics and physical causes II N ew ton’s Principia: theoretical concepts N ew to n ’s background framework N ew to n ’s theoretical concept o f a centripetal force III N ew ton’s classic inferences from phenomena Jupiter’s moons 15 20 21 22 23 Primary planets 24 26 Inverse-square acceleration fields 28 IV Unification and the moon T he m oon ’s orbit 66 Appendix 2: N ew ton’s satellite data 69 The table for Jupiter’s moons 69 Pound’s measurements 71 Saturn’s moons 74 Appendix 3: Empirically determining periods, apsides, mean-distances, and Area Rule motion in Kepler’s ellipse 76 78 Kepler’s equation and Area R u le motion in Kepler’s ellipse 81 C hapter 3: Inferences from Phenom ena (Propositions and B ook 3) I N ew ton’s definitions Gravitation toward the earth 32 The m oon-test 33 N ew ton ’s definitions o f centripetal force Empirical success 34 Proposition and R u le Proposition and R u le II N ew ton’s scholium to the definitions and his Laws o f Motion 35 The scholium on time, space, place, and motion 36 The Laws o f M otion and their corollaries 37 N ew ton ’s scholium to the Laws (empirical support offered) 84 86 86 88 95 95 99 103 Jupiter’s moons and Saturn’s moons 109 109 41 Primary planets 116 Resolving the two chief world systems problem 41 Measurements supporting inverse-square centripetal acceleration fields 123 Lessons from Newton on scientific method 42 42 VI Gravity as a universal force o f pair-wise interaction Applying Law 40 40 Universal force o f interaction M ore informative than H -D method III The arguments for propositions and book IV Lessons for philosophy o f science D uhem on N ew to n ’s inferences N ew to n ’s hypotheses non Jingo 44 Objections by D uhem and some philosophers A methodology o f seeking successively m ore accurate approximations 45 D uhem and H -D confirmation A contrast with Laplace 47 Glym our’s bootstrap confirmation Security through strength; acceptance vs assigning high probability 48 N ew ton ’s inferences vs Glyniour’s bootstrap confirmations: laws, 50 Inverse-square acceleration fields and gravity as a universal force o f pair-wise not just material conditionals Chapter 2: N ew ton ’s Phenom ena R o m e r on the speed o f light N ew to n ’s phenom enon Satellites of Saturn 126 126 127 130 132 135 51 Kepler’s elliptical orbits 137 139 51 53 N ew ton ’s ideal o f empirical success 142 interaction between bodies I The moons o f Jupiter II 76 Determining apsides and mean-distances Determining periods 31 31 64 Appendix 1: R om er on the speed o f light: details and responses Basics V Generalization by induction: Newton on method VII Xlll 55 Appendix 1: Pendulum calculations 143 XIV DETAILED C O N T E N T S DETAILED C O N T E N T S Appendix 2: N ew ton’s proofs o f propositions 1—4 book 146 Proposition 146 Proposition 149 Chapter 6: Unification and the M oon -T est: Critical Assessment I Exaggerated precision Proposition 150 Proposition 152 220 221 Assessing precision and support for N ew ton ’s precession correction factor 221 Westfall on fudge factors in the m oon-test 223 156 The m oon-test in N ew ton ’s original version o f book 229 N ew ton ’s basic precession theorem 156 The m oon-test in the first and second editions 232 A Derivation extending it to include orbits o f large eccentricity 157 The correction to Tycho 235 Standards o f N ew ton ’s day 237 Appendix 3: N ew ton’s precession theorem and eccentric orbits Chapter 4: Unification and the M oon-T est (Propositions and B ook 3) 160 II Empirical success and the m oon-test argument I The argument for proposition Directed toward the earth 161 ' 161 Inverse-square 162 II Proposition and the moon-test 165 The m oon-test The tw o-body correction III The scholium to proposition 238 N ew to n ’s inference does not depend on his dubious correction factor, nor upon his selection o f which estimates to cite 238 Can the lunar distance calculated from Huygens’s measurement o f g be counted as accurate? 239 W h at about the distance o f corollary proposition 37? 241 170 Empirical success and resihence 245 174 Concluding remarks 247 165 Regulae Philosophandi: R u le and Rule 176 Octants and N ew to n ’s variational orbit 248 248 Appendix: The moon-test o f corollary proposition 37 book Treating the H arm onic R ule as a law 176 The scholium m oon-test argument 178 Oblate earth 249 179 T w o-b ody correction 250 T he one minutes’ fall at orbit The precession correction 251 252 The one second’s fall at latitude 45° 252 The correction for Paris (latitude ° ') 253 186 Effects o f rotation 254 N ew ton ’s treatment o f the motion o f the m oon 186 Aoki on the m oon-test o f corollary 254 Clairaut, d’Alembert, and Euler 191 N ew ton ’s definitions o f centripetal force IV Empirical success and the moon-test 181 The m oon-test as an agreeing measurement Resiliency V The lunar precession problem 181 184 Chapter : Generalization hy Induction (Propositions and B ook 3) Chapter 5: Christiaan Huygens: A Great Natural Philosopher W h o Measured Gravity and an Illuminating Foil for N ew ton on M ethod I Huygens on gravity and N ew ton’s inferences II XV 194 I Proposition The basic argument 257 257 258 195 Regulae Philosophandi: R ule 260 Gravity as mutual interaction 261 Huygens’s measurement 195 Gravity varies with latitude 200 The shape o f the earth 203 Huygens’s hypothesis as to the cause o f gravity 206 Huygens on N ew ton ’s inference to inverse-square gravity 212 Corollaries o f proposition 265 265 271 Regulae Philosophandi: R ule 3: N ew to n ’s discussion 274 II Proposition 6: proportionality to mass from agreeing measurements The basic argument Lessons on scientific method 214 Rule 3: N ew to n ’s explicit application to gravity Empirical success and resilience 215 M ore bounds from phenomena Extending inverse-square gravity 217 Bounds from un-polarized orbits 277 280 282 Concluding remark 283 XVI DETAILED C O N T E N T S DETAILED C O N T E N T S XVll 285 II Beyond hypotheses? N ordtvedt’s calculation 285 The challenge 346 347 Chandrasekhar on N ew to n ’s calculation 287 Newton’s initial response 348 Another proposal for N ew ton ’s calculation 288 Appendix; Polarized satellite orbits as measures o f A h C h a p te rs: Gravity as a Universal Force o f Interaction (Propositions -1 B ook 3) I Proposition 290 291 The argument for proposition 293 Corollaries to proposition 294 From inverse-square fields o f acceleration toward planets to gravity as a universal force o f pair-wise attraction between bodies II The attractive forces o f spherical bodies applied to planets Proposition book Measuring surface gravities: corollary o f proposition 300 Measuring relative masses: corollary o f proposition 303 The system o f the world Take stable Keplerian orbits as a first approximation 361 361 Acceptance and accumulating support An ideal of empirical success, not a necessary criterion for acceptance 364 Chapter 10: N ew to n ’s M ethodology and the Practice o f Science 372 368 I Empirical success, theory acceptance, and empirical support Newton’s scientific method adds features that significantly enrich the basic hypothetico-deductive model of scientific method 373 373 Accumulating support 376 II M ercury’s perihelion The classical Mercury perihelion problem Einstein’s solution as support for General Relativity: an answer to Kuhn’s 378 378 challenge on criteria across revolutions The Dicke-Goldenberg challenge to General Relativity and Shapiro’s radar 380 318 time delay measurement Some conclusions from the Mercury perihelion problem 382 324 Inverse-square attraction to particles from inverse-square attraction 328 328 Extending N ew ton ’s p ro o f o f proposition 71 to support measuring inverse-square attraction toward particles from inverse-square attraction toward a spherical shell made o f those attracting particles IV Beyond hypotheses: yes Empirical success and Rule 4: Newton’s second thought? 305 312 318 N ew to n ’s proofs o f propositions 70 and 71 book 360 375 Appendix 2: The attractive forces o f spherical bodies Appendix 3; Propositions 70 and 71 book Is Newton’s application of Law a deduction from the phenomena? Successive approximations 315 to spheres using an integral given by Chandrasekhar 355 358 304 Appendix 1: N ew ton’s proof o f proposition 69 book 1 Basic propositions from book 355 Combining acceleration fields Law and Law for a sun-Jupiter system: H-D method is not enough 296 299 299 III The two chief world systems problem III Gravitation as attraction between solar system bodies? 384 III Our Newton vs Laplace’s Newton 385 IV Approximations and Laudan’s confutation o f convergent realism 389 V Postscript: measurement and evidence - N ew ton’s method at work 331 in cosmology today 394 Appendix 4; Measuring planetary properties from orbits; details o f N ew ton’s calculations 333 References Measuring surface gravities; corollary proposition 333 Acknowledgements fo r use o f Images and Text 411 Measuring planetary masses and densities: corollaries and o f proposition 335 Index 415 Chapter 9: Beyond Hypotheses: N ew ton ’s M ethodology vs H ypothetico-D eductive M ethodology I Newton on method 338 339 N ew ton ’s scholium to proposition 69 book 339 The hypotheses non Jingo paragraph 343 397 Free ebooks ==> www.Ebook777.com Abbreviations Corresp N ew ton, I (1959—1977) Tire Gorrespondence o f Isaac Neivton Turnbull, H W (ed., vols I—III), Scott, J.F (ed., vol IV), Hall, A R and Tilling, L (eds., vols V—VII) Cambridge; Cambridge University Press C&W An Introduction to Newton’s Scientific Method Cohen, I.B and W hitm an, A (trans.) (1999) Isaac Newton, The Principia, Mathematical Principles o f Natural Philosophy: A N ew Translation Los Angeles: University o f California Press ESA A Seidelmann, P.K (ed.) (1992) Explanatory Supplement to the Astronomical Almanac Mill Valley: University Science Books GHA 2^ GH A 2B Taton, R and Wilson, C (1989) The General History o f Astronomy, vol 2, our present work sets forth the mathematical principles o f natural philosophy Planetary Astronomy from the Renaissance to the R ise o f Astrophysics, Part A : Tycho For the basic problem [lit whole difficulty] o f philosophy seems to be to discover Brahe to Newton Cambridge: Cambridge University Press the forces o f nature from the phenom ena o f motions and then to demonstrate the Taton, R and Wilson, C (1995) Tire General History o f Astronomy, vol 2, Planetary Astronomy from the Renaissance to the Rise o f Astrophysics, Part B : The Eighteenth and Nineteenth Centuries Cambridge: Cambridge University Press other phenom ena from these forces (C & W , )' O ur epigram is from N ew ton’s preface to his masterpiece, Philosophiae Naturalis Principia Mathematica {Mathematical Principles o f Natural Philosophy) It was published in Huygens Huygens, C Discourse on the Cause o f Gravity Bailey, K (trans.), Bailey, K and 1687 when he was 44 years old In it he argued for universal gravity W e still count 1690 Smith, G E (ann.), manuscript gravity as one o f the four fundamental forces o f nature The publication o f N ew ton’s Kepler 1992 Math Papers Kepler, J (1992) N ew Astronomy Donahue, W H (trans.) Cambridge: Principia was pivotal in the transformation o f natural philosophy into natural science as Cambridge University Press we know it today Whiteside, D T (ed.) (1967—81) The Mathematical Papers o f Isaac Newton, vols Cambridge: Cambridge University Press New ton used some phenomena o f orbital motions o f planets and satellites as a basis from which to argue for his theory W e shall see that these phenomena are patterns exhibited in sets o f data New ton cites in their support W e shall seek to understand the method by which he transformed these data into evidence for universal gravity This will mostly be an effort to explicate the first part of the endeavor described in our epigram from N ew ton’s preface, to discover the forces o f nature from the phenom ena o f motions New ton went on to apply his theory to refine our knowledge o f the motions o f solar system bodies and the gravitational interactions on which they depend The second part o f the endeavor described in our epigram, and then to demonstrate the other phenom ena from these forces, is exemplified in N ew ton’s applications of universal gravity to demonstrate the basic solar system phenomena o f elliptical orbits and some o f their corrections for ’ This passage is from New ton’s preface to the first edition o f his Principia Quotations from the Principia are from the translation by I.B Cohen and Anne Whitman: the citation (C&W , 382) is to that translation, Cohen and Whitman 1999 www.Ebook777.com 396 n e w t o n ’s m e t h o d o l o g y a n d t h e p r a c t i c e o f s c i e n c e quantitative Just as the earlier measurements had indicated less precisely, the W M A P results confirmed that the universe has the large-scale geometry o f flat space (Kirshner 0 , -5 ) Even though the C M B measurements don’t detect cosmic acceleration directly, as the supernova References measurements do, taken together, they point with good precision to a universe with both dark matter and dark energy Things were fitting together - and the better you measured them the better they fit Quantitative agreement is the ring o f tm th This is the reason why, by the autumn o f 20 , our colloquium speaker didn’t bother to make the case that a A-dom inated universe was the right picture (Kirshner 0 , 265) Airy, G B ([1834], 1969) Gravitation: An Elementary Explanation o f the Principal Perturbations in the Solar System Ann Arbor: N E O Press Aiton, E J (1954) Galileo’s theory o f the tides Annals o f Science, 10: 4 - - (1955a) T h e contributions o f N ew ton, Bernoulli and Euler to the theory o f the tides Kirshner’s remarks strongly suggest that N ew ton’s methodology continues to guide Annals o f Science, 11: - cosmology today It appears that it was the striking realizations o f N ew ton’s ideal of - (1955b) Descartes’s theory o f the tides Annals of Science, 11: 3 -4 empirical success as convergent accurate measurements o f parameters by diverse - (1972) The Vortex Theory o f Planetary Motions N ew York: American Elsevier phenomena that turned dark energy from a wild hypothesis into an accepted back­ - (1989a) Polygons and parabolas: Some problems concerning the dynamics o f planetary ground assumption that guides further empirical research into the large-scale structure and development o f our universe - (1989b) The Cartesian vortex theory GHA 2A, -2 These developments illustrate a feature o f agreeing measurements from diverse phenomena that is especially important for turning data into evidence T o the extent that the sources o f potential systematic error o f the different measurements can be regarded as independent, the agreement o f the measurements contributes additional support for counting them as accurate rather than as mere artifacts o f systematic error.^ orbits Centaurus, 31: - - (1995) The vortex theory in competition with Newtonian celestial dynamics GEL4 2B, -2 Alexander, H G (ed.) (1956) The Leihniz-Clark Correspondence Manchester; Manchester University Press Aoki, S (1992) The m oon-test in N ew ton ’s Principia: Accuracy o f inverse-square law o f universal gravitation Archive for History o f Exact Sciences, 44: -9 Battemran, R (2002) The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction, and Emergence N ew Y ork: O xford University Press - (2005) Critical phenomena and breaking drops: Infinite idealizations in physics Studies in History and Philosophy o f Modern Physics, 36(2); 2 - 4 The systematic errors of the supernova measurements and the systematic errors of the Cosmic Microwave Background measurements can be very much expected to be independent This is compeUingly argued in a dissertation which Dylan Gault defended in December 2009 See Gault (2009) Wayne Myrvold and I were co-supervisors Bayes, T (unpublished) Letter to Joh n Canton Canton Papers, Correspondence, vol , folio London: R oyal Society Library Belkind, O (2007) N ew to n ’s conceptual argument for absolute space International Studies in the Philosophy o f Science, (3 ); - Berlinski, D (2000) Newton’s Gift: How Sir Isaac Newton Unlocked the System o f the World N ew Y o rk : Simon & Schuster Bertoloni Meli, D (1991) Public claims, private worries; N ew ton ’s Principia and Leibniz’s theory o f planetary m otion Studies in History and Philosophy o f Science, 22: - - (1993) Equivalence and Priority: Newton versus Leibniz Oxford: Clarendon Press Biener, Z and Smeenk, C (forthcoming) C otes’ queries: M atter and method in N ew ton ’s Principia In: Janiak, A and Schliesser, E (eds.) Interpreting Newton: Critical Essays Cambridge: Cambridge University Press Blackwell, R J (trans.) (1977) Christiaan Huygens: The motion o f colliding bodies Isis, 68 (244): -9 - (trans.) (1986) Christiaan Huygens’s The Pendulum Clock or Geometrical Demonstration, Concerning the Motion o f Pendula as Applied to Clocks Ames: The Iowa State University Press Bos, H J.M (1972) Huygens, Christiaan In: GiUispie, C C (ed in chief), Dictionary of Scientific Biography: Volume VI N ew York: Charles Scribner’s Sons, -6 Boulos, P (1999) From natural philosophy to natural science: Empirical success and N ew to n ’s legacy Ph.D dissertation University o f W estern Ontario 398 REFERENCES REFERENCES Bow ditch, N (trans.) 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(1970) Historical and Philosophical Perspectives of Science Minneapolis; University o f Minnesota Press Sussman, G.J and W isdom, J (1992) Chaotic evolution o f the solar system Science, 257: -6 SwercHow, N M and Neugebauer, O (1984) Mathematical Astronomy in Copemims’s De Revolutionibus New York: Spiinger-Verlag Taton, R and Wilson, C (1989) The General History o f Astronomy, vol 2, Planetary Astronomy from the Renaissance to the Rise o f Astrophysics, Part A: Tycho Brahe to Newton Cambridge; Cambridge University Press {GHA 2A) - a n d -(1995) The General History o f Astronomy, vol 2, Planetary Astronomy from the Renaissance to the Rise of Astrophysics, Part B: The Eighteenth and Nineteenth Centuries Cam ­ bridge: Cambridge University Press {GHA 2B) REFERENCES 409 - (1995) Measuring solar parallax; The Venus transits o f 1761 and 1769 and their nineteenthcentury sequels GHA 2B, -6 Waff, C B (1976) Universal gravitation and the motion o f the m oon’s apogee: The establishment and reception o f N ew ton’s inverse-square law Ph.D dissertation Johns Hopkins University Available from Ann Arbor: University Microfilms - (1995a) Clairaut and the m otion o f the lunar apse: The inverse-square law undergoes a test GHA 2B, - (1995b) Predicting the mid-eighteenth-century return o f Halley’s Com et GHA 2B, -8 W eingartner, P , Schurz, G , and D o m , G (eds.) (1998) The Role o f Pragmatics in Contemporary Philosophy Vienna: H older-Pinchler-Tem psky, -8 Westfall, R S (1973) N ew ton and the fudge factor Science, 9(4057): - - (1980) Never at Rest: A Biography of Isaac Newton Cambridge; Cambridge University Press W hew ell, W (1860) On the Philosophy o f Discovery Cambridge; Cambridge University Press Whiteside, D T (ed.) (1 -8 ) The Mathematical Papers of Isaac Newton, vols Cambridge: Cambridge University Press (Math Papers) - (1976) N ew to n ’s lunar theory; From high hope to disenchantment Vistas in Astronomy, 19; - W ill, C M (1971) Theoretical frameworks for testing relativistic gravity.II Parametrized post- Theerm an, P and Seef, A F (eds.) (1993) Action and Reaction: Proceedings of a Symposium to Newtonian hydrodynamics and the N ordtvedt effect Astrophysical Journal 163: 1 - Commemorate the Tercentenary o f Newton ’s Principia Newark: University o f Delaware Press Thoren, V E (1990) The Lord o f Uraniborg: A Biography of Tycho Brahe Cambridge; Cambridge - (1986) Was Einstein Right? Putting General Relativity to the Test N ew Y ork: Basic Books University Press Todhunter, I ([1873], 1962) A History o f the Mathematical Tlieories o f Attraction and the Figure o f the Earth N ew Y ork: D over Publications, Inc Truesdell, C (1970) Reactions o f late Baroque mechanics to success, conjecture, error and failure in N ew to n ’s Principia In; Palter, R (ed.) The Annus Mirabilis o f Sir Isaac Newton 1666-1966 Cambridge, Mass.: The M IT Press, -2 Valluri, S R , Harper, W L and Biggs, R (1999) N ew to n ’s precession theorem , eccentric orbits and M ercury’s orbit In: Piran, T (ed.), Ruffmi, R (series ed.), Proceedings o f the Eighth Marcel Grossmann Meeting on General Relativity, Part A Singapore: W orld Scientific Publishing Co., -8 - Wilson, C , and Harper, W L (1997) N ew ton ’s apsidal precession theorem and eccentric orbits Journal for the History o f Astronomy, 28: -2 van Fraassen, B C (1980) The Scientific Image O xford: O xford University Press - (1983) Glymour on evidence and explanation In: Earman, J (ed.) Testing Scientifk Theories Minneapolis: University o f Minnesota Press, -7 - (1985) Empiricism in the philosophy o f science In: Churchland, P.M and H ooker, C.A (eds.) Images o f Science Chicago; University o f Chicago Press, -3 - (1989) Laws and Symmetry O xford; Clarendon Press - (2002) The Empirical Stance N ew Haven: Yale University Press - (2009) The perils o f Perrin, in the hands o f philosophers Philosophical Studies, 143: -2 Van Helden, A (1985) Measuring The Universe: Cosmic Dimensions from Aristarchus to Halley Chicago: University o f Chicago Press - (trans.) (1989) Sidereus Nuncius or The Siderial Messenger: Galileo Galilei Chicago: University o f Chicago Press - (1993) Theory and Experiment in Gravitational Physics, 2nd revised edn Cambridge: C am ­ bridge University Press (2006) The confrontation between general relativity and experiment Living Rev Relativi­ ty, 9, O nhne Article: cited 0 , h tt p ;//w w w livingreview s.org/lrr-2006-3 - and N ordtvedt, K (1972) Conservation laws and preferred frames in relativistic gravity I Preferred-frame theories and an extended P P N formalism Astrophysical Journal 177: 7 —74 W ilson, C.A (1970) From Kepler’s laws, so called, to universal gravitation: Empirical factors Archive for History of Exact Sciences, 6(2): 1 -1 - (1980) Perturbations and solar tables from Lacaille to Delambre; The rapprochement o f observation and theory, part I Archivefor History of Exact Sciences, 22(3): 54—188 - (1985) The great inequality o f Jupiter and Saturn from Kepler to Laplace Archive for History of Exact Sciences, 3 (1 -3 ): -2 (1987) D ’Alembert versus Euler on the precession o f the equinoxes and the mechanics o f rigid bodies Archivefor History o f Exact Sciences, 37{3): 233—73 - (1989a) Astronomy from Kepler to Newton: Historical Studies London: Variorum Reprints - (1989b) T he N ewtonian achievement in astronomy GITA 2A, 3 -7 (1993) Clairaut’s calculation o f the eighteenth-century return o f Halley’s Com et Journal for the History of Astronomy, 24: -1 (1995) The precession o f the equinoxes from N ew ton to d’Alembert and Euler GHA 2B, -5 -(1999) Redoing N ew ton ’s experiment for establishing the proportionality o f mass and weight Tlie St.John’s Review, X L V (2 ): - 410 REFERENCES W ilson, C A (2000), From Kepler to N ew ton; Telling the tale In; Dalitz, R H and Nauenberg, M (eds.), The Foundations o f Newtonian Scholarship Singapore; W orld Scientific Publishing C o., 2 - - (2001) N ewton on the m oon ’s variation and apsidal motion In; Buchwald, J.Z and Cohen, LB (eds.), Isaac Newton’s Natural Philosophy Cambridge, Mass.: T h e M IT Press, -8 Acknowledgements for use of Images and Text (2002) N ew ton and celestial mechanics In: C ohen, l.B and Smith, G E (eds.), The Cambridge Companion to Newton Cambridge: Cambridge University Press, 2 -2 Wilson, M (2006) Wandering Significance: A n Essay On Conceptual Behavior N ew Y ork: Oxford University Press The author would like to thank the following for the creation o f images and for permission, where applicable, to reproduce copyrighted material: W ren, C (1668) Dr Christopher W ren ’s theory concerning the same subject ‘The Law o f Nature concerning Collision o f Bodies’ Philosophical Transactions (1 6 -7 ), vol 3: - Yoder, J (1988) Unrolling Tim e: Christiaan Huygens and the M athematization o f Nature Cambridge: Cambridge University Press Zenneck, J (2007) Gravitation In R en n J (ed.), T he Genesis o f General Relativity, vol Springer, 1 -2 Figure 1.1 Retrograde motion o f Mars; Photographer T un(j T ezel for the use o f the image located at http://w w w nasaim ages.O rg/luna/servlet/detail/N V A 2~4~4~5999~106525:Z-is-for-M ars Figure 1.2 Epicycle deferent, Figure 1.3 Equant: “Nicolaus Copernicus; Making the Earth a Planet” by O w en Gingerich and James H MacLachlan (2005), pp and 41 by permission o f O xford University Press Zytkow , J (1986) W hat revisions does bootstrap testing need? Philosophy o f Science, 53; 1 -9 Figures 1.4 Echptic, 1.5 T he twelve constellations, 1.6 The precession o f the equinoxes, 1.7 Precession o f equinoxes explained, 1.12 The Harmonic Rule as illustrated by satellites o f the sun, 2.2 The Harm onic R ule as illustrated by Jupiter’s moons, 2.3 The Harmonic Rule as illustrated by Saturn’s moons, 2.6 The Harmonic R ule as illustrated by satellites o f the sun using both Kepler’s and BouUiau’s data, 3.2 The Harmonic R ule as illustrated by satellites o f the sun using both Kepler’s and BouUiau’s data, 4.1 Empirical support added to Paris pendulum estimates from the agreeing m oontest estimates, 5.2 Empirical support added to Paris estimate + estimates from other latitudes from m oon-test estimates o f edition 3, 6.1 Diurnal parallax, 6.2 Empirical support added to all ten cited pendulum estimates from the eleven cited syzygy corrected moon-test estimates, 7.1 Polarized orbit, 7.2 Polarized orbit, and the image in proof o f lemma in Chpt appendix 3.2 : Suomi Ghosh Figure 1.8 Retrograde motion o f Mars: The anonymous author who made their work available on the Wikimedia commons under the following licenses; the G N U Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation, with no Invariant Sections, no Front-C over Texts, and no B ack-C over Texts; the Creative Comm ons AttributionShare Alike 3.0 Unported license; and the Creative Comm ons Attribution-Share Aftke 2.5 Generic, Generic and 1.0 Generic license The image has been altered as allowed by these licenses, without the knowledge o f the original author o f the work The transformed images appearing in this book fall under the same licenses Figure 1.9 The Tychonic system and (the identical) Figure 2.5 The Tychonic system; Fastfission, w ho made their work available on the W ikimedia commons and donated their work to the Public Domain Figure 1.11 Ellipse with the Area Rule; Stw, w ho made their work available on the Wikimedia com m ons under the following licenses: the G N U Free Docum entation License, Version 1.2 or any later version published by the Free Software Foundation, with no Invariant Sections, no F ro n t-C o v er Texts, and no B ack -C over Texts; the Creative Com m ons Attribution-Share Alike Unported license; and the Creative Com m ons Attribution-Share Alike 2.5 Generic, Generic and 1.0 Generic license The image has been altered as allowed by these licenses 412 ACKNOWLEDGEMENTS F O R USE OF IMAGES AND TEX T ACKNOWLEDGEMENTS FOR USE OF IMAGES AND TEX T 413 w ithout the knowledge o f the original author o f the work The transformed images appearing in From Area R ule to centripetal force Figure 1.18 The distances explored by each planet in our this book fall under the same licenses solar system (just the legend) Figure 2.1 Telescope observations ofju p iter’s moons Figure 2.4 Figure 1.14 Cartesian coordinates: Soumi Ghosh and Alkarex Both works are available under the G N U Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation, with no Invariant Sections, no Front-C over Texts, and no Back-Cover Texts; and the Creative Comm ons Attribution-Share Alike 3.0 Unported license The original image (of the Leaning Tow er o f Pisa) by Alkarex was altered by Soumi Ghosh without Alkarex’s knowledge as allowed by these licenses The transformed images appearing in this book fall under the same licenses Phases o f Venus as evidence against Ptolemy, Figure Kepler’s pretzel diagram Figure 2.8 Kepler’s data for Mars at aphelion and at perihelion, figure 2.9 The Area mle for an eccentric circle Figure the Area R ule in Kepler’s elliptical orbit Figure 3.1 N ew to n ’s illustration o f gravity, the diagram in N ew to n ’s p roof o f C or o f The Laws o f M otion, all three figures in the p roof o f 1.2 o f appendix Chpt 3, the figures in the proofs o f propositions and in appendix o f Chpt 3, the figures in the proofs o f N ew to n ’s proposition and its corollaries in appendix o f Chpt 3, the illustration o f inverse-square force and spring force orbits in appendix o f Chpt 3, the image for Huygens’s rotating cylindrical vessel experiment in Chpt 5, sec 1.4, Figure 8.2 Figure 1.17 Precession o f planetary orbit h yp degrees per revolution Figure 3.3 Precession per Huygens’s representation o f the relative sizes o f bodies in the solar system, the diagram illustrating revolution: James O verton (altered from original) N ew to n ’s p ro o f o f proposition 69 in appendix o f Chpt 8, the figure from N ew to n ’s p ro o f o f Figure 1.18 (other than the legend) The distances explored by each planet in our solar system proposition 70 book in appendix and in appendix o f Chpt 8, the figure from N ew to n ’s Figure (other than the legend) The distance 7Au is not explored by any planet, Figure 6.2 p roof o f proposition 73 o f book in appendix o f Chpt 8, the figure from N ew to n ’s p ro o f o f Empirical support added to all ten cited pendulum estimates from the above cited eleven syzygy proposition 71 book and its repetition in appendix o f Chpt 8, the figure from N ew to n ’s corrected m oon-test estimates o f d, and the Figure Plotting Inverse 1.5 Law, Inverse square Law, argument to construe terrestrial gravity as attraction in Chpt section II.2.iii, Figure 10.1 Hall’s and Inverse 2.5 Law attraction: W ayne Myrvold suggestion Figure 10.2 B ro w n ’s new result Figure 10.4 Blake’s depiction o f N ew ton, Figure Figures in p ro o f o f 1.1 o f appendix o f Chpt 3: Gemma Murray (altered from original) created by Soumi Ghosh from the W ikimedia com m ons are aU in the Public Domain either due T h e diagram in the p roof o f proposition o f Appendix o f Chpt 3, and the diagram for to copyright expiry or donation by creators 10.5 Chandrasekhar’s integral in appendix o f Chapter 8: Newton’s Principiafor the Common Reader by Chandrasekhar S (1995), pp 71 and , by permission o f O xford University Press Figure N = /4 , Figure 3.7 N = /4 : W ayne Lau, Michael Floskin (editor o f the Journalfor the History of Astronomy), and the Journalfor the History of Astronomy, originally published in Valluri, S R , W ilson, C , and Idarper, W L (1997) N ew ton ’s apsidal precession theorem and eccentric orbits Journal for the History o f Astronomy, 28: -2 Figure 5.1 N ew ton ’s channels and extensive quotations o f text from the Principia are from: Cohen LB and W hitm an A trans Isaac N ew ton The Principia, Mathematical Principles of Natural Philosophy: A New Translation, Los Angeles: University o f California Press, 1999, with permission Figure 8.1 and 9.1 A tw o-body system o f the sun (Helios) and Jupiter: From Smith G “H ow did N ew ton discover universal gravity?” Tire St.John’s Reuiew, vol X L V , num ber two, 1999, pp - , by permission o f The St.John’s Review Figure 10.3 Radar Tim e-D elay: Irwin Shapiro and the American Physical Society for the use of Figure (124.1) from Shapiro, I.L, Ash, M E , Ingalls, R P , Smith, W B , Campbell, D B , Dyce, R B , Jurgens, R F , Pettengill, G H , “Fourth Test o f General Relativity: N ew Radar Result” Physical R eview Letters, 26, no 18, 1 -5 , 1971 Copyright (1971) by the American Physical Society Figure 1.10 Kepler’s diagram depicting the motion o f Mars on a geocentric conception o f the solar system Figure 1.13 The phases o f Venus, Figure 1.15 Huygens’s telescope Figure 1.16 N ew ton investigating light, and the symbols (e.g., astronomical, Greek) used in images Index Figures, tables etc are given in italics absolute space -8 absolute time -7 accelerative measures (Newton) 22, 93, 123, ,1 ,1 action at a distance 21, 209, 215, 262, 339, 346, 352, 6 -8 Aim and Structure o f Physical Theory, The (Duhem) 126 agreeing measurements vi, viii, 3, 22, 30, 30n.65, 31, 3 -5 , -7 , -4 , 41, 70, 76, 87n.3, 120, -6 , 124n.57, 132, 138n.86, 142, 141-2n 91, 160, 172-3, 173n.30, 180, -6 , 195, 198, -1 , -1 , 221, -7 , -6 , 265, 267, 275n.42, 276, -8 , 344, -6 , 363, 369, 370, 373, 374n.6, 375, 382, 389, 390, 392-3 n , 394, 396 Alton, E J 364-5n 43 Alfonsine tables American Ephemeris 2>11, 377n.9 aphelia 27 Area Rule phenomenon (Newton) and centripetal force 43, 45, 140, 160 description 14 and elliptical orbits 140 and Jupiter 135 and the Moon -2 , 65, 65n.42, 162 moons ofjupiter -7 , 50, 51, 53, 1 -1 moons o f Saturn 55, 110 for the primary planets -4 , 117, 259, 298 violations o f 45 Aries 6, 6n.7 Aristotle 3, 9, 5-1 , 16n.28 astronomical units 307n.21 astronomy 3, -1 , 57n.21, 62, 97, 187n.52, 192, 365, 377n.9, 379, 385, 392n.53, 394 mathematical -4 medieval Arabic 5n.4 solar system predictive 365, 377n.9, 379 cosmological -6 Battemran, Robert -7 Bayes, Thomas 221, 238, 4 -5 , 374 Belkind, Ori 96n.21 Bentley, Richard 367, 367n.53 Bertoloni Meli, Domenico 177 Biener, Zvi 273n.38 Blake, William -8 , 38 bootstrap conditions (Glymour) 31, 119, -6 , ,1 Borelli, Giovanni 69 BouUiau, Ismael 27, -2 , 17-18, 308 Brackenridge, Bruce 86n.2 Bradley, James 19n.36, 50, 68, 237, 366 Brahe, Tycho Earth is at rest 305 geo-heliocentric system 14, 27, 42, 49, 58, 8-9n , 59, 60 introduction -1 , l ln and Kepler’s laws 130-1 Moon distance estimate 166, 2 -1 , 229, 232, -8 , 237n.35, 241, 279 M oon’s mean motion discovery 162 observatory at Uraniborg 66, 66n.46 the Tychonic system 10 violations of the Area Rule 32 Brans-Dicke theory 270, -4 , 383n.28 Brown, Ernest 372, 380, 383, 385 bucket experiment (Newton) -6 , 5n l6 Cajori, F 175n.33, 229 CaUisto 70, -3 , 282n.53 Cartesian coordinates 7-18, 18 Cassini, D 205 Cassini, Giovanni 51, In.7, 55n l3 , 56, 6 -7 , -7 , -5 , 221, -1 , -2 Cassini, J 205 Cavendish, Henry 369 Cayenne experiment 0 -3 centrifugal force 19, 213 centripetal force acceleration fields -3 , 42, 94, 4n l2, -6 , -3 , 208, 257, 265 acceleration in an elliptical orbit 120n.48, 124, 141, 141n.90 acceleration of the moon 173, 267, 279n.48 all planets 265 and Area Rule phenomenon -6 , 48, 110 -1 on bodies at equal distances 296 definitions o f 8 -9 , -8 and the deviation o f the Sun from center of gravity 46, -8 , -1 , 5 -8 and Earth’s gravity 160, 204, 208, 267 explanation -3 , 25, 30n.65, 8 -9 generalization by induction -7 , -8 4i6 in d ex centripetal force (cont.) and the Harmonic Rule 115-16, 115 hypothetical system of moons 77-8, 180-1 and Jupiter’s moons 1 ,2 measures of -3 the Moon in orbit 38, 95, 160, 164, 167-72, 174, 186, 390 the motion of bodies 339-41 motive quantity 92, 140 planets without moons -7 , 259—61 quantities o f a -4 , 123-6 the Sun towards Jupiter 356 toward the Sun 355 Chandrasekhar, S 86n.2, lOln.27, 151, 168n.21, 253n.72, -8 , 291, 296, 322, 322n.45, -7 , 326n.50, 332n.52 Christensen, David 31, 133-4, 136 Clairaut, Alexis 125, 125n.59, -2 , 344, 6 ,3 Clavius, Christopher 57n l8 clockwork deterministic system 47 Cohen, I B 6 -7 , 67n.49, 236 comets 30, 25-6, 192n.3, 213, 344, 344n l2 conceptual commitment 97n.22, 367, 367n.54 confirmation vi, vii, 3, 21, 31, 10 -4 , 119, 130, 131, -7 , 140, 142, 206n.42, 366, -4 , 389, 390n.48 consilience of inductions (Whewell) 173, 173n.30, 258n.l constellations 6—7 ‘Copemican scholium’ (Smith) 46, 376 Copernicus, Nicholas 5n.5, -1 , lO n ll, l l n l , 14, 27, 42, 60, 305 corollaries to Laws of Motion cor 101, 147, 147n.95 cor 1 -2 , 104, 107 cor 102 cor 19, 21, 102, 112n.39, 305, 311 cor -9 , 99n.23, 102-3, 148, 311 cor 99, 103, 112, 112n.41, 148-9, 151, ,3 1 to proposition book cor 152 cor 110 to proposition book cor 1 1 , 135 cor l ll n to proposition book cor 113, 151 cor 113, 151 cor 113, 151 to proposition book cor 153 cor 153-4 cor 26, 109, 114-15, 119, 154, 230, 230n l7 INDEX cor 26, 114-15, 119-20, 135, 141, 141n.91, 154 cor 154-5, 167 to proposition 13 book cor 313, 313n.37 to proposition 45 book cor -8 , 116, 12 -2 , 156-7, 163 cor 16 -5 , n ll, 168, 187-90, 187n.50, 189n.58, 222, 252 to proposition 65 book cor 268-9n 32 cor 268-9n 32 to proposition 69 book cor 317 cor 317 cor 317 to proposition 74 book cor 295, -1 , 325, 3 -2 , 332n.52 to proposition 75 book cor 321 cor -2 cor 322 to proposition 76 book cor 323 cor 323 cor 323 cor 323 cor 323 cor 323 to proposition 24 book cor 266, 266n.24 cor 266, 266n.24 to proposition book the corollary 165 to proposition book cor (first part 259) (second part 62-3) cor 259, 293 to proposition book cor -2 cor 36, 38, -3 , 274, 276n.44, 277n.46 cor 273 cor 273 cor -4 , 294n.6, 340n.3 to proposition book cor 340n.3 cor 41, 295 cor -6 to proposition book cor 0 -3 , 3 -5 cor 41, 264, 3 -4 , 3 -6 cor 3 -7 to proposition 37 book cor 239n.41 cor 214n.47, 221, 225, -2 , -5 cosmic microwave background (CMB) -6 , 396n.57 Cotes, Roger 41, 2 -8 , 235, 262, 3 -9 , 346, -5 , 349n l7, 351n.21, 352, -6 , 362n.38, 369 d’Alembert, Jean-Baptiste -2 , 240, 366 Damour, T 283, 285, 285n.56 dark energy 3, -6 data vi, vii, ix, -3 , 6, 10, lO n ll, 11, 13, 13n.20, 18n.35, 19, 21, -4 , 26, 27, 30, 30n.65, 31, 39, 43, 49, 50, 51, -5 , 56, 58, -1 , 62, 65, 66n.44, 68, -7 , 70n.62, 73n.76, 74n.77, -7 , 78, -8 , 116, 118, -6 , -2 , 3 -4 , 141, 141n.91, 160, 162, 176, 81-6, 184n.46, 200, -1 , 2 -1 , 2 -3 , 2 -3 , -3 , 234, 238, 240, -6 , 247, 266, 271, 278, - ,2 , 300, 307, 307n.21, -1 , 308n.26, 5 -6 , 356n.30, 366, 374, 377, 382n.25, -5 , 395, 396 and Galileo ,5 - and Huygens 32, 33, 55n.33, 197-9, ,2 and R om er’s estimate of the speed of light 6 -7 bounds on Eotvos’s ratios 283 Newton’s cited data from Pound -4 phen -5 , 69-71 phen - ,7 - phen 59 phen -2 , 117 phen -4 moon-test 3rd edition basic 3 -4 , 181-2 moon-test original version 231 moon-test 1st edition 233 moon-test 2nd edition 234 Shapiro’s radar time delay 384 supernova results 395 Tycho and Kepler 76, 79 W M AP results 396 deductions from phenomena (Newton) 4 -5 , 28-9, -6 deferent circles 4, definitions (Newton) Basics - (8 - ) Centripetal force -8 (88-94) De Motu (Newton) 21, 46 Densmore, Dana 86n.2, 34 n l6 De Revolutionibus (Copernicus) 10 Descartes, Rene -1 , 17n.32, 141, 170, 194, 2 -1 , 341, 369, 373 Dialogue Concerning the Two C hief World Systems (Galileo) ,9 ,3 Dicke, Robert 382 DiSalle, Robert 96, n l9 417 Discourse on the Cause o f Gravity (Huygens) 19, -1 ,3 Diurnal Parallax, -1 , 236 Figure 6.1, 236n.34 Dorling, Jon 374 Duhem, Pierre -8 , -2 , -ln , 135, ,3 7 Earth ‘at rest’ theory -8 , -1 , 305 and centrifugal force 202, 202n.28, -1 common center o f gravity o f 312 and Copernicus and gravity -9 , 160, 186, 267, 283, 302 and inverse-square accelerative gravity toward aU planets -1 , -8 and inverse-square gravitation 172-3, -6 , 2 -1 , 215, -6 and Lunar precession 186 -9 and the Moon -2 , 37, -2 , 225, 227, 234, 264, ,3 ,3 nutation o f axis (1748) 366 orbit o f 2, 59 periodic time 60 position in respect o f Jupiter -3 , 6 -8 and Pound’s observations -2 Ptolemy model rotation of 7, -59n 25 shape o f -6 , 214 and Tycho Brahe 11, 11 n 15, 58-59n 25 and variation of gravity below surface 204, -1 ecliptic -9 Edidin, A 134n.81 Einstein, Albert vi, vii, 3, 14, 48, 95, 6n l9, 97n.22, 285, 370, 372, 378, 380n.21, -2 , 381n.22, 385, 392, 394 elasticity 106—7 elliptical orbit 1, 2, 11, 13, 42, 62, -8 , 98, 11 -2 , 120, 120n.48, 127, 39-41, -8 , 187, 249n.55, 281, 281n.52, 313, 322n.44, 333, 364 empirically determining apsides and mean-distance -8 period -8 Kepler’s equation and Area Rule motion -8 distance in 120n.48 empirical success vi, -3 , -5 , 37, 41, 43, 47, 49, 128n.65, 132, 141, 142, 160, 161, ,1 -6 , 195, -1 , 221, -4 , 261, 303, 338, 339, 342, 344, 346, 347, -6 , -3 , 362n.39, -7 , 372, -5 , 377, 380, -2 , 382n.24, 385, 390, 391, 393, 396 Eotvos, Lorand 278n.47, 280, 280-2 n , 283 ephemerides 6n.6, 377, 377n.9 4i8 INDEX in d ex equant points 4, equinoxes -7 , precession o f 7, 8, Eudoxus 3n.3 Euler, L 91-3, 193n.70, 221, 240, 6 -8 Europa 3n l0, 54, 69 Extravagant Universe, Tire (Kirshner) 394 Feyerabend, Paul 127, 129n.66 Flamsteed, John 163n.8, 189, 2 -1 , -3 , 233n.27, 237, -4 , 302 FLR W space-time structure 394—5 Forster, Malcolm 141-2n.91, 173, 173-4n.31 Friedmann, Alexander 394 fudging data 226, 232, 238, 5 -6 Galilei, Galileo and Copernicus 305, 305n l7 descent o f heavy bodies 103, 103n.28 and explanation o f tides 264, 264n.21 fundamental principle o f uniform acceleration 265 and Huygens 19 idealized mathematical models 16, 16n.29, 224 introduction 2, 14 on mechanics 6-17, 16n.29 and Mersenne 196 moons o f Jupiter 51, 66n.43 observation o f phases o f Venus 4-15, 58 resolution o f motions 391 garden path problem (Smith) -4 Gauss, Carl Friedrich 184, 198, 215, 228, ,2 General Relativity -5 , 392 geoheliocentric system (Tycho Brahe) 10, 11, 14, 58, 58n.24, 59 Geometry (Descartes) 17 Glymour, Clark 31, 119, 132-6, 132n.73, 133n.76, 134n.79, 139-40, 142 Goldenberg, H Mark 382 gravity acceleration of 31, 32n.72, -4 , n ll, 172, 177, 178, ,2 , 279 as attraction 41, 88, 103, 138, 195, 225, 258, -3 , 273, 304, 306, 323, -5 , 353, 355, 360, 369 causes o f 19, 20, 23, 42, 93n.l 1, 201, 204, -1 , -4 , -6 , 344 the cause o f orbital motion 15, 93n.l centripetal force 36, 46, 8 -9 , 90, 174, 179, 180, 208, 212, 214, 239, 260, 290, 298, 300, 376, 390 common centers of 21, 42, 46, 96, 97, 102, 174, 175, 234, 250, 251, 305, 306, 307, 311, 312, 352 different from magnetic force 274 effects on satellites -7 , 347 and Huygens 195-212 as interaction 40, 41, 205, 290, 292, -8 , 338, 350, ,3 inverse-square diminution 172-3, 192-3, 2 -1 , -1 , -4 , 350 and 3rd Law o f Motion ,3 -6 and the Laws o f Motion 45, 107n.33, 109 Moon towards Earth 348 and the planets 138-9, 267, -3 , 304, 306 properties o f 23, 44, 343, 345, 349, 349n l7 and proposition book -2 , -6 relativistic theories o f 3, 48, 370, 378, -5 strength o f 31n.67, -3 , 32n.72, 38, 172, 215, 217, 239, 345 terrestrial 17, 19, 31, 35, 37, 38, 95, 161, 165, 169, 172, 174, 178, 181, 186, 195, 208, 211, 221, 239, 247, 255, 256, 323, 354, 5 ,3 towards the Sun 212, 264, 345 universal force see universal gravity varies with latitude 0 -3 vortex theories o f 17, 95, -1 , -9 , ,3 ,3 ,3 Gregory, David 170n.25, 188, 188n,56, ,2 8 Grice, Paul 134n.80 H -D method see hypothetico-deductive model (H-D) HaU, Asaph 372, -8 , 379, 379n, 383 Halley, Edmund -1 , -8 , 67n.53, 67n.57, 73, 25-6, 189, 241, 263, 263n l7, 1n l0, 344n l2, 365 Halley’s comet 125-6, 157, 344 Hardy, Lucian 387 harmonic oscillator power law 300, 322n.44, 324, 325n.48, 327n.51 Harmonic Rule (Kepler) accelerative measures 26, 94, 114, 115, 120, -7 and Christensen 133-4 and direct deductions from phenomena 45 explanation 13-14, 13, 13n.19-20 higher-order phenomenon 171 hypothetical system o f moons 176, 176-7, 180 and inverse-square forces -3 , 114—16, 115, 40-1, 160, 259, 268 and the Moon 162-3 moons of Jupiter 24, 26, 50, 53, 54, -7 , 69, 70n.62, 109, 114, 116 moons of Saturn 56, 57, 110 phenomenon 4, 117 and the planets -2 , 117-25, 118, 118n.47, 127n.63, 134-6, 142, 268, 268n.30, 298, -1 , 310n.31, 376 Harmony of the World, The (Kepler) 13 Harper, W L 19n.39, 97n.22, 106n.32, 123n,55, 132n.74, 142n.91, 173n.29, 173n.30, 205n.33, 210n.45, 58n l, 260n.8, 265n.22, 271n.36, 273n.39, n ll, 347n l5 , n l9 , 367n.54, 374n.6, 378n l3 , 382n.24, 388n.45 Helvelius, Johannes 237 Hipparchus Horrocks, Jeremiah 65, 162, 18 -9 Horrocksian models 88-9, 191 Huygens, Christiaan 2n.2, -2 , 31n.67, -3 , 34, 35n.77 and Galileo 19 and gravity 95-2 , 197n, 202n, 204n.32, 211n.46, -7 , -8 , -4 , 342, 346, 354, 354n.28, 367 and hypothetico-deductive model 2n.2, 42, -4 introduction 19-20, 20, -5 inverse-square gravity 2 -1 , -3 and mechanical philosophy 44, 95 and Moon-test calculation 160, 169, 181, ,2 -3 , 228, 231, 233, 238, -6 and pendulums -4 , 32n.72, 197n l2 post-reflection velocities 106n.32 sizes o f bodies in the solar system 309 a useful foil -1 , 219n and vortex theories 341, 364 hypotheses nonJingo (Newton) 4 -5 , 94n l2 , 338, ,3 - , 349 Hypothesis (Newton) 98 hypothetico-deductive model (H-D) vi, vii, -3 , 2n.2, -3 , 114, -6 , 140, 206n.42, 215, n l, -3 , 346, 362, -1 , -5 , 377, 380, 385, 390, 390n.48 impenetrability 277 inertia -8 inference (Descartes) 18-19 inverse-square law acceleration fields -3 , -7 , 40, -6 , 123-9, 258, 263, -2 attraction towards a sphere 41 of the circumterrestrial force 230 and Earth’s gravity 160, 195, 208, -1 , -1 from aphelia at rest -8 and Glymour 133 and gravity 29, -3 , -6 , 303 and the Harmonic Rule 11 -1 , 119, 140, ,2 and Huygens 239 hypothetical system o f moons 177, 180-1 and the lunar precession -5 , 167, 184-6, 192 419 moons o f Jupiter 1 ,2 ,3 5 and the planets -1 , 122, 136, 138, 265, 298, 300 planets without moons ,3 and proposition 304 toward Jupiter/Satum/the Sun 257, 363 toward point masses 299 toward the Sun 312, 344, 350, 364 variation deduced from orbital phenomena 128-31 lo 51, -4 , 6 -9 Janiak, Andrew -1 , 209n.43, 345n l3, 46n l4, -8 , 367n.54 Jupiter 3, 13, 14, 19, -6 , 24n.49, 27n.61, 29, 30, 30n.65, 36, 39, 47, -5 , 51n.7, 59, 60, 61, 62, 63, 64, 6 -8 , -7 , 78, 78n.88, 81, 85, 94, 10 -1 , 117, 118, 119, -5 , 131n.71, -7 , 138, 142, 161, 162, 176, 205n.33, 208, 214, 258, 259, -4 , 63n l6, 263n l7 , 264n l8 , 267, -7 , 276, -4 , 281n.50, -7 , -8 , 8 -9 , -8 , 0 -2 , 304, -7 , 307n.21, 307n.22, -9 , 308n.26, 308n.27, -1 , 314, 3 -4 , 334n.57, 335, 3 -7 , 339, 343, 353, 5 -8 , 356n.30, -9 , 360, -3 , 363n.40, -6 , 369, 376, 385, 389n.46 and acceleration fields -3 , -5 , 142, 28 -1 and Area Rule 135 gravitation towards -6 , -4 , -1 inverse-square law 10 -1 , 125, 259 Earth’s position in respect o f 53, 67, 72 forces maintaining in orbit -3 , 1 -2 and Galileo 14, -2 Harmonic Rule for Jupiter’s moons -5 mass in solar masses 304, -8 , 3 -7 , 334n.57, 334n.58 moons of see moons o f Jupiter no hardness, a gas giant 276 and Pound’s observations 71—2 ratio of surface gravity to that of earth -2 and Saturn perturbations 47, -4 , 314, 365, ,3 tidal forces from sun 11 -1 , 112n.41 fe-value 69, 3 -4 Kant, Immanuel 370 Kepler, Johannes and the Area Rule 63, 63n elliptical orbits 42, -9 , 62, -4 , 212, 313, -5 , 392 Harmonic Rule see Hamionic Rule (Kepler) introduction 11, 12, -1 , 13n.9, 15 laws of planetary motion 29, 57-8n 22, 126-31, 3 -5 , 135n.85 420 INDEX Kepler, Johannes (cont.) lunar theory 65 planetary measurements from the Sun 308 pretzel diagram -4 , 63n.34, 64 rule o f areas 1 -1 , 109, 160 Sun-centred system 27, 305 and universal gravity 375 kinematical solution 357 Kircher, Athanasius 2 -1 , 2 -9 , -2 , - ,2 - , ,2 Kirshner, Robert 373n l, -6 KoUerstrom, Nicholas 189 Koyre, A 199n.l6 Kuhn, T S 132n.72, -1 , 380n.21, 381n.22, 382n.24, 388, 388n.44, 389n.46, 392, -3n 52 Lacaille, Nicolas-Louis 237, 366 Lakatos, Imre -8 , 128n.65, 129n.66 Lambert, Johann Heinrich 365 Laplace, P S 47, 47n l00, 129, 131, 131n.71, 264, 283, 314, 365, -7 , -6 , 386n.40, 388, 391 Laudan, Larry -9 ,3 laws of orbital motion (Kepler) 11-13 Laws of Motion accepted propositions 45, 62 application to orbital systems - central role o f 135 and centripetal forces 24—5 concept o f impressed force 88 concepts of space, time and motion 96 Corollary 101, 147 Corollary 1 -2 , 104, 107 Corollary 102 Corollary 19, 21, 112 Corollary -9 , 02-3, 148 Corollary 148, 151, 154, 162 highest evidence of a proposition 349 and Huygens 205, 205n.33 and Kepler’s laws 130 Law 17, 19, 99, 339, -1 , 350n, 353, -6 Law 9 -1 0 Law 21, 40, 45, 45n.93, 100-1, 104-5, 107, 107n,33, 109, -3 , -4 , -8 , 304, 3 -5 , 341n.6, 351n.20, 353, 355, -6 , 362n.39, 363n, -9 , 368n.55, -6 Scholium 41, -4 , 108 and subjunctive conditionals 137 unifoma rotation 96 laws of planetary motion (Kepler) 126 -7 Laymon, Ronald 35-6, 140 least squares vii, 26n.54, 34, 54, 55, 70n.62, 74n.77, 160, 182-4, 198, 215, 2 -1 , Free ebooks ==> www.Ebook777.com INDEX 2 -3 , 228, 232, 233, 234, 234n.30, 235, 242n.47, 245, 256n.30 Leibniz, Gottfried Wilhelm 44, 95, 176-7, 262, -3 , 306, 341, 386n.39 Lemaitre, Georges 394 Le Monnier, M 221, 240-1 Le Verrier, Urbain 377, 379, 381 light, speed o f 51, 53, 66 lodestone 91 locally acting causes 338, 352, 367 lunar distance estimates 34, 35n.77, 65n.42, 190, 220, 222, 231, 234, 239, 241, 242 lunar theory (Horrocks) 65 McGuire, J E 277n.43 Mach, Ernst 95 McMuUin, Eman -7 Maglo, Koffi 368n.57 magnetic force 91, 352 Malament, David 392 Mars Kepler’s period and mean-distance from Tycho’s data -8 motion o f 11, 12, 13, 63 orbits the Sun 59 retrograde motion o f 4, -1 , 9, 170 smaller than Jupiter 308-11 Viking experiment 384 material conditional 25, 31, 133-7, 134n.79, 134n.81 matter force o f 87 measure of 86—7 Maupertuis, Pierre-Louis Moreau 206 Mayer, Tobias 366 mechanics 15-20, 21, 47, 48, 88, 101-2, 103-9, 131n.71, 175n.33, 175n.34, 205, 206, 285n.56, 322, 366, 368, 370, 376n.8, 380n.31, 385 celestial mechanics 131n.71, 175n.33, 175n.34, 285n.56, 376n.8, 385, 387, and Huygens -6 practice as empirical support for Laws of Motion 103 -9 Mercator, Gerardus 62 Mercury 57, 59, 122, -1 , 310n.33, 372, -8 , 384, 392 Mersenne, Marin 196, 198 Milky Way 14 Moon, the and the Area Rule 45, 162 centripetal acceleration o f 171 Diurnal Parallax 236, 236 and Earth 37, 227, 264, 348, 352, -9 Earth-Moon mass ratios 176, 176n estimates o f distance 165-8 force maintaining in orbit -3 , 163n.8, 169, 172, 179 and Galileo 14 and gravity 90, 160 Horrocks theory 65 and inverse-square variation 162, 215 motion perturbed by the Sun -5 , 65n nodes and inclination of orbit 264 precession o f 122, -9 in syzygies -6 , 166n, -7 , 189, 221, -7 and unification -5 moons o f Jupiter absence o f polarization 270, -3 , 282 Area Rule phenomenon 50, 53, 113, 162 and Galileo 14 and the Harmonic Rule 39, 50, -7 , 69, 70n,62, 11 -1 , 118 and inverse-square forces 119, 214, 355 orbits of 24, 24n.49, 26, -4 , 52, 54, 55, -7 , 71 and Proposition 109-11 and the Sun 162, -9 , 269n.33 Moon-test argument -5 , 34, 35n.77, -9 , 16R-1, 16 -5 , 67n l6, 169, 73-4, 177-8, 18 -6 , 182, 190, 195, -1 , ,2 ,2 , 218n.52, 2 -3 , 231, 234, -4 , 239, 242, 246, 267, 271, 300, 390 motion and Aristotle 16n.28, 17 description o f 1—2 Laws o f (Descartes) 19 measure o f -9 projectile 6-1 , -9 quantity o f 104 Myrvold, Wayne C 123n.55, 185n 46-7, 374, 374n.6 n-body solution 392 Newcomb, Simon 47, 130, 176, 366, 372, 377, 379, 379n l5 Newton and the Reality o f Force (Janiak) 209 Newton on method -7 , -4 , 4 -5 , 3 -4 Nordtvedt, Kenneth 269n.33, 271, 283 Nordtvedt effects 271 parametrized post-Newtonian formalism (PPN) 382, 382n Pardies, Ignatius -3 , -3 n pendulums cycloidal 197n, 198 and Earth’s gravity -1 , -8 in experiments -9 , 87, 10 -6 and Huygens 19, -5 , 31n.67, 35n.77 and Newton 21 proving proposition 6, 24, -7 , 267n www.Ebook777.com 421 seconds measurement 160, -6 , 181-2, 185, 195-2 , 201, 210, -1 , 247 perturbation theory 47, n l0 phenomena (Newton) -4 , 50 53, -1 , 114 5 -7 -6 -2 , 117 -4 , 116-17 6 -5 , 162 phlogiston theory o f chemistry -2 physical causes 4, 11, -2 , 23, 93, 179, 264, 378, 342, 346 Picard, Jean-Felix 66, 66n.44, 6 -7 n l6 , 205 planets and centripetal forces 2 -3 , 43 circling the sun 11, lln ,1 distances explored 29 and gravity 37, -6 , -3 n Harmonic Rule -1 , 73, 13n.19, -4 , 40n.86, 61, 123 introduction inverse-square variation of accelerations -8 , -3 Keplerian orbital motions -8 maintaining in orbit 135 motions o f 30, 98, 123 periods/mean distances 60, 117 precession o f orbits 28, 121, 136, 160 primary 22, -7 , 11 -2 , 139 retrograde motion of polarized satellite orbits -7 , -3 , -9 Popper, Karl 2n.2 positivist program 137 Pound, James 19n.36, 26, 50, 5 -6 , -2 , 355, 356n.30 precession correction 2 -3 , 252 precision 32, 39, 40n.86, 66n.43, 77, 87, 105, 131, 160, 161, 190, 200, 220, 2 -3 , 2 -5 , 228, 233, 238, 252n.68, 334n.55, 359n.35, 366, 377n.9, 380, -4 , 396 prediction vi, 2, 2n.2, 4, 14, 30, 35, 37, -3 , 43n.90, 128n,65, 131, 132, 132n.72, 189n.57, 215, n l0 , 339, 346, 362n.39, 363n.40, 363n.42, -4 , 375, 377, 382n.24, 385, 389, 389n.47, 390 Prindpia (Newton) 1, -1 , 46, 49, 224, 244, ,2 - , 347, 349, -9 , 377, 388 Prindpia Philosophiae (Descartes) 17 properties of planets from orbits 291, 0 -4 , 3 -7 propositions book prop 42, 43, 110, -9 , 176 prop 109, 116, 14 -5 , 152, 161 prop 63, 109, 1 ,1 -1 , 161 prop 109, 114, 115, 116, -5 , ,1 , ,2 , 300, 333 I NDE X 422 423 INDEX propositions book (cont.) prop 45 -8 , 28n.63, 116, 21-2, 122n.52, 156, 157n l01, 163-4, n ll, 165, 168, 187, 187n.49, 188, 189, 189n.58, ,2 2 , 252 prop 60 -5 , 234n.29, 239n.42, 250-1 prop 65 268, 268n.32 prop 66 8 -9 , 313 prop 69 40, -4 , -1 , 3 -4 , 346 prop 70 318, 328 prop 71 319, 320, -3 prop 72 319 prop 73 -2 prop 74 -6 , -2 , 225 prop 75 299, -2 , 322n.44 prop 76 299, 2 -3 propositions book prop 24 -6 , 266n.24, 266n.25 propositions book prop -6 , 109-116, 176 prop 2 -8 , 116-23, 126 prop 3 -2 , 32n.70, -5 , 16 -5 , 230 prop -5 , 165-74, 176-81, -1 , -3 , -9 , 242 prop 5 -7 , -6 , 269 prop -4 , 210, -8 , 92n l, 293, 293n.4, 4 -5 prop -1 , 264, -9 , 304, 339, 347 prop 41, 264, 9 -3 , 369 prop 10 306 prop 11 98, 305, 313 prop 42, 98, 306 prop 13 313 prop 19 204 props -2 187, 248 prop 29 65n.41, 65n.42, 162n.6, 189, 248 prop 30 187 prop 31 187 prop 34 187 prop 35 187, 188, 189, 249n.55 prop 37 175n 33, 214n 47, 2 -8 , 234n 28, 239n 41, -2 , -5 , 5 -6 Prutenic tables 10 Ptolemy -6 , -1 , lO n ll, 15, 57, 58n.25, 220, 305 Quine-Duhem thesis 132-3 Re^ulae Philosophandi (Rules for Reasoning in Natural Philosophy) 3 -8 , 170-1, -1 , -8 Rule 33, -6 , 169-74, 173n.30, 178-81, 185, 206n.42, 239, 260, 260n.39, 273n.39 Rule 33, -6 , 169-72, 173n.30, 174, 178-81, 217, -9 , 273n.39 Rule 3 -9 , 45n.93, 87n.4, 107, 123, -8 , 273n.38, 276n.44, 277n.46, 292n.3, 355, 361, 362n.38, 375 Rule -7 , 36n.79, 45, 45n.93, 49, 97n.22, 107-8, 123, 141, 141-2n 91, 219, 219n.58, 224, -6 , 264, 274, 284, 306, 314, -4 , 362n.38, -7 , 375, ,3 Reichenbach, Hans 96 Relativity General 95 Special 95, 97n.22 retrograde motion -4 , 4, Riccioli, Giovanni Battista 196, 198 Richer, Jean 0 - ,2 ,2 Roberts, John 25n.50 Robertson, Howard Percy 394 Rom er, Ole Christensen -4 , 53n 8/9, 6 -8 , 67n Rosenkrantz, Roger 134-6 Rudolphine Tables (Kepler) 14 Rules for Philosophizing/Reasoning 3 -8 , 36n.79, 42, 45 Rules for Reasoning (Newton) 169 Saturn 3, 13, 19, 24, 29, 30, 36, 39, 47, 51n.7, 5 -7 , -6 , -5 , 77, 78, 78n.88, 81, 85, 94, 109, 110, 117-18, 123-5, 131n.71, 138, 142, 176, 195, 208, 214, -9 , -4 , 270, 281, 281n.51, 281n.52, -4 , 0 -2 , 304, -8 , -1 , 314, 3 -7 , 344, 344n l2, 363, 364, 365, 369, 376, 385, 389n.44 and acceleration fields -3 , 123-5, 142, 281 gravitation towards -6 , -4 , 281, 281n.51, 302 Harmonic Rule for Saturn’s moons -7 inverse-square law 110, 125, -6 and Jupiter perturbations 47, -4 , 314, 365, 369, 385 and Laplace 47, 47n l00, 264, 264n l9, 365, 369, -6 satellites of 5 -7 , 56, 56n l4, 57, -5 , 109-10, 270 mass in solar masses 304, -8 , 3 -5 , 334n.59 Schliesser, Eric 93n l0, 37-8, 138n, 194 Scholium on time, space, place & motion 17n.32, 21, 85, -9 to the Laws o f Motion 41, 103-9 to proposition book 111 to proposition book 63, 113, 162 to proposition 69 book 23, 23n.46, -5 n l4 , 209n.43, 318, 3 -4 , 344, 345n l3, 346, 346n l4, 352 to proposition book 176-80 to proposition book 260 to proposition 35 book 163n.8, 188-9 general scholium to book 3, 94n l4 , ,3 Schwarzschild solution 392 scientific inference 2, 2n.2, 31, 35, 43n.90, 132-3, 135, 136, 141-2n 91, 257, 58n l, -7 , 362, 371n.61, 372, 374, 374n.3, 374n.6, 390 scientific method vi, vii, ix, x, -3 , 15, 20, -1 , -9 , 84, n ll, 128n.65, 137, 142, 141-2n 91, 195, -1 , 247, 257, 258n l, 262, 298, 347, 370, -5 , 377, 378, 381n.22, -5 , 388n.45, -1 , 392-3n 53 scientific progress vi, 48, 373, 388, 388n.45, 391 Shapiro, Alan 343 n l0 Shapiro, Irwin 50, 383, 385 Shimony, Abner 374, 374n.3 Siderius Nuncius (Galileo) 14, 16 simplifying assumptions 173n.30, 214n.47, 221, 2 ,2 Simpson, Thomas 2 -1 , -8 , 244 skepticism -1 ,3 Smeenk, Christopher 273n.38 Smith, George 46, 46n.97, -1 , 187, 187n.49, 194, 196n.3, 198n l5, 200n, 309, 314, -7 , 369n.58, -8 , 389n.45, 393 Smith, Sheldon 22 -3 n , 126n.62 Solar System 47, 58, 385, 386n.38, -3 Stanley, Jason 374n.6 Stein, Howard -3 , 87n.3, n l2 , -6 , 103, 123, -8 , 262, 298, 341n.7, -8 Sun,the accelerative forces toward -7 ‘at rest’ theory 305 and centripetal force 46 and elliptical orbits 98 and gravity 2 -1 , -3 gravity towards 281, 312, 344 inverse-square law 257 and Jupiter 112 -1 , 112n, -8 , -6 , 357, 359n.35, 363n.40 and Lunar precession 186 -9 and the M oon’s motion -5 , 162, 164 orbit of orbit of Earth 170 parallax of 302n.9 polarizations towards 27 -1 and the primary planets 16-26, 124-5n.57, 307 transit of Mercury 14 systematic dependencies -6 , 25, 31, 41, 43, ,1 , 110-13, 1 -1 , 119, -2 , 129, 135-7, 139, 140, 141, 154, 156-9, 172, 290, 291, 296, 303, 321, 325, 332, 332n.52, 350, 389, 390, 392-3n 53 Area Rule and centripetal force -6 , 25, 110-13 Harmonic Rule and inverse-square 1 -1 Absence of precession and inversesquare -2 , 15 -9 inverse-square to particles -7 , 3 -2 System o f the World (Newton) 229, 296 syzygies 65n.42, 165, 166, 166n l2, 175n.33, 186, 187, 187n.49, 188, 189, -3 , 248, 249n.55, 250n.62, 256 Teeter Dobbs, Betty l ll n tempered Bayesianism (Shimony) 374 theory acceptance 49, 257, 370, 372, 373, 374, 374n.6, 375, 390 theory-mediated measurements vi, vii, 3, 19, 31n.67, 33, 45n.93, -7 , 109, 119, 126n.65, 129, 194, 195 -2 0 , 257, 339, -8 , 375, 385 thought experiment (Newton) -6 , -6 n l7 tidal forces 162 Titan 56n Treatise/Discourse (Huygens) 42, 373 two-body correction 174 Two chief world systems problem -1 , 364 hypothesis 305 Two New Sciences (Galileo) 16, 16n.29 Tycho see Brahe, Tycho universal gravity accepting the stronger theory 48 application of the third mle 280 argument for 15, 22, 22-3n 45 and Huygens 215 incompatible with Keplerian orbital phenomena 45 introduction -2 Jupiter and Saturn mutual perturbation 365 and Kepler’s laws 12 -3 , 375 and the moon-test calculation 174 motions o f solar system bodies 98, 3 -1 Newton’s argument for 263, 367—8 pair-wise interaction between bodies 40, 137-8, 296, 298, 391 and proposition 291 Ursus, Nicholas l l n l Usselman, Mel -2 van Fraassen, Bas 48 Van Helden, A 302n Venus orbits the Sun 57, 7n l8, 59 phases of 14, 15, 58 smaller than Jupiter -1 , 310n.34 vernal equinox -7 , 6n.7 424 INDEX Vokrouhlick, D 283 vortex theory (Descartes) 17, 17n.32, 170-1, 194, 213, 259, 262, -2 , 348, 364 WafF, C B 190 Walker, Arthur Geoffrey 394 Wallis, John 352, 352n.22 wave theory of light (Huygens) 19 Free ebooks ==> www.Ebook777.com Westfall, Richard 2 -1 , 2 -8 , -5 , 247 Whewell, William 173, -9 , 258n.l Whiteside, D T 188 Wilkinson Microwave Anisotropy Probe (WMAP) -6 Wilson, Curtis 176, 187, 191, 264n, -6 Wilson, Mark 387 Wren, Christopher 106, 106n.32, 210 www.Ebook777.com ... theory acceptance, and empirical support Newton s scientific method adds features that significantly enrich the basic hypothetico-deductive model of scientific method 373 373 Accumulating support... I thank them This work on N ew ton’s scientific method has benefited from students and colleagues who participated in my graduate seminars on Newton and method These included over the years four... Lessons from Newton on scientific method 42 42 VI Gravity as a universal force o f pair-wise interaction Applying Law 40 40 Universal force o f interaction M ore informative than H -D method III