Undergraduate Lecture Notes in Physics

Undergraduate Lecture Notes in Physics For further volumes: http://www.springer.com/series/8917 Undergraduate Lecture Notes in Physics (ULNP) publishes authoritative texts cov- ering topics throughout pure and applied physics. Each title in the series is suitable as a basis for undergraduate instruction, typically containing practice problems, worked examples, chapter summaries, and suggestions for further reading. ULNP titles must provide at least one of the following: • An exceptionally clear and concise treatment of a standard undergraduate subject. • A solid undergraduate-level introduction to a graduate, advanced, or non- standard subject. • A novel perspective or an unusual approach to teaching a subject. ULNP especially encourages new, original, and idiosyncratic approaches to physics teaching at the undergraduate level. The purpose of ULNP is to provide intriguing, absorbing books that will continue to be the reader’s preferred reference throughout their academic career. Series Editors Neil Ashby Professor Emeritus, University of Colorado, Boulder, CO, USA William Brantley Professor, Furman University, Greenville, SC, USA Michael Fowler Professor, University of Virginia, Charlottesville, VA, USA Michael Inglis Professor, SUNY Suffolk County Community College, Selden, NY, USA Heinz Klose Oldenburg, Niedersachsen, Germany Helmy Sherif Professor Emeritus, University of Alberta, Edmonton, AB, Canada Charles Keeton Principles of Astrophysics Using Gravity and Stellar Physics to Explore the Cosmos 123 Charles Keeton Department of Physics and Astronomy Rutgers University Piscataway, NJ, USA ISSN 2192-4791 ISSN 2192-4805 (electronic) ISBN 978-1-4614-9235-1 ISBN 978-1-4614-9236-8 (eBook) DOI 10.1007/978-1-4614-9236-8 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2014935057 © Springer Science+Business Media New York 2014 This work is subject to copyright. 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Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) To my parents, who helped me find my path Preface This book is designed to show how physical principles can be used at the advanced undergraduate level to understand astronomical systems such as planets, stars, galaxies, and the universe as a whole. It emerges from a pair of courses at Rutgers University that attract not just astrophysics students but a broad audience of physics and engineering students. The organization is therefore “physics-first”: we start with key principles of physics and then examine applications to astronomical systems. At Rutgers, each half of the book constitutes a coherent semester-length course; while there is a little overlap (notably with cosmology in Chaps. 11 and 20), the two halves are largely independent and complementary. Part I focuses on gravity, because this is the dominant force in many astronomical systems and it governs many types of motions we observe. The goal of Chaps. 2–11 is to develop a progressively richer understanding of gravity and the way astrophysicists use gravitational motion to investigate mass. Part II centers on one of the “big questions” we humans ask. Why are we here? is admittedly beyond the realm of physics, but a related question is within our reach: How did we come to be here? As the Sun was forming, various elements came together in the right combination to form a rocky planet with a tenuous atmosphere. On this planet Earth, the energy from the Sun and the gas in the atmosphere were just right to allow the emergence of life. The energy that sustains us originates deep inside our star, thanks to E D mc2. The atoms that comprise our bodies were forged in previous generations of stars. Literally, we are star dust. The goal of Chaps. 12–20 is to understand the roles that electromagnetism as well as gas, atomic, and nuclear physics play in this remarkable story. I hope this book will help you learn to think like an astrophysicist. Rather than memorizing facts about specific astronomical systems, you will learn to break the systems into pieces you can analyze and understand using material that should be familiar from introductory physics and vector calculus. (The necessary physics topics are reviewed as they arise; vital aspects of vector calculus are reviewed in Appendix A.) Then you will be equipped to investigate interesting systems that you vii viii Preface encounter in the future, even if they are not addressed in this book. Astrophysics is a dynamic field of research—and one in which you can understand the physical principles that underlie even the newest discoveries. So let’s have fun! Piscataway Chuck Keeton December 2013 Acknowledgements “No book is an island, entire of itself.” That is not what John Donne actually wrote, but it could have been. It is certainly apt here. This book would not exist in its present form without the help of many people. Arthur Kosowsky originally developed the structure for the astrophysics courses at Rutgers, which is reflected in the makeup of this book. Saurabh Jha, Eric Gawiser, and John Moustakas have taught from this material at various stages of development, and provided critical feedback. All contributed ideas for homework problems; and many rounds of students have (perhaps to their chagrin) field-tested a lot of the problems. The Rutgers Department of Physics and Astronomy, and in particular the astrophysics group, has provided an environment where excellence in research and teaching are both encouraged and supported. Art Congdon, Allan Moser, Erik Nordgren, Barnaby Rowe, and Tim Jones have done yeomen’s work with the manuscript. They provided extensive and insightful comments throughout the drafting process, catching everything from typos to muddled thinking. All remaining errors are my fault, not theirs! Many researchers have graciously let me use images and figures to illustrate the material. They are too numerous to list here, but are credited in the figure captions. A number of books have contributed to my own learning, but two in particular stand out. An Introduction to Modern Astrophysics by Bradley W. Carroll and Dale A. Ostlie is a monumental survey of astrophysics at the undergraduate level. The “big orange book” maintains a respected place on every astronomer’s bookshelf. Astrophysics in a Nutshell by Dan Maoz is a more focused treatise that shares a lot of the spirit animating this book. Both have influenced my thinking about how to present this material, as indicated throughout the text. Last but not least, my wife and son have not merely endured this absorbing project, but actively endorsed it. To Kelly: thank you for letting me dream. To Evan: if you can dream it, you can do it, but it might take more effort than you imagine. This work has received financial support from the U.S. National Science Foundation through grant AST-0747311. ix Contents 1 Introduction: Tools of the Trade .......................................... 1 1.1 WhatIsGravity? ..................................................... 1 1.2 DimensionsandUnits................................................ 4 1.2.1 Fundamental Dimensions .................................. 5 1.2.2 ConstantsofNature......................................... 6 1.2.3 Astrophysical Units......................................... 7 1.2.4 DimensionalAnalysis...................................... 8 1.3 UsingtheTools....................................................... 10 1.3.1 PhasesofanElectronGas.................................. 11 1.3.2 Stars, Familiar and Exotic .................................. 14 Problems ..................................................................... 16 References.................................................................... 17 Part I Using Gravity and Motion to Measure Mass 2 Celestial Mechanics......................................................... 21 2.1 MotionsintheSky ..................................................

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