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From Eudoxus to Einstein A History of Mathematical Astronomy C. M. LINTON Department of Mathematical Sciences, Loughborough University cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge cb2 2ru, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521827508 © C. M. Linton 2004 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2004 isbn-13 isbn-10 978-0-511-21646-6 eBook (NetLibrary) 0-511-21646-7 eBook (NetLibrary) isbn-13 isbn-10 978-0-521-82750-8 hardback 0-521-82750-7 hardback Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Contents Preface page ix 1 Introduction 1 2 Spheres and circles 25 3 The Ptolemaic universe 51 4 Developments in geocentric astronomy 85 5 The heliocentric universe 119 6 Tycho Brahe, Kepler, and the ellipse 153 7 Galileo, the telescope, and Keplerian astronomy 201 8 The universal theory of gravitation 239 9 Celestial mechanics 291 10 The asteroids and the outer planets 355 11 New metho