Physics of the Earth and the Solar System Dynamics and Evolution, Sp
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GEOPHYSICS AND ASTROPHYSICS MONOGRAPHS
Editor B. M. McCORMAC, Lockheed Palo Alto Research Laboratory, Palo Alto, Calif, U.S.A.
Editorial Board R. GRANT ATHAY, High Altitude Observatory, Boulder, Colo., U.S.A. P. BANKS, Radioscience Laboratory, Stanford University, Stanford, Calif., U.S.A. D. M. HUNTEN, Department of Planetary Science, University ofArizona, Tucson, Ariz., U.S.A. M. KUPERUS, Sonnenborgh Observatory, University of Utrecht, The Netherlands R. LOST, European Space Agency, Paris, France R. ROSNER, Department ofAstronomy and Astrophysics, University of Chicago, Ill., U.S.A. G. WEILL, GDTA, Toulouse, France
Volume 31
PHYSICS OF THE EARTH
AND THE SOLAR SYSTEM
Dynamics and Evolution, Space Navigation, Space-Time Structure by BRUNO BERTOTII Department of Nuclear and Theoretical Physics, University of Pavia, Italy
and PAOLO FARINELLA Department of Mathematics, University of Pisa, Italy
KLUWER ACADEMIC PUBLISHERS DORDRECHT I BOSTON I LONDON
Library of Congress Cataloging in Publication Data Bertotti. B.• 1930Physics of the earth and the solar system / Bruno Bertotti. Paolo Farinella. p. cm. -- (Geophysics and astrophysics monographs; v. 31) I. Solar system. Paolo. II. Title. OB50 I . B4B 1990 523.2--dc20
2. Geopnysics. III. Serles.
3. Astrophysics.
I. Farinella.
89-27782
ISBN-l3: 978-94-010-7355-4 DOl: 10.1 007/978-94-009-1916-7
e-ISBN-13: 978-94-009-1916-7
Published by Kluwer Academic Publishers, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. Kluwer Academic Publishers incorporates the publishing programmes of D. Reidel, Martinus Nijhoff, Dr W. Junk and MTP Press. Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, 101 Philip Drive, Norwell, MA 02061, U.S.A. In all other countries, sold and distributed by Kluwer Academic Publishers Group, P.O. Box 322, 3300 AH Dordrecht, The Netherlands.
Printed on acid1ree paper
All Rights Reserved © 1990 by Kluwer Academic Publishers Softcover reprint ofthe hardcover 1st edition 1990 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.
CONTENTS INTRODUCfION USEFUL PHYSICAL QUANTITIES
ix xiii
1. DYNAMICAL PRINCIPLES 1.1. Gravitational equilibrium 1.2. Dynamical equations 1.3. Dynamics of solid bodies 1.4. Transport 1.5. Magnetohydrodynamics 1.6. Conservation of magnetism and vorticity 1.7. Kinetic theory Problems
1 1 7 9 13 18 21 23 27
2. THE GRA VITATIONAL FIELD OF A PLANET 2.1. Spherical harmonics 2.2. Harmonic representation of the gravity field of a planet 2.3. Low order gravitational potential 2.4. Fine structure of the gravity field of the earth Problems
29 29 34 37 40 43
3. THE ROTATION OF THE EARTH AND OTHER PLANETS 3.1. Measurements of time and distance 3.2. Rotating frames 3.3. Slow rotation of a fluid body 3.4*. Equilibrium shapes of bodies in rapid rotation 3.5. Rigid body dynamics:
