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  • 1.Theory and Problems ofAstronomy STACY E. PALEN Department of Astronomy University of WashingtonSchaums Outline Series New YorkMcGRAW-HILL Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney Toronto

2. abcMcGraw-HillCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Manufactured in the United States of America. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher. 0-07-139993-3 The material in this eBook also appears in the print version of this title: 0-07-136436-6.All trademarks are trademarks of their respective owners. Rather than put a trademark symbol after every occurrence of a trademarked name, we use names in an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringement of the trademark. Where such designations appear in this book, they have been printed with initial caps. McGraw-Hill eBooks are available at special quantity discounts to use as premiums and sales promotions, or for use in corporate training programs. For more information, please contact George Hoare, Special Sales, at or (212) 9044069.TERMS OF USE This is a copyrighted work and The McGraw-Hill Companies, Inc. (McGraw-Hill) and its licensors reserve all rights in and to the work. Use of this work is subject to these terms. Except as permitted under the Copyright Act of 1976 and the right to store and retrieve one copy of the work, you may not decompile, disassemble, reverse engineer, reproduce, modify, create derivative works based upon, transmit, distribute, disseminate, sell, publish or sublicense the work or any part of it without McGraw-Hills prior consent. You may use the work for your own noncommercial and personal use; any other use of the work is strictly prohibited. Your right to use the work may be terminated if you fail to comply with these terms. THE WORK IS PROVIDED AS IS. McGRAW-HILL AND ITS LICENSORS MAKE NO GUARANTEES OR WARRANTIES AS TO THE ACCURACY, ADEQUACY OR COMPLETENESS OF OR RESULTS TO BE OBTAINED FROM USING THE WORK, INCLUDING ANY INFORMATION THAT CAN BE ACCESSED THROUGH THE WORK VIA HYPERLINK OR OTHERWISE, AND EXPRESSLY DISCLAIM ANY WARRANTY, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. McGraw-Hill and its licensors do not warrant or guarantee that the functions contained in the work will meet your requirements or that its operation will be uninterrupted or error free. Neither McGraw-Hill nor its licensors shall be liable to you or anyone else for any inaccuracy, error or omission, regardless of cause, in the work or for any damages resulting therefrom. McGraw-Hill has no responsibility for the content of any information accessed through the work. Under no circumstances shall McGraw-Hill and/or its licensors be liable for any indirect, incidental, special, punitive, consequential or similar damages that result from the use of or inability to use the work, even if any of them has been advised of the possibility of such damages. This limitation of liability shall apply to any claim or cause whatsoever whether such claim or cause arises in contract, tort or otherwise. DOI: 10.1036/0071399933 3. The purpose of this Outline is to serve as a supplement to a basic astronomy text. Much of the material here is abbreviated, and students should use this book as a guide to the key concepts in modern astronomy, but not as an all-inclusive resource. Topics covered range from planetary astronomy to cosmology, in the modern context. The rst chapter covers most of the phsyics required to obtain a basic understanding of astronomical phenomena. The student will most likely come back to this chapter again and again as they progress through the book. The order of the topics has been set by the most common order of these topics in textbooks (near objects to far objects), but many of the chapters are quite independent, with few references to previous chapters, and may be studied out of order. The text includes many worked mathematical problems to support the eorts of students who struggle particularly in this area. These detailed problems will help even mathematically adept students to see how to solve astronomical problems involving several steps. I wish to thank the many people who were instrumental to this work, including the unknown reviewer who gave me so many useful comments, and especially the editors, Glenn Mott of McGraw-Hill and Alan Hunt of Keyword Publishing Services Ltd., who guided a novice author with tremendous patience. I also wish to thank John Armstrong for proofreading the very rst (and therefore very rough!) draft and all my colleagues at the University of Washington who served as sources of knowledge and inspiration. STACY PALENiii Copyright 2002 The McGraw-Hill Companies, Inc. Click Here for Terms of Use. 4. This page intentionally left blank. 5. CHAPTER 1Physics Facts About About About AboutCHAPTER 21Masses Gases Light Distance1 13 15 25The Sky and Telescopes31Coordinate Systems and Timescales InstrumentationCHAPTER 331 42Terrestrial Planets49Formation of Terrestrial Planets Evolution of the Terrestrial Planets Mercury Venus Earth Moon Mars Moons of MarsCHAPTER 450 53 56 59 62 67 71 72Jovian Planets and Their Satellites77Jupiter Saturn Uranus Neptune Moons RingsCHAPTER 6Debris91Comets Meteorites Asteroids Pluto and CharonCHAPTER 578 79 79 80 81 8791 95 99 103The Interstellar Medium and Star Formation107The Interstellar Medium Star Formation107 117v Copyright 2002 The McGraw-Hill Companies, Inc. Click Here for Terms of Use. 6. Contentsvi CHAPTER 7Main-Sequence Stars and the Sun Equilibrium of Stars Observable Properties of Stars The SunCHAPTER 8Stellar Evolution Why Do Stars Evolve? How Do Stars Evolve? Stars8MSun: Supernovae Where Do We Come From?CHAPTER 9125 125 126 137153 153 156 158 162 163Stellar Remnants (White Dwarfs, Neutron Stars, and Black Holes) 173 Degenerate Gas Pressure White Dwarfs Neutron Stars Black HolesCHAPTER 10173 174 176 179Galaxies and Clusters183The Milky Way Normal Galaxies Active Galaxies and QuasarsCHAPTER 11Cosmology Hubbles Law Hubbles Law and the Expansion of the Universe Hubbles Law and the Age of the Universe Hubbles Law and the Size of the Universe The Big Bang Life in the Universe183 189 196203 203 204 204 205 205 214APPENDIX 1Physical and Astronomical Constants219APPENDIX 2Units and Unit Conversions221APPENDIX 3Algebra Rules223APPENDIX 4History of Astronomy Timeline225INDEX231 7. Physics FactsSee Appendix 1 for a list of physical and astronomical constants, Appendix 2 for a list of units and unit conversions, Appendix 3 for a brief algebra review, and the tables in Chapters 3 and 4 for planetary data, such as masses, radii, and sizes of orbits.About Masses MASS Mass is an intrinsic property of an object which indicates how many protons, neutrons, and electrons it has. The weight of an object is a force and depends on what gravitational inuences are acting (whether the object is on the Earth or on the Moon, for example), but the mass stays the same. Mass is usually denoted by either m or M, and is measured in kilograms (kg).VOLUME The volume of a body is the amount of space it lls, and it is measured in meters cubed (m3 ). The surface of a sphere is S 4r2 and its volume V 4=3r3 , where r is the radius andis 3.1416.1 Copyright 2002 The McGraw-Hill Companies, Inc. Click Here for Terms of Use. 8. CHAPTER 1 Physics Facts2 DENSITYThe density of an object, the ratio of the mass divided by the volume, is often depicted by(Greek letter rho): it is usually measured in kg/m3 : m VGRAVITY Gravity is the primary force acting upon astronomical objects. Gravity is always an attractive force, acting to pull bodies together. The force of gravity between two homogeneous spherical objects depends upon their masses and the distance between them. The further apart two objects are, the smaller the force of gravity between them. The gravity equation is called Newtons law of gravitation: FGMm d2where M and m are the masses of the two objects, d is the distance between their centers, and G is the gravitational constant: 6:67 1011 m3=kg=s2 . The unit of force is the newton (N), which is equal to 1 kg m=s2 . If the sizes of the two objects are much smaller than their distance d, then the above equation is valid for arbitrary shapes and arbitrary mass distributions.THE ELLIPSE The planets orbit the Sun in nearly circular elliptical orbits. An ellipse is described by its major axis (length 2a) and its minor axis (length 2b), as shown in Fig. 1-1. For each point A on the ellipse, the sum of the distances to the foci AF and AF 0 is constant. More specically: AF AF 0 2a 0 The eccentricity of the ellipse is given by e FF=2a. In terms of the semi-major axis, a, and the semi-minor axis, b, we have s2 b e 1 aThe Sun occupies one of the foci in the ellipse described by a planet. Assume that the Sun occupies the focus F. When the planet is on the major axis and at the point nearest F, then the planet is at perihelion. On the far point on the major axis, the planet is at aphelion. By denition, dp da 2a where dp is the planetSun distance at perihelion and da is the distance at aphelion. 9. CHAPTER 1 Physics Facts3KEPLERS LAWS Keplers First Law. Planets orbit in ellipses, with the Sun at one focus. Keplers Second Law. The product of the distance from the focus and the transverse velocity is a constant. The transverse velocity is the velocity perpendicular to a line drawn from the object to the focus (see Fig. 1-1). As a hint for working problems, consider that when a planet is at aphelion or perihelion (farthest and closest to the Sun), all of the velocity is trans


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