The Origin and Evolution of the Solar System The Graduate Series in Astronomy Series Editors: M Elvis, Harvard–Smithsonian Center for Astrophysics A Natta, Osservatorio di Arcetri, Florence The Graduate Series in Astronomy includes books on all aspects of theoretical and experimental astronomy and astrophysics. The books are written at a level suitable for senior undergraduateand graduate students, and will also be useful to practising astronomers who wish to refresh their knowledge of a particular field of research. Other books in the series Dust in the Galactic Environment D C B Whittet Observational Astrophysics R E White (ed) Stellar Astrophysics R J Tayler (ed) Dust and Chemistry in Astronomy T J Millar and D A Williams (ed) The Physics of the Interstellar Medium J E Dyson and D A Williams Forthcoming titles The Isotropic Universe, 2nd edition D Raine Dust in the Galactic Environment, 2nd edition D C B Whittet The Graduate Series in Astronomy The Origin and Evolution of the Solar System M M Woolfson Department of Physics University of York, UK Institute of Physics Publishing Bristol and Philadelphia c IOP Publishing Ltd 2000 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publisher. Multiple copying is permitted in accordance with the terms of licences issued by the Copyright Licensing Agency under the terms of its agreement with the Committee of Vice-Chancellors and Principals. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. ISBN 0 7503 0457 X (hbk) 0 7503 0458 8 (pbk) Library of Congress Cataloging-in-Publication Data are available Series Editors: M Elvis, Harvard–Smithsonian Center for Astrophysics A Natta, Osservatorio di Arcetri, Florence Publisher: Nicki Dennis Commissioning Editor: John Navas Production Editor: Simon Laurenson Production Control: Sarah Plenty Cover Design: Victoria Le Billon Marketing Executive: Colin Fenton Published by Institute of Physics Publishing, wholly owned by The Institute of Physics, London Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK US Office: Institute of Physics Publishing, The Public Ledger Building, Suite 1035, 150 South Independence Mall West, Philadelphia, PA 19106, USA Typeset in T E X using the IOP Bookmaker Macros Printed in the UK by Bookcraft, Midsomer Norton, Somerset Contents Introduction xv PART 1 The general background 1 1 The structure of the Solar System 3 1.1 Introduction 3 1.2 Planetary orbits and solar spin 4 1.2.1 Two-body motion 4 1.2.2 Solar system orbits 6 1.2.3 Commensurable orbits 8 1.2.4 Angular momentum distribution 10 1.3 Planetary structure 10 1.3.1 The terrestrial planets 10 1.3.2 The major planets 12 1.3.3 Pluto 13 1.4 Satellite systems, rings and planetary spins 14 1.4.1 Classification 14 1.4.2 The Jovian system 15 1.4.3 The Saturnian system 18 1.4.4 Satellites of Uranus and Neptune 20 1.4.5 Spins and satellites of Mercury, Venus, Mars and Pluto 23 1.4.6 The Earth–Moon system 24 1.5 Asteroids 30 1.5.1 Characteristics of the major asteroids 30 1.5.2 The distribution of asteroid orbits: Kirkwood gaps 32 1.5.3 The compositions of asteroids 32 1.6 Meteorites 35 1.6.1 Falls and finds 36 1.6.2 Stony meteorites 37 1.6.3 Stony-irons 38 1.6.4 Iron meteorites 38 viii Contents 1.6.5 Isotopic anomalies in meteorites 39 1.7 Comets 41 1.7.1 Types of comet orbit 41 1.7.2 The physical structure of comets 43 1.7.3 The Kuiper belt 45 2 Observations and theories of star formation 46 2.1 Stars and stellar evolution 46 2.1.1 Brightness and distance 46 2.1.2 Luminosity, temperature and spectral class 48 2.1.3 The motions of stars relative to the Sun 50 2.1.4 The masses of stars 51 2.1.5 The Hertzsprung–Russell diagram and main-sequence stars 52 2.1.6 The spin rates of stars 54 2.1.7 Evolution of stars away from the main sequence 54 2.2 The formation of dense interstellar clouds 59 2.2.1 Dense interstellar clouds 59 2.2.2 Heating and cooling in the ISM 59 2.2.3 The pressure-density relationship for thermal equilibrium 62 2.2.4 Jeans’ stability criterion 63 2.2.5 Mechanisms for forming cool dense clouds 65 2.3 The evolution of proto-stars 72 2.3.1 The Hayashi model 72 2.4 Observations of star formation 75 2.4.1 Infrared observations 75 2.4.2 Radio-wave observations 75 2.5 Observation of young stars 77 2.5.1 Identifying young stellar clusters 77 2.5.2 Age–mass relationships in young clusters 78 2.6 Theories of star formation 79 2.6.1 Stars and stellar clusters 79 2.6.2 A general theory of star formation in a galactic cluster 80 2.7 Planets around other stars 95 2.8 Circumstellar discs 98 3 What should a theory explain? 100 3.1 The nature of scientific theories 100 3.1.1 What is a good theory? 100 3.1.2 The acceptance of new theories 101 3.1.3 Particular problems associated with the Solar System 102 3.2 Required features of theories 103 3.2.1 First-order features 103 3.2.2 Second-order features 104 3.2.3 Third-order features 106 Contents ix PART 2 Setting the theoretical scene 109 4 Theories up to 1960 111 4.1 The historical background 111 4.1.1 Contributions of the ancient world 111 4.1.2 From Copernicus to Newton 113 4.2 Buffon’s comet theory 117 4.3 The Laplace nebula theory 118 4.3.1 Some preliminary ideas 118 4.3.2 The nebula model of Solar System formation 119 4.3.3 Objections and difficulties 120 4.4 The Roche model 121 4.4.1 Roche’s modification of Laplace’s theory 121 4.4.2 Objections to Roche’s theory 122 4.5 The Chamberlin and Moulton planetesimal theory 124 4.5.1 The planetesimal idea 124 4.5.2 The Chamberlin–Moulton dualistic theory 125 4.5.3 Objections to the Chamberlin–Moulton theory 126 4.6 The Jeans tidal theory 127 4.6.1 A description of the tidal theory 127 4.6.2 The tidal disruption of a star 129 4.6.3 The break-up of a filament and the formation of proto- planets 130 4.6.4 Objections to Jeans’ theory 131 4.7 The Schmidt–Lyttleton accretion theory 133 4.7.1 The Schmidt hypothesis 133 4.7.2 Lyttleton’s modification of the accretion theory 134 4.7.3 The problems of the accretion theory 135 4.8 The von Weizs¨acker vortex theory 136 4.8.1 The basic model 136 4.8.2 Objections to the von Weizs¨acker model 137 4.9 The major problems revealed 137 4.9.1 The problem of angular momentum distribution 137 4.9.2 Planet formation 138 4.9.3 Implications from the early theories 139 x Contents PART 3 Current theories 141 5 A brief survey of modern theories 143 5.1 The method of surveying theories 143 5.2 The Proto-planet Theory 144 5.3 The Capture Theory 146 5.4 The Solar Nebula Theory 149 5.5 The Modern Laplacian Theory 151 5.6 Analysing the modern theories 155 6 The Sun, planets and satellites 156 6.1 Surveying extant theories 156 6.2 Formation of the Sun: dualistic theories 156 6.2.1 The magnetic braking of solar spin 158 6.2.2 The solar spin axis 162 6.3 Formation of the Sun: monistic theories 163 6.3.1 Removing angular momentum from a collapsing nebula 163 6.4 Formation of planets 169 6.4.1 Planets from the Proto-planet Theory 169 6.4.2 Planets from the Capture Theory 171 6.4.3 Planets from the Solar Nebula Theory 184 6.4.4 Planets from the Modern Laplacian Theory 192 6.5 Formation of satellites 195 6.5.1 Satellites from the Proto-planet Theory 196 6.5.2 Satellites from the Modern Laplacian Theory 198 6.5.3 Satellites from the Capture Theory 198 6.6 Successes and remaining problems of modern theories 204 6.6.1 The Solar Nebula Theory 204 6.6.2 The Accretion Theory 205 6.6.3 The Modern Laplacian Theory 205 6.6.4 The Capture Theory 206 6.6.5 The Proto-planet Theory 207 7 Planetary orbits and angular momentum 209 7.1 The evolution of planetary orbits 209 7.1.1 Round-off due to tidal effects 209 7.1.2 Round-off in a resisting medium 210 7.1.3 Bode’s law 214 7.1.4 Commensurability of the Jovian satellite system 215 7.1.5 Commensurability of planetary orbits 216 7.2 Initial planetary orbits 221 7.2.1 The Accretion and Solar Nebula Theories 222 7.2.2 The Proto-planet Theory 223 7.2.3 The Capture Theory 223 Contents xi 7.3 Angular momentum 225 7.3.1 Angular momentum and the Proto-planet Theory 225 7.3.2 Angular momentum and the Modern Laplacian and Solar Nebula Theories 227 7.3.3 Angular momentum and the Capture Theory 228 7.3.4 Angular momentum and the Accretion Theory 229 7.4 The spin axes of the Sun and the planets 229 7.4.1 Spin axes and the Solar Nebula Theory 230 7.4.2 Spin axes and the Modern Laplacian Theory 232 7.4.3 Spin axes and the Accretion Theory 232 7.4.4 Spin axes and the Proto-planet Theory 233 7.4.5 Spin axes and the Capture Theory 234 8 A planetary collision 237 8.1 Interactions between proto-planets 237 8.1.1 Probabilities of interactions leading to escape 237 8.1.2 Probabilities of interactions leading to a collision 242 8.1.3 Numerical calculation of characteristic times 243 8.2 The Earth and Venus 244 8.2.1 A planetary collision; general considerations 245 8.2.2 A collision between planets A and B 246 9 The Moon 251 9.1 The origin of the Earth–Moon system 251 9.1.1 The fission hypothesis 251 9.1.2 Co-accretion of the Earth and the Moon 254 9.1.3 Capture of the Moon from a heliocentric orbit 255 9.1.4 The single impact theory 256 9.1.5 The Earth–Moon system from a planetary collision 261 9.2 The chemistry of the Earth and the Moon and formation of the Moon 263 9.2.1 Possible models of Moon formation 265 9.3 The physical structure of the Moon 267 9.3.1 Hemispherical asymmetry by bombardment 269 9.3.2 A collision history of the Moon 271 9.3.3 Mascons 272 9.3.4 Mascons and basalts in mare basins 274 9.3.5 Volcanism and the evolution of the Moon 276 9.3.6 Calculations of thermal evolution 278 9.4 Lunar magnetism 282 9.4.1 A dynamo theory 284 9.4.2 The induction model of lunar magnetism 285 9.5 Summary 293 xii Contents 10 Smaller planets and irregular satellites 294 10.1 Introduction 294 10.2 Mars 295 10.2.1 Mars according to accretion theories 296 10.2.2 Mars according to the planet-collision hypothesis 296 10.2.3 The Martian crust 298 10.2.4 The COM–COF offset 300 10.2.5 Polar wander on Mars 302 10.3 A general description of Mercury 303 10.3.1 Mercury and accretion theories 305 10.3.2 Mercury and the Capture Theory 306 10.4 Neptune, Pluto and Triton 307 10.4.1 Encounter scenarios for the Neptune–Triton–Pluto system 308 10.4.2 Comments on the Neptune–Triton–Pluto system 311 10.5 Irregular satellites 313 10.6 Summary 314 11 Asteroids, meteorites and comets 316 11.1 Asteroid formation 316 11.2 Meteorites 317 11.2.1 Stony meteorites 318 11.3 Stony irons 322 11.4 Iron meteorites 324 11.5 Information from meteorites 325 11.6 Isotopic anomalies in meteorites 326 11.6.1 Oxygen isotopic anomalies 327 11.6.2 Magnesium in meteorites 328 11.6.3 Neon in meteorites 330 11.6.4 Anomalies in silicon carbide grains 331 11.6.5 The deuterium anomaly 332 11.7 Explanations of isotopic anomalies in meteorites 332 11.7.1 A planetary collision origin for isotopic anomalies 334 11.8 Comets—a general survey 354 11.8.1 New comets and the Oort cloud 357 11.9 The inner-cloud scenario 364 11.10 Kuiper-belt objects 366 11.11 Comets from the planetary collision 367 11.12 Ideas about the origin and features of small bodies 368 [...]... analysed The only theory to essay a complete picture of the origin and evolution of the solar system is the Capture Theory developed by the author and colleagues since the early 1960s This explains the basic structure of the solar system in terms of well-understood mechanisms that have a nite probability of having occurred The way in which planets form, and the way that their orbits originate and evolve... is the line of intersection of the orbital plane with the ecliptic This line is called the line of nodes; the point on the line where the orbit crosses the ecliptic going from south to north is the ascending node and the descending node where it goes from north to south The structure of the Solar System 6 Figure 1.2 The longitude of the ascending node, ê, and the argument of the perihelion, The other... Theory and the Solar Nebula theory, and gives the main theoretical basis for each of them Also discussed, but not so fully, is the Accretion Theory, an older model of solar- system formation with some positive features These theories are examined in detail to determine the extent to xv xvi Introduction which they provide a plausible mechanism for the origin of the solar system and their strengths and weaknesses... The comets, responsible for some of the most spectacular celestial apparitions, will be the topic of the last section of this chapter Inhabiting the furthest reaches of the Solar System the population of comets is, perhaps, the least well understood feature of the Solar System The conventional classication of solar- system objects is now challenged by recent discoveries of remote bodies inhabiting the. .. that dene the orbit in space are shown in gure 1.2 The rst of these is the longitude of the ascending node, , which is the angle between the ascending node and the rst point of Aires The second angle is the argument of the perihelion, , which is the angle between the ascending node and the perihelion in the direction of the orbiting body Sometimes and , which are not coplanar, are added together and referred... The structure of the Solar System 1.1 Introduction Before one can sensibly consider the origin of the Solar System it is rst necessary to familiarize oneself with its present condition Consequently this rst chapter will provide an overview of the main features of the system of planets The treatment will be particularly relevant to the study of solar- system cosmogony Factors relating to the origin of. .. less than that of Neptune In projection onto the plane of the ecliptic the orbits of these two planets would cross but because of the special relationship of the two orbits the planets never come closer together than 18 AU In recent years it has become technically feasible to study numerically the evolution of orbits of the Solar System over periods of time comparable with the age of the system Computer... bodies and almost certainly have cores, consisting of iron with a small proportion of nickel, overlaid by a silicate mantle The interpretation of their densities is in terms of the relative size of the core to that of the whole body and also the total mass of the planet that will determine the degree of compression The relative sizes of the ve terrestrial bodies, together with an indication of their... its primary Its orbital and spin periods are both the same as the spin period of Pluto so the pair of bodies rotate about the centre of mass as a rigid system The structure of the Solar System 24 (a) (b) Figure 1.11 A Moon-globe showing (a) the near-side (b) the far-side 1.4.6 The EarthMoon system The Moon is the fth most massive satellite in the Solar System With a mass  ắắ kg and a diameter 3476 km... mysterious fashion on the way in Computer graphics are not constrained by the petty requirements of science! The democratic principle is not necessarily a sound way to determine the plausibility of a scientic theory and there are many examples in the history of science that tell us so The geocentric theory of the solar system, the phlogiston theory of burning and the concept of chemical alchemy were . 255 9.1.4 The single impact theory 256 9.1.5 The Earth–Moon system from a planetary collision 261 9.2 The chemistry of the Earth and the Moon and formation of the Moon 263 9.2.1 Possible models of Moon. overview of the main features of the system of planets. The treat- ment will be particularly relevant to the study of solar- system cosmogony. Factors relating to the origin of stars and their evolution. Angular momentum and the Capture Theory 228 7.3.4 Angular momentum and the Accretion Theory 229 7.4 The spin axes of the Sun and the planets 229 7.4.1 Spin axes and the Solar Nebula Theory 230 7.4.2