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Astronomy 2e
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SENIOR CONTRIBUTING AUTHORS ANDREW FRAKNOI, FROMM INSTITUTE, UNIVERSITY OF SAN FRANCISCO DAVID MORRISON, NASA (EMERITUS) AND SETI INSTITUTE SIDNEY C. WOLFF, NOIRLAB (EMERITA)
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OpenStax Rice University 6100 Main Street MS-375 Houston, Texas 77005
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To learn more about OpenStax, visit https://openstax.org. Individual print copies and bulk orders can be purchased through our website.
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©2022 Rice University. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0). Under this license, any user of this textbook or the textbook contents herein must provide proper attribution as follows:
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- If you redistribute this textbook in a digital format (including but not limited to PDF and HTML), then you must retain on every page the following attribution: “Access for free at openstax.org.”
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For questions regarding this licensing, please contact support@openstax.org.
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Trademarks The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, OpenStax CNX logo, OpenStax Tutor name, Openstax Tutor logo, Connexions name, Connexions logo, Rice University name, and Rice University logo are not subject to the license and may not be reproduced without the prior and express written consent of Rice University.
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HARDCOVER BOOK ISBN-13 B&W PAPERBACK BOOK ISBN-13 DIGITAL VERSION ISBN-13 ORIGINAL PUBLICATION YEAR 1 2 3 4 5 6 7 8 9 10 RS 22
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978-1-711470-57-3 978-1-711470-56-6 978-1-951693-50-3 2022
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OPENSTAX
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OpenStax provides free, peer-reviewed, openly licensed textbooks for introductory college and Advanced Placement® courses and low-cost, personalized courseware that helps students learn. A nonprofit ed tech initiative based at Rice University, we’re committed to helping students access the tools they need to complete their courses and meet their educational goals.
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RICE UNIVERSITY
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OpenStax, OpenStax CNX, and OpenStax Tutor are initiatives of Rice University. As a leading research university with a distinctive commitment to undergraduate education, Rice University aspires to path-breaking research, unsurpassed teaching, and contributions to the betterment of our world. It seeks to fulfill this mission by cultivating a diverse community of learning and discovery that produces leaders across the spectrum of human endeavor.
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PHILANTHROPIC SUPPORT
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OpenStax is grateful for the generous philanthropic partners who advance our mission to improve educational access and learning for everyone. To see the impact of our supporter community and our most updated list of partners, please visit openstax.org/impact.
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Arnold Ventures Chan Zuckerberg Initiative Chegg, Inc. Arthur and Carlyse Ciocca Charitable Foundation Digital Promise Ann and John Doerr Bill & Melinda Gates Foundation Girard Foundation Google Inc. The William and Flora Hewlett Foundation The Hewlett-Packard Company Intel Inc. Rusty and John Jaggers The Calvin K. Kazanjian Economics Foundation Charles Koch Foundation Leon Lowenstein Foundation, Inc. The Maxfield Foundation
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Burt and Deedee McMurtry Michelson 20MM Foundation National Science Foundation The Open Society Foundations Jumee Yhu and David E. Park III Brian D. Patterson USA-International Foundation The Bill and Stephanie Sick Fund Steven L. Smith & Diana T. Go Stand Together Robin and Sandy Stuart Foundation The Stuart Family Foundation Tammy and Guillermo Treviño Valhalla Charitable Foundation White Star Education Foundation Schmidt Futures William Marsh Rice University
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Study where you want, what you want, when you want.
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When you access your book in our web view, you can use our new online highlighting and note-taking features to create your own study guides.
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Our books are free and flexible, forever. Get started at openstax.org/details/books/astronomy-2e
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Access. The future of education. openstax.org
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CONTENTS
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Preface 1
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1 Science and the Universe: A Brief Tour 9
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Introduction 9 1.1 The Nature of Astronomy 11 1.2 The Nature of Science 11 1.3 The Laws of Nature 12 1.4 Numbers in Astronomy 13 1.5 Consequences of Light Travel Time 15 1.6 A Tour of the Universe 16 1.7 The Universe on the Large Scale 21 1.8 The Universe of the Very Small 24 1.9 A Conclusion and a Beginning 26 For Further Exploration 28
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2 Observing the Sky: The Birth of Astronomy 29
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Thinking Ahead 29 2.1 The Sky Above 30 2.2 Ancient Astronomy 39 2.3 Astrology and Astronomy 46 2.4 The Birth of Modern Astronomy 50 Key Terms 57 Summary 57 For Further Exploration 58 Collaborative Group Activities 59 Exercises 60
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3 Orbits and Gravity 63
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Thinking Ahead 63 3.1 The Laws of Planetary Motion 64 3.2 Newton’s Great Synthesis 69 3.3 Newton’s Universal Law of Gravitation 74 3.4 Orbits in the Solar System 78 3.5 Motions of Satellites and Spacecraft 81 3.6 Gravity with More Than Two Bodies 84 Key Terms 88 Summary 89 For Further Exploration 90 Collaborative Group Activities 91 Exercises 91
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4 Earth, Moon, and Sky 95
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Thinking Ahead 95 4.1 Earth and Sky 96 4.2 The Seasons 99 4.3 Keeping Time 105 4.4 The Calendar 108 4.5 Phases and Motions of the Moon 111 4.6 Ocean Tides and the Moon 116 4.7 Eclipses of the Sun and Moon 119 Key Terms 126 Summary 126 For Further Exploration 127 Collaborative Group Activities 129 Exercises 130
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5 Radiation and Spectra 135
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Thinking Ahead 135 5.1 The Behavior of Light 136 5.2 The Electromagnetic Spectrum 142 5.3 Spectroscopy in Astronomy 150 5.4 The Structure of the Atom 154 5.5 Formation of Spectral Lines 159 5.6 The Doppler Effect 163 Key Terms 168 Summary 169 For Further Exploration 170 Collaborative Group Activities 171 Exercises 171
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6 Astronomical Instruments 175
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Thinking Ahead 175 6.1 Telescopes 176 6.2 Telescopes Today 182 6.3 Visible-Light Detectors and Instruments 192 6.4 Radio Telescopes 195 6.5 Observations outside Earth’s Atmosphere 202 6.6 The Future of Large Telescopes 207 Key Terms 210 Summary 210 For Further Exploration 211 Collaborative Group Activities 212 Exercises 213
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7 Other Worlds: An Introduction to the Solar System 217
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Thinking Ahead 217 7.1 Overview of Our Planetary System 218 7.2 Composition and Structure of Planets 229 7.3 Dating Planetary Surfaces 233 7.4 Origin of the Solar System 236 Key Terms 239 Summary 239 For Further Exploration 240 Collaborative Group Activities 241 Exercises 242
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8 Earth as a Planet 245
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Thinking Ahead 245 8.1 The Global Perspective 246 8.2 Earth’s Crust 250 8.3 Earth’s Atmosphere 257 8.4 Life, Chemical Evolution, and Climate Change 261 8.5 Cosmic Influences on the Evolution of Earth 266 Key Terms 272 Summary 273 For Further Exploration 273 Collaborative Group Activities 275 Exercises 276
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9 Cratered Worlds 279
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Thinking Ahead 279 9.1 General Properties of the Moon 280 9.2 The Lunar Surface 286 9.3 Impact Craters 290 9.4 The Origin of the Moon 296 9.5 Mercury 297 Key Terms 304 Summary 304 For Further Exploration 304 Collaborative Group Activities 306 Exercises 307
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10 Earthlike Planets: Venus and Mars 311
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Thinking Ahead 311 10.1 The Nearest Planets: An Overview 311 10.2 The Geology of Venus 317 10.3 The Massive Atmosphere of Venus 322
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10.4 The Geology of Mars 325 10.5 Water and Life on Mars 334 10.6 Divergent Planetary Evolution 345 Key Terms 347 Summary 347 For Further Exploration 348 Collaborative Group Activities 350 Exercises 350
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11 The Giant Planets 353
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Thinking Ahead 353 11.1 Exploring the Outer Planets 354 11.2 The Giant Planets 359 11.3 Atmospheres of the Giant Planets 365 Key Terms 375 Summary 375 For Further Exploration 375 Collaborative Group Activities 377 Exercises 378
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12 Rings, Moons, and Pluto 381
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Thinking Ahead 381 12.1 Ring and Moon Systems Introduced 382 12.2 The Galilean Moons of Jupiter 383 12.3 Titan and Triton 392 12.4 Pluto and Charon 397 12.5 Planetary Rings (and Enceladus) 404 Key Terms 415 Summary 415 For Further Exploration 416 Collaborative Group Activities 418 Exercises 419
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13 Comets and Asteroids: Debris of the Solar System 421
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Thinking Ahead 421 13.1 Asteroids 422 13.2 Asteroids and Planetary Defense 432 13.3 The “Long-Haired” Comets 436 13.4 The Origin and Fate of Comets and Related Objects 445 Key Terms 453 Summary 453 For Further Exploration 454 Collaborative Group Activities 456
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Exercises 457
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14 Cosmic Samples and the Origin of the Solar System 459
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Thinking Ahead 459 14.1 Meteors 460 14.2 Meteorites: Stones from Heaven 465 14.3 Formation of the Solar System 470 14.4 Comparison with Other Planetary Systems 476 14.5 Planetary Evolution 480 Key Terms 486 Summary 486 For Further Exploration 487 Collaborative Group Activities 489 Exercises 489
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15 The Sun: A Garden-Variety Star 493
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Thinking Ahead 493 15.1 The Structure and Composition of the Sun 494 15.2 The Solar Cycle 504 15.3 Solar Activity above the Photosphere 509 15.4 Space Weather 513 Key Terms 520 Summary 520 For Further Exploration 521 Collaborative Group Activities 523 Exercises 523
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16 The Sun: A Nuclear Powerhouse 527
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Thinking Ahead 527 16.1 Sources of Sunshine: Thermal and Gravitational Energy 527 16.2 Mass, Energy, and the Theory of Relativity 530 16.3 The Solar Interior: Theory 539 16.4 The Solar Interior: Observations 545 Key Terms 551 Summary 551 For Further Exploration 552 Collaborative Group Activities 552 Exercises 553
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17 Analyzing Starlight 557
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Thinking Ahead 557
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17.1 The Brightness of Stars 557 17.2 Colors of Stars 561 17.3 The Spectra of Stars (and Brown Dwarfs) 563 17.4 Using Spectra to Measure Stellar Radius, Composition, and Motion 570 Key Terms 579 Summary 579 For Further Exploration 580 Collaborative Group Activities 581 Exercises 581
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18 The Stars: A Celestial Census 585
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Thinking Ahead 585 18.1 A Stellar Census 585 18.2 Measuring Stellar Masses 589 18.3 Diameters of Stars 596 18.4 The H–R Diagram 601 Key Terms 610 Summary 610 For Further Exploration 611 Collaborative Group Activities 611 Exercises 612
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19 Celestial Distances 617
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Thinking Ahead 617 19.1 Fundamental Units of Distance 618 19.2 Surveying the Stars 621 19.3 Variable Stars: One Key to Cosmic Distances 630 19.4 The H–R Diagram and Cosmic Distances 636 Key Terms 640 Summary 640 For Further Exploration 641 Collaborative Group Activities 642 Exercises 643
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20 Between the Stars: Gas and Dust in Space 647
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Thinking Ahead 647 20.1 The Interstellar Medium 648 20.2 Interstellar Gas 651 20.3 Cosmic Dust 659 20.4 Cosmic Rays 666 20.5 The Life Cycle of Cosmic Material 668 20.6 Interstellar Matter around the Sun 670 Key Terms 672
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Summary 672 For Further Exploration 673 Collaborative Group Activities 674 Exercises 675
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21
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The Birth of Stars and the Discovery of Planets outside the Solar System 679
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Thinking Ahead 679 21.1 Star Formation 680 21.2 The H–R Diagram and the Study of Stellar Evolution 689 21.3 Evidence That Planets Form around Other Stars 692 21.4 Planets beyond the Solar System: Search and Discovery 695 21.5 Exoplanets Everywhere: What We Are Learning 703 21.6 New Perspectives on Planet Formation 709 Key Terms 713 Summary 713 For Further Exploration 714 Collaborative Group Activities 716 Exercises 717
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22 Stars from Adolescence to Old Age 719
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Thinking Ahead 719 22.1 Evolution from the Main Sequence to Red Giants 720 22.2 Star Clusters 726 22.3 Checking Out the Theory 729 22.4 Further Evolution of Stars 735 22.5 The Evolution of More Massive Stars 743 Key Terms 747 Summary 747 For Further Exploration 748 Collaborative Group Activities 749 Exercises 750
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23 The Death of Stars 753
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Thinking Ahead 753 23.1 The Death of Low-Mass Stars 754 23.2 Evolution of Massive Stars: An Explosive Finish 759 23.3 Supernova Observations 766 23.4 Pulsars and the Discovery of Neutron Stars 772 23.5 The Evolution of Binary Star Systems 779 23.6 The Mystery of the Gamma-Ray Bursts 782 Key Terms 791 Summary 791
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For Further Exploration 792 Collaborative Group Activities 794 Exercises 795
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24 Black Holes and Curved Spacetime 799
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Thinking Ahead 799 24.1 Introducing General Relativity 800 24.2 Spacetime and Gravity 805 24.3 Tests of General Relativity 808 24.4 Time in General Relativity 811 24.5 Black Holes 813 24.6 Evidence for Black Holes 820 24.7 Gravitational Wave Astronomy 824 Key Terms 829 Summary 829 For Further Exploration 830 Collaborative Group Activities 832 Exercises 833
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25 The Milky Way Galaxy 835
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Thinking Ahead 835 25.1 The Architecture of the Galaxy 836 25.2 Spiral Structure 844 25.3 The Mass of the Galaxy 848 25.4 The Center of the Galaxy 851 25.5 Stellar Populations in the Galaxy 857 25.6 The Formation of the Galaxy 859 Key Terms 865 Summary 865 For Further Exploration 866 Collaborative Group Activities 868 Exercises 868
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26 Galaxies 871
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Thinking Ahead 871 26.1 The Discovery of Galaxies 872 26.2 Types of Galaxies 875 26.3 Properties of Galaxies 880 26.4 The Extragalactic Distance Scale 883 26.5 The Expanding Universe 887 Key Terms 894 Summary 894 For Further Exploration 895
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Collaborative Group Activities 896 Exercises 897
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27 Active Galaxies, Quasars, and Supermassive Black Holes 899
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Thinking Ahead 899 27.1 Quasars 899 27.2 Supermassive Black Holes: What Quasars Really Are 907 27.3 Quasars as Probes of Evolution in the Universe 915 Key Terms 922 Summary 922 For Further Exploration 922 Collaborative Group Activities 924 Exercises 925
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28 The Evolution and Distribution of Galaxies 927
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Thinking Ahead 927 28.1 Observations of Distant Galaxies 928 28.2 Galaxy Mergers and Active Galactic Nuclei 935 28.3 The Distribution of Galaxies in Space 942 28.4 The Challenge of Dark Matter 955 28.5 The Formation and Evolution of Galaxies and Structure in the Universe 962 Key Terms 969 Summary 969 For Further Exploration 970 Collaborative Group Activities 972 Exercises 974
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29 The Big Bang 977
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Thinking Ahead 977 29.1 The Age of the Universe 978 29.2 A Model of the Universe 985 29.3 The Beginning of the Universe 993 29.4 The Cosmic Microwave Background 999 29.5 What Is the Universe Really Made Of? 1006 29.6 The Inflationary Universe 1012 29.7 The Anthropic Principle 1016 Key Terms 1019 Summary 1019 For Further Exploration 1021 Collaborative Group Activities 1022 Exercises 1023
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30 Life in the Universe 1027
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Thinking Ahead 1027 30.1 The Cosmic Context for Life 1028 30.2 Astrobiology 1030 30.3 Searching for Life beyond Earth 1039 30.4 The Search for Extraterrestrial Intelligence Key Terms 1058 Summary 1058 For Further Exploration 1059 Collaborative Group Activities 1061 Exercises 1062
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1047
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A How to Study for an Introductory Astronomy Class 1065 B Astronomy Websites, Images, and Apps 1067 C Scientific Notation 1073 D Units Used in Science 1077 E Some Useful Constants for Astronomy 1079 F Physical and Orbital Data for the Planets 1081 G Selected Moons of the Planets 1083 H Future Total Eclipses 1087 I The Nearest Stars, Brown Dwarfs, and White Dwarfs 1089 J The Brightest Twenty Stars 1093 K The Chemical Elements 1095 L The Constellations 1101 M Star Chart and Sky Event Resources 1107
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Index 1109
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Preface 1
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Preface
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Welcome to Astronomy 2e, an OpenStax resource. This textbook was written to increase student access to high-quality learning materials, maintaining highest standards of academic rigor at little to no cost.
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About OpenStax
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OpenStax is a nonprofit based at Rice University, and it’s our mission to improve student access to education. Our first openly licensed college textbook was published in 2012 and our library has since scaled to over 50 books for college and AP® courses used by hundreds of thousands of students. OpenStax Tutor, our low-cost personalized learning tool, is being used in college courses throughout the country. Through our partnerships with philanthropic foundations and our alliance with other educational resource organizations, OpenStax is breaking down the most common barriers to learning and empowering students and instructors to succeed.
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About OpenStax resources
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Customization
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Astronomy 2e is licensed under a Creative Commons Attribution 4.0 International (CC BY) license, which means that you can distribute, remix, and build upon the content, as long as you provide attribution to OpenStax and its content contributors.
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Because our books are openly licensed, you are free to use the entire book or pick and choose the sections that are most relevant to the needs of your course. Feel free to remix the content by assigning your students certain chapters and sections in your syllabus, in the order that you prefer. You can even provide a direct link in your syllabus to the sections in the web view of your book.
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Instructors also have the option of creating a customized version of their OpenStax book. The custom version can be made available to students in low-cost print or digital form through their campus bookstore. Visit your book page on OpenStax.org for more information.
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Errata
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All OpenStax textbooks undergo a rigorous review process. However, like any professional-grade textbook, errors sometimes occur. Since our books are web based, we can make updates periodically when deemed pedagogically necessary. If you have a correction to suggest, submit it through the link on your book page on OpenStax.org. Subject-matter experts review all errata suggestions. OpenStax is committed to remaining transparent about all updates, so you will also find a list of past errata changes on your book page on OpenStax.org.
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Format
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You can access this textbook for free in web view or PDF through OpenStax.org, and for a low cost in print.
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About Astronomy 2e
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Astronomy 2e is written in clear non-technical language, with the occasional touch of humor and a wide range of clarifying illustrations. It has many analogies drawn from everyday life to help non-science majors appreciate, on their own terms, what our modern exploration of the universe is revealing. The book can be used for either a one-semester or two-semester introductory course (bear in mind, you can customize your version and include only those chapters or sections you will be teaching.) It is made available free of charge in electronic form (and low cost in printed form) to students around the world.
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Coverage and scope
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Astronomy 2e was written by its three senior authors (see below) and was updated, reviewed, and vetted by a wide range of astronomers and astronomy educators in a strong community effort. It is designed to meet scope and sequence requirements of introductory astronomy courses nationwide.
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2 Preface
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Chapter 1: Science and the Universe: A Brief Tour Chapter 2: Observing the Sky: The Birth of Astronomy Chapter 3: Orbits and Gravity Chapter 4: Earth, Moon, and Sky Chapter 5: Radiation and Spectra Chapter 6: Astronomical Instruments Chapter 7: Other Worlds: An Introduction to the Solar System Chapter 8: Earth as a Planet Chapter 9: Cratered Worlds Chapter 10: Earthlike Planets: Venus and Mars Chapter 11: The Giant Planets Chapter 12: Rings, Moons, and Pluto Chapter 13: Comets and Asteroids: Debris of the Solar System Chapter 14: Cosmic Samples and the Origin of the Solar System Chapter 15: The Sun: A Garden-Variety Star Chapter 16: The Sun: A Nuclear Powerhouse Chapter 17: Analyzing Starlight Chapter 18: The Stars: A Celestial Census Chapter 19: Celestial Distances Chapter 20: Between the Stars: Gas and Dust in Space Chapter 21: The Birth of Stars and the Discovery of Planets outside the Solar System Chapter 22: Stars from Adolescence to Old Age Chapter 23: The Death of Stars Chapter 24: Black Holes and Curved Spacetime Chapter 25: The Milky Way Galaxy Chapter 26: Galaxies Chapter 27: Active Galaxies, Quasars, and Supermassive Black Holes Chapter 28: The Evolution and Distribution of Galaxies Chapter 29: The Big Bang Chapter 30: Life in the Universe Appendix A: How to Study for Your Introductory Astronomy Course Appendix B: Astronomy Websites, Pictures, and Apps Appendix C: Scientific Notation Appendix D: Units Used in Science Appendix E: Some Useful Constants for Astronomy Appendix F: Physical and Orbital Data for the Planets Appendix G: Selected Moons of the Planets Appendix H: Upcoming Total Eclipses Appendix I: The Nearest Stars, Brown Dwarfs, and White Dwarfs Appendix J: The Brightest Twenty Stars Appendix K: The Chemical Elements Appendix L: The Constellations Appendix M: Star Charts and Sky Event Resources
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Currency and accuracy
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Astronomy 2e has information and images from the LIGO and VIRGO gravitational-wave detectors, the Perseverance/Ingenuity mission to Mars, the Juno mission to Jupiter, and many other recent projects in astronomy. The discussion of exoplanets has been updated with recent information—indicating not just individual examples, but trends in what sorts of planets seem to be most common. Black holes receive their own chapter, and the role of supermassive black holes in active galaxies and galaxy evolution is clearly
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Access for free at openstax.org
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Preface 3
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explained. Chapters have been reviewed by subject-matter experts for accuracy and currency.
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Flexibility
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Because there are many different ways to teach introductory astronomy, we have made the text as flexible as we could. Math examples are shown in separate sections throughout, so that you can leave out the math or require it as you deem best. Each section of a chapter treats a different aspect of the topic being covered; a number of sections could be omitted in shorter overview courses and can be included where you need more depth. And, as we have already discussed, you can customize the book in a variety of ways that have never been possible in traditional textbooks.
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Student-centered focus
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This book is written to help students understand the big picture rather than get lost in random factoids to memorize. The language is accessible and inviting. Helpful diagrams and summary tables review and encapsulate the ideas being covered. Each chapter contains interactive group activities you can assign to help students work in teams and pool their knowledge.
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Interactive online resources
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Interesting “Links to Learning” are scattered throughout the chapters, which direct students to online animations, short videos, or enrichment readings to enhance their learning. Also, the resources listed at the end of each chapter include links to websites and other useful educational videos.
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Feature boxes that help students think outside the box
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A variety of feature boxes within the chapters connect astronomy to the students’ other subjects and humanize the face of astronomy by highlighting the lives of the men and women who have been key to its progress. Besides the math examples that we’ve already mentioned, the boxes include:
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Making Connections. This feature connects the chapter topic to students’ experiences with other fields, from poetry to engineering, popular culture, and natural disasters. Voyagers in Astronomy. This feature presents brief and engaging biographies of the people behind historically significant discoveries, as well as emerging research. Astronomy Basics. This feature explains basic science concepts that we often (incorrectly) assume students know from earlier classes. Seeing for Yourself. This feature provides practical ways that students can make astronomical observations on their own.
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End-of-chapter materials to extend students’ learning
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Chapter Summaries. Summaries give the gist of each section for easy review. For Further Exploration. This section offers a list of suggested articles, websites, and videos so students can delve into topics of interest, whether for their own learning, for homework, extra credit, or papers. Review Questions. Review questions allow students to show you (or themselves) how well they understood the chapter. Thought Questions. Thought questions help students assess their learning by asking for critical reflection on principles or ideas in the chapter. Figuring For Yourself. Mathematical questions, using only basic algebra and arithmetic, allow students to apply the math principles given in the example boxes throughout the chapter. Collaborative Group Activities. This section suggests ideas for group discussion, research, or reports.
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Beautiful art program
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Our comprehensive art program is designed to enhance students’ understanding of concepts through clear and effective illustrations, diagrams, and photographs. Here are a few examples.
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4 Preface Figure 1 How a Pulsar Beam Sweeps over Earth.
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Figure 2 Structure of the Milky Way Galaxy. Access for free at openstax.org
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Preface 5 Figure 3 Masses in the Stellar Graveyard.
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Figure 4 Pluto Close Up.
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6 Preface
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Additional resources
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Student and instructor resources We’ve compiled additional resources for both students and instructors, including Getting Started Guides, PowerPoint slides, and an instructor answer guide. Instructor resources require a verified instructor account, which you can apply for when you log in or create your account on OpenStax.org. Take advantage of these resources to supplement your OpenStax book. Community Hubs OpenStax partners with the Institute for the Study of Knowledge Management in Education (ISKME) to offer Community Hubs on OER Commons – a platform for instructors to share community-created resources that support OpenStax books, free of charge. Through our Community Hubs, instructors can upload their own materials or download resources to use in their own courses, including additional ancillaries, teaching material, multimedia, and relevant course content. We encourage instructors to join the hubs for the subjects most relevant to your teaching and research as an opportunity both to enrich your courses and to engage with other faculty. To reach the Community Hubs, visit https://www.oercommons.org/groups/openstax-astronomy/ 1283/?__hub_id=27 (https://www.oercommons.org/groups/openstax-astronomy/1283/?__hub_id=27). Partner resources OpenStax Partners are our allies in the mission to make high-quality learning materials affordable and accessible to students and instructors everywhere. Their tools integrate seamlessly with our OpenStax titles at a low cost. To access the partner resources for your text, visit your book page on OpenStax.org.
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About the authors
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Senior contributing authors
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Figure 5 Senior contributing authors: Andrew Fraknoi (left), David Morrison (center), Sidney C. Wolff (right)
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Andrew Fraknoi, Fromm Institute, University of San Francisco Andrew Fraknoi retired as Chair of the Astronomy Department at Foothill College in 2017 and now teaches courses for older adults at the University of San Francisco and San Francisco State University. He served as the Executive Director of the Astronomical Society of the Pacific from 1978–1992. His work with the society included editing Mercury Magazine, the Universe in the Classroom newsletter, and Astronomy Beat. He is editor/co-author of The Universe at Your Fingertips 2.0, a collection of teaching activities, and co-author of Solar Science, a book for middle-school teachers. He was also co-author of a syndicated newspaper column on astronomy, and appears regularly on local and national radio. With Sidney Wolff, he was founder of the refereed journal, Astronomy Education Review. In addition, he has organized six national symposia on teaching introductory astronomy, and for 10 years, has led the AAS Ambassadors workshops, training young astronomers to be better at outreach. He received the AAS Education Award, the Klumpke-Roberts Prize of the
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Access for free at openstax.org
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Preface 7
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ASP, the Gemant Prize of the American Institute of Physics, and the Faraday Award of the NSTA.
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David Morrison, NASA (Emeritus) and SETI Institute David Morrison received his PhD in astronomy from Harvard, where he was one of Carl Sagan’s graduate students. He is a founder of the field of astrobiology and is known for research on small bodies in the solar system (Asteroid 2410 Morrison is named for him). He spent his early career at University of Hawaii’s Institute for Astronomy, where he was Director of the IRTF at Maunakea Observatory. Morrison has held senior NASA positions including Director of Space Research at Ames Research Center, Chief of the Space Science Division, and founding Director of the Lunar Science Institute. He’s been on science teams for the Voyager, Galileo, and Kepler missions, and he received NASA Outstanding Leadership Medals and Exceptional Achievement Medal. His contributions to public understanding of science have been recognized by education prizes from the Astronomical Society of the Pacific, the American Astronomical Society, and NASA. Committed to the struggle against pseudoscience, he serves as Contributing Editor of Skeptical Inquirer.
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Sidney C. Wolff, NOIRLab (Emerita) After receiving her PhD from the UC Berkeley, Dr. Wolff was involved with the astronomical development of Maunakea. In 1984, she became the Director of Kitt Peak National Observatory, and was director of National Optical Astronomy Observatory. She led the design and development phases of the Gemini Observatory and the Rubin Observatory. Most recently, she has worked on plans for user support for the next generation of large ground-based telescopes. Dr. Wolff has published over ninety refereed papers on star formation and stellar atmospheres. She has served as President of the AAS and the ASP. Her book, The Boundless Universe: Astronomy in the New Age of Discovery, won the 2016 IPPY (Independent Publisher Book Awards) Silver Medal in Science.
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All three senior contributing authors have received the Education Prize of the American Astronomical Society and have had an asteroid named after them by the International Astronomical Union. They have worked together on a series of astronomy textbooks over the past two decades.
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Contributing authors
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John Beck, Stanford University Susan D. Benecchi, Planetary Science Institute John Bochanski, Rider University Howard Bond, Pennsylvania State University, Emeritus, Space Telescope Science Institute Jennifer Carson, Occidental College Bryan Dunne, University of Illinois at Urbana-Champaign Martin Elvis, Harvard-Smithsonian Center for Astrophysics Debra Fischer, Yale University Heidi Hammel, Association of Universities for Research in Astronomy Tori Hoehler, NASA Ames Research Center Douglas Ingram, Texas Christian University Steven Kawaler, Iowa State University Lloyd Knox, University of California, Davis Mark Krumholz, Australian National University James Lowenthal, Smith College Geoff Mathews, Foothill College Siobahn Morgan, University of Northern Iowa Daniel Perley, California Institute of Technology Claire Raftery, National Solar Observatory Deborah Scherrer, retired, Stanford University Phillip Scherrer, Stanford University Sanjoy Som, Blue Marble Space Institute of Science, NASA Ames Research Center
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8 Preface
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Wes Tobin, Indiana University East William H. Waller, retired, Tufts University, Rockport (MA) Public Schools Todd Young, Wayne State College
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Reviewers
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Elisabeth R. Adams, Planetary Science Institute Alfred N. Alaniz, San Antonio College Charles Allison, Texas A&M University–Kingsville Douglas Arion, Carthage College Timothy Barker, Wheaton College Marshall Bartlett, The Hockaday School Charles Benesh, Wesleyan College Gerald B. Cleaver, Baylor University Kristi Concannon, King’s College Anthony Crider, Elon University Scott Engle, Villanova University Matthew Fillingim, University of California, Berkeley Robert Fisher, University of Massachusetts, Dartmouth Carrie Fitzgerald, Montgomery College Christopher Fuse, Rollins College Shila Garg, Emeritus, The College of Wooster Richard Gelderman, Western Kentucky University Lee Hartman, University of Michigan Beth Hufnagel, Anne Arundel Community College Francine Jackson, Brown University Joseph Jensen, Utah Valley University John Kielkopf, University of Louisville James C. Lombardi, Jr., Allegheny College Amy Lovell, Agnes Scott College Charles Niederriter, Gustavus Adolphus College Richard Olenick, University of Dallas Matthew Olmstead, King’s College Zoran Pazameta, Eastern Connecticut State University David Quesada, Saint Thomas University Valerie A. Rapson, Dudley Observatory Joseph Ribaudo, Utica College Dean Richardson, Xavier University of Louisiana Andrew Rivers, Northwestern University Marc Sher, College of William & Mary Christopher Sirola, University of Southern Mississippi Ran Sivron, Baker University J. Allyn Smith, Austin Peay State University Jason Smolinski, Calvin College Michele Thornley, Bucknell University Richard Webb, Union College Terry Willis, Chesapeake College David Wood, San Antonio College Jeremy Wood, Hazard Community and Technical College Jared Workman, Colorado Mesa University Kaisa E. Young, Nicholls State University
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Access for free at openstax.org
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1 • Introduction
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9
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1 Science and the Universe: A Brief Tour
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Figure 1.1 Distant Galaxies. These two interacting islands of stars (galaxies) are so far away that their light takes hundreds of
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millions of years to reach us on Earth (photographed with the Hubble Space Telescope). (credit: modification of work by NASA, ESA, the Hubble Heritage (STScl/AURA)-ESA/Hubble Collaboration, and K. Noll (STScl))
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Chapter Outline
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1.1 The Nature of Astronomy 1.2 The Nature of Science 1.3 The Laws of Nature 1.4 Numbers in Astronomy 1.5 Consequences of Light Travel Time 1.6 A Tour of the Universe 1.7 The Universe on the Large Scale 1.8 The Universe of the Very Small 1.9 A Conclusion and a Beginning
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Introduction
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We invite you to come along on a series of voyages to explore the universe as astronomers understand it today. Beyond Earth are vast and magnificent realms full of objects that have no counterpart on our home planet. Nevertheless, we hope to show you that the evolution of the universe has been directly responsible for your presence on Earth today.
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Along your journey, you will encounter:
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• a canyon system so large that, on Earth, it would stretch from Los Angeles to Washington, DC (Figure 1.2).
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10 1 • Science and the Universe: A Brief Tour
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Figure 1.2 Mars Mosaic. This image of Mars is centered on the Valles Marineris (Mariner Valley) complex of canyons, which is as long as the United States is wide. (credit: modification of work by NASA)
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• a crater and other evidence on Earth that tell us that the dinosaurs (and many other creatures) died because of a cosmic collision.
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• a tiny moon whose gravity is so weak that one good throw from its surface could put a baseball into orbit. • a collapsed star so dense that to duplicate its interior we would have to squeeze every human being on
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Earth into a single raindrop. • exploding stars whose violent end could wipe clean all of the life-forms on a planet orbiting a neighboring
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star (Figure 1.3). • a “cannibal galaxy” that has already consumed a number of its smaller galaxy neighbors and is not yet
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finished finding new victims. • a radio echo that is the faint but unmistakable signal of the creation event for our universe.
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Figure 1.3 Stellar Corpse. We observe the remains of a star that was seen to explode in our skies in 1054 (and was, briefly, bright enough to be visible during the daytime). Today, the remnant is called the Crab Nebula and its central region is seen here. Such exploding stars are crucial to the development of life in the universe. (credit: NASA, ESA, J. Hester (Arizona State University))
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Such discoveries are what make astronomy such an exciting field for scientists and many others—but you will
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Access for free at openstax.org
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1.1 • The Nature of Astronomy 11
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explore much more than just the objects in our universe and the latest discoveries about them. We will pay equal attention to the process by which we have come to understand the realms beyond Earth and the tools we use to increase that understanding.
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We gather information about the cosmos from the messages the universe sends our way. Because the stars are the fundamental building blocks of the universe, decoding the message of starlight has been a central challenge and triumph of modern astronomy. By the time you have finished reading this text, you will know a bit about how to read that message and how to understand what it is telling us.
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1.1 The Nature of Astronomy
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Astronomy is defined as the study of the objects that lie beyond our planet Earth and the processes by which these objects interact with one another. We will see, though, that it is much more. It is also humanity’s attempt to organize what we learn into a clear history of the universe, from the instant of its birth in the Big Bang to the present moment. Throughout this book, we emphasize that science is a progress report—one that changes constantly as new techniques and instruments allow us to probe the universe more deeply.
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In considering the history of the universe, we will see again and again that the cosmos evolves; it changes in profound ways over long periods of time. For example, the universe made the carbon, the calcium, and the oxygen necessary to construct something as interesting and complicated as you. Today, many billions of years later, the universe has evolved into a more hospitable place for life. Tracing the evolutionary processes that continue to shape the universe is one of the most important (and satisfying) parts of modern astronomy.
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1.2 The Nature of Science
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The ultimate judge in science is always what nature itself reveals based on observations, experiments, models, and testing. Science is not merely a body of knowledge, but a method by which we attempt to understand nature and how it behaves. This method begins with many observations over a period of time. From the trends found through observations, scientists can model the particular phenomena we want to understand. Such models are always approximations of nature, subject to further testing.
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As a concrete astronomical example, ancient astronomers constructed a model (partly from observations and partly from philosophical beliefs) that Earth was the center of the universe and everything moved around it in circular orbits. At first, our available observations of the Sun, Moon, and planets did fit this model; however, after further observations, the model had to be updated by adding circle after circle to represent the movements of the planets around Earth at the center. As the centuries passed and improved instruments were developed for keeping track of objects in the sky, the old model (even with a huge number of circles) could no longer explain all the observed facts. As we will see in the chapter on Observing the Sky: The Birth of Astronomy, a new model, with the Sun at the center, fit the experimental evidence better. After a period of philosophical struggle, it became accepted as our view of the universe.
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When they are first proposed, new models or ideas are sometimes called hypotheses. You may think there can be no new hypotheses in a science such as astronomy—that everything important has already been learned. Nothing could be further from the truth. Throughout this textbook you will find discussions of recent, and occasionally still controversial, hypotheses in astronomy. For example, the significance that the huge chunks of rock and ice that hit Earth have for life on Earth itself is still debated. And while the evidence is strong that vast quantities of invisible “dark energy” make up the bulk of the universe, scientists have no convincing explanation for what the dark energy actually is. Resolving these issues will require difficult observations done at the forefront of our technology, and all such hypotheses need further testing before we incorporate them fully into our standard astronomical models.
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This last point is crucial: a hypothesis must be a proposed explanation that can be tested. The most straightforward approach to such testing in science is to perform an experiment. If the experiment is
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12 1 • Science and the Universe: A Brief Tour
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conducted properly, its results either will agree with the predictions of the hypothesis or they will contradict it. If the experimental result is truly inconsistent with the hypothesis, a scientist must discard the hypothesis and try to develop an alternative. If the experimental result agrees with predictions, this does not necessarily prove that the hypothesis is absolutely correct; perhaps later experiments will contradict crucial parts of the hypothesis. But, the more experiments that agree with the hypothesis, the more likely we are to accept the hypothesis as a useful description of nature.
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One way to think about this is to consider a scientist who was born and lives on an island where only black sheep live. Day after day the scientist encounters black sheep only, so he or she hypothesizes that all sheep are black. Although every observed sheep adds confidence to the hypothesis, the scientist only has to visit the mainland and observe one white sheep to prove the hypothesis wrong.
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When you read about experiments, you probably have a mental picture of a scientist in a laboratory conducting tests or taking careful measurements. This is certainly the case for a biologist or a chemist, but what can astronomers do when our laboratory is the universe? It’s impossible to put a group of stars into a test tube or to order another comet from a scientific supply company.
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As a result, astronomy is sometimes called an observational science; we often make our tests by observing many samples of the kind of object we want to study and noting carefully how different samples vary. New instruments and technology can let us look at astronomical objects from new perspectives and in greater detail. Our hypotheses are then judged in the light of this new information, and they pass or fail in the same way we would evaluate the result of a laboratory experiment.
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Much of astronomy is also a historical science—meaning that what we observe has already happened in the universe and we can do nothing to change it. In the same way, a geologist cannot alter what has happened to our planet, and a paleontologist cannot bring an ancient animal back to life. While this can make astronomy challenging, it also gives us fascinating opportunities to discover the secrets of our cosmic past.
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You might compare an astronomer to a detective trying to solve a crime that occurred before the detective arrived at the scene. There is lots of evidence, but both the detective and the scientist must sift through and organize the evidence to test various hypotheses about what actually happened. And there is another way in which the scientist is like a detective: they both must prove their case. The detective must convince the district attorney, the judge, and perhaps ultimately the jury that his hypothesis is correct. Similarly, the scientist must convince colleagues, editors of journals, and ultimately a broad cross-section of other scientists that her hypothesis is provisionally correct. In both cases, one can only ask for evidence “beyond a reasonable doubt.” And sometimes new evidence will force both the detective and the scientist to revise their last hypothesis.
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This self-correcting aspect of science sets it off from most human activities. Scientists spend a great deal of time questioning and challenging one another, which is why applications for project funding—as well as reports for publication in academic journals—go through an extensive process of peer review, which is a careful examination by other scientists in the same field. In science (after formal education and training), everyone is encouraged to improve upon experiments and to challenge any and all hypotheses. New scientists know that one of the best ways to advance their careers is to find a weakness in our current understanding of something and to correct it with a new or modified hypothesis.
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This is one of the reasons science has made such dramatic progress. An undergraduate science major today knows more about science and math than did Sir Isaac Newton, one of the most renowned scientists who ever lived. Even in this introductory astronomy course, you will learn about objects and processes that no one a few generations ago even dreamed existed.
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1.3 The Laws of Nature
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Over centuries scientists have extracted various scientific laws from countless observations, hypotheses, and experiments. These scientific laws are, in a sense, the “rules” of the game that nature plays. One remarkable
|
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Access for free at openstax.org
|
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1.4 • Numbers in Astronomy 13
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discovery about nature—one that underlies everything you will read about in this text—is that the same laws apply everywhere in the universe. The rules that determine the motion of stars so far away that your eye cannot see them are the same laws that determine the arc of a baseball after a batter has hit it out of the park.
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Note that without the existence of such universal laws, we could not make much headway in astronomy. If each pocket of the universe had different rules, we would have little chance of interpreting what happened in other “neighborhoods.” But, the consistency of the laws of nature gives us enormous power to understand distant objects without traveling to them and learning the local laws. In the same way, if every region of a country had completely different laws, it would be very difficult to carry out commerce or even to understand the behavior of people in those different regions. A consistent set of laws, though, allows us to apply what we learn or practice in one state to any other state.
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This is not to say that our current scientific models and laws cannot change. New experiments and observations can lead to new, more sophisticated models—models that can include new phenomena and laws about their behavior. The general theory of relativity proposed by Albert Einstein is a perfect example of such a transformation that took place about a century ago; it led us to predict, and eventually to observe, a strange new class of objects that astronomers call black holes. Only the patient process of observing nature ever more carefully and precisely can demonstrate the validity of such new scientific models.
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One important problem in describing scientific models has to do with the limitations of language. When we try to describe complex phenomena in everyday terms, the words themselves may not be adequate to do the job. For example, you may have heard the structure of the atom likened to a miniature solar system. While some aspects of our modern model of the atom do remind us of planetary orbits, many other of its aspects are fundamentally different.
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This problem is the reason scientists often prefer to describe their models using equations rather than words. In this book, which is designed to introduce the field of astronomy, we use mainly words to discuss what scientists have learned. We avoid complex math, but if this course piques your interest and you go on in science, more and more of your studies will involve the precise language of mathematics.
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1.4 Numbers in Astronomy
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In astronomy we deal with distances on a scale you may never have thought about before, with numbers
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larger than any you may have encountered. We adopt two approaches that make dealing with astronomical
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numbers a little bit easier. First, we use a system for writing large and small numbers called scientific notation
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(or sometimes powers-of-ten notation). This system is very appealing because it eliminates the many zeros
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that can seem overwhelming to the reader. In scientific notation, if you want to write a number such as
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500,000,000, you express it as
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. The small raised number after the 10, called an exponent, keeps track of
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the number of places we had to move the decimal point to the left to convert 500,000,000 to 5. If you are
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encountering this system for the first time or would like a refresher, we suggest you look at Appendix C and
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Example 1.1 for more information. The second way we try to keep numbers simple is to use a consistent set of
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units—the metric International System of Units, or SI (from the French Système International d’Unités). The
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metric system is summarized in Appendix D (see Example 1.2).
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LINK TO LEARNING
|
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Watch this brief PBS animation (https://openstax.org/l/30scinotation) that explains how scientific notation works and why it’s useful.
|
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A common unit astronomers use to describe distances in the universe is a light-year, which is the distance light
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14 1 • Science and the Universe: A Brief Tour
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travels during one year. Because light always travels at the same speed, and because its speed turns out to be the fastest possible speed in the universe, it makes a good standard for keeping track of distances. You might be confused because a “light-year” seems to imply that we are measuring time, but this mix-up of time and distance is common in everyday life as well. For example, when your friend asks where the movie theater is located, you might say “about 20 minutes from downtown.”
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So, how many kilometers are there in a light-year? Light travels at the amazing pace of
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kilometers per
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second (km/s), which makes a light-year
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kilometers. You might think that such a large unit would
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reach the nearest star easily, but the stars are far more remote than our imaginations might lead us to believe.
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Even the nearest star is 4.3 light-years away—more than 40 trillion kilometers. Other stars visible to the
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unaided eye are hundreds to thousands of light-years away (Figure 1.4).
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Figure 1.4 Orion Nebula. This beautiful cloud of cosmic raw material (gas and dust from which new stars and planets are being
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made) called the Orion Nebula is about 1400 light-years away. That’s a distance of roughly
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kilometers—a pretty big
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number. The gas and dust in this region are illuminated by the intense light from a few extremely energetic adolescent stars. (credit:
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NASA, ESA, M. Robberto (Space Telescope Science Institute/ESA) and the Hubble Space Telescope Orion Treasury Project Team)
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EXAMPLE 1.1
|
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Scientific Notation
|
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In 2015, the richest human being on our planet had a net worth of $79.2 billion. Some might say this is an astronomical sum of money. Express this amount in scientific notation.
|
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Solution
|
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$79.2 billion can be written $79,200,000,000. Expressed in scientific notation it becomes
|
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EXAMPLE 1.2
|
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Getting Familiar with a Light-Year
|
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How many kilometers are there in a light-year?
|
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Access for free at openstax.org
|
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1.5 • Consequences of Light Travel Time 15
|
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Solution
|
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Light travels
|
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km in 1 s. So, let’s calculate how far it goes in a year:
|
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• There are 60 (
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) s in 1 min, and
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min in 1 h.
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• Multiply these together and you find that there are
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s/h.
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• Thus, light covers
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• There are 24 or
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h in a day, and 365.25 (
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) days in 1 y.
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• The product of these two numbers is
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h/y.
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• Multiplying this by
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km/h gives
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km/light-year.
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That’s almost 10,000,000,000,000 km that light covers in a year. To help you imagine how long this distance is, we’ll mention that a string 1 light-year long could fit around the circumference of Earth 236 million times.
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1.5 Consequences of Light Travel Time
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There is another reason the speed of light is such a natural unit of distance for astronomers. Information about the universe comes to us almost exclusively through various forms of light, and all such light travels at the speed of light—that is, 1 light-year every year. This sets a limit on how quickly we can learn about events in the universe. If a star is 100 light-years away, the light we see from it tonight left that star 100 years ago and is just now arriving in our neighborhood. The soonest we can learn about any changes in that star is 100 years after the fact. For a star 500 light-years away, the light we detect tonight left 500 years ago and is carrying 500-year-old news.
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Because many of us are accustomed to instant news from the Internet, some might find this frustrating.
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“You mean, when I see that star up there,” you ask, “I won’t know what’s actually happening there for another 500 years?”
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But this isn’t the most helpful way to think about the situation. For astronomers, now is when the light reaches us here on Earth. There is no way for us to know anything about that star (or other object) until its light reaches us.
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But what at first may seem a great frustration is actually a tremendous benefit in disguise. If astronomers really want to piece together what has happened in the universe since its beginning, they must find evidence about each epoch (or period of time) of the past. Where can we find evidence today about cosmic events that occurred billions of years ago?
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The delay in the arrival of light provides an answer to this question. The farther out in space we look, the longer the light has taken to get here, and the longer ago it left its place of origin. By looking billions of lightyears out into space, astronomers are actually seeing billions of years into the past. In this way, we can reconstruct the history of the cosmos and get a sense of how it has evolved over time.
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This is one reason why astronomers strive to build telescopes that can collect more and more of the faint light in the universe. The more light we collect, the fainter the objects we can observe. On average, fainter objects are farther away and can, therefore, tell us about periods of time even deeper in the past. Instruments such as the Hubble Space Telescope (Figure 1.5) and the Very Large Telescope in Chile (which you will learn about in the chapter on Astronomical Instruments), are giving astronomers views of deep space and deep time better than any we have had before.
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16 1 • Science and the Universe: A Brief Tour
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Figure 1.5 Telescope in Orbit. The Hubble Space Telescope, shown here in orbit around Earth, is one of many astronomical instruments in space. (credit: modification of work by European Space Agency)
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1.6 A Tour of the Universe
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We can now take a brief introductory tour of the universe as astronomers understand it today to get acquainted with the types of objects and distances you will encounter throughout the text. We begin at home with Earth, a nearly spherical planet about 13,000 kilometers in diameter (Figure 1.6). A space traveler entering our planetary system would easily distinguish Earth from the other planets in our solar system by the large amount of liquid water that covers some two thirds of its crust. If the traveler had equipment to receive radio or television signals, or came close enough to see the lights of our cities at night, she would soon find signs that this watery planet has sentient life.
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Figure 1.6 Humanity’s Home Base. This image shows the Western hemisphere as viewed from space 35,400 kilometers (about 22,000 miles) above Earth. Data about the land surface from one satellite was combined with another satellite’s data about the clouds to create the image. (credit: modification of work by R. Stockli, A. Nelson, F. Hasler, NASA/ GSFC/ NOAA/ USGS)
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Our nearest astronomical neighbor is Earth’s satellite, commonly called the Moon. Figure 1.7 shows Earth and the Moon drawn to scale on the same diagram. Notice how small we have to make these bodies to fit them on
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1.6 • A Tour of the Universe 17
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the page with the right scale. The Moon’s distance from Earth is about 30 times Earth’s diameter, or approximately 384,000 kilometers, and it takes about a month for the Moon to revolve around Earth. The Moon’s diameter is 3476 kilometers, about one fourth the size of Earth.
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Figure 1.7 Earth and Moon, Drawn to Scale. This image shows Earth and the Moon shown to scale for both size and distance. (credit: modification of work by NASA)
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Light (or radio waves) takes 1.3 seconds to travel between Earth and the Moon. If you’ve seen videos of the Apollo flights to the Moon, you may recall that there was a delay of about 3 seconds between the time Mission Control asked a question and the time the astronauts responded. This was not because the astronauts were thinking slowly, but rather because it took the radio waves almost 3 seconds to make the round trip.
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Earth revolves around our star, the Sun, which is about 150 million kilometers away—approximately 400 times as far away from us as the Moon. We call the average Earth–Sun distance an astronomical unit (AU) because, in the early days of astronomy, it was the most important measuring standard. Light takes slightly more than 8 minutes to travel 1 astronomical unit, which means the latest news we receive from the Sun is always 8 minutes old. The diameter of the Sun is about 1.5 million kilometers; Earth could fit comfortably inside one of the minor eruptions that occurs on the surface of our star. If the Sun were reduced to the size of a basketball, Earth would be a small apple seed about 30 meters from the ball. It takes Earth 1 year (3 × 107 seconds) to go around the Sun at our distance; to make it around, we must travel at approximately 110,000 kilometers per hour. (If you, like many students, still prefer miles to kilometers, you might find the following trick helpful. To convert kilometers to miles, just multiply kilometers by 0.6. Thus, 110,000 kilometers per hour becomes 66,000 miles per hour.) Because gravity holds us firmly to Earth and there is no resistance to Earth’s motion in the vacuum of space, we participate in this extremely fast-moving trip without being aware of it day to day.
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Earth is only one of eight planets that revolve around the Sun. These planets, along with their moons and swarms of smaller bodies such as dwarf planets, make up the solar system (Figure 1.8). A planet is defined as a body of significant size that orbits a star and does not produce its own light. (If a large body consistently produces its own light, it is then called a star.) Later in the book this definition will be modified a bit, but it is perfectly fine for now as you begin your voyage.
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18 1 • Science and the Universe: A Brief Tour
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Figure 1.8 Our Solar Family. The Sun, the planets, and some dwarf planets are shown with their sizes drawn to scale. The orbits of the planets are much more widely separated than shown in this drawing. Notice the size of Earth compared to the giant planets. (credit: modification of work by NASA)
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We are able to see the nearby planets in our skies only because they reflect the light of our local star, the Sun. If the planets were much farther away, the tiny amount of light they reflect would usually not be visible to us. The planets we have so far discovered orbiting other stars were found from the pull their gravity exerts on their parent stars, or from the light they block from their stars when they pass in front of them. We can’t see most of these planets directly, although a few are now being imaged directly. The Sun is our local star, and all the other stars are also enormous balls of glowing gas that generate vast amounts of energy by nuclear reactions deep within. We will discuss the processes that cause stars to shine in more detail later in the book. The other stars look faint only because they are so very far away. If we continue our basketball analogy, Proxima Centauri, the nearest star beyond the Sun, which is 4.3 light-years away, would be almost 7000 kilometers from the basketball. When you look up at a star-filled sky on a clear night, all the stars visible to the unaided eye are part of a single collection of stars we call the Milky Way Galaxy, or simply the Galaxy. (When referring to the Milky Way, we capitalize Galaxy; when talking about other galaxies of stars, we use lowercase galaxy.) The Sun is one of hundreds of billions of stars that make up the Galaxy; its extent, as we will see, staggers the human imagination. Within a sphere 10 light-years in radius centered on the Sun, we find roughly ten stars. Within a sphere 100 light-years in radius, there are roughly 10,000 (104) stars—far too many to count or name—but we have still traversed only a tiny part of the Milky Way Galaxy. Within a 1000-light-year sphere, we find some ten million (107) stars; within a sphere of 100,000 light-years, we finally encompass the entire Milky Way Galaxy. Our Galaxy looks like a giant disk with a small ball in the middle. If we could move outside our Galaxy and look down on the disk of the Milky Way from above, it would probably resemble the galaxy in Figure 1.9, with its spiral structure outlined by the blue light of hot adolescent stars.
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1.6 • A Tour of the Universe 19
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Figure 1.9 Spiral Galaxy. This galaxy of billions of stars, called by its catalog number NGC 1073, is thought to be similar to our own Milky Way Galaxy. Here we see the giant wheel-shaped system with a bar of stars across its middle. (credit: NASA, ESA)
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The Sun is somewhat less than 30,000 light-years from the center of the Galaxy, in a location with nothing much to distinguish it. From our position inside the Milky Way Galaxy, we cannot see through to its far rim (at least not with ordinary light) because the space between the stars is not completely empty. It contains a sparse distribution of gas (mostly the simplest element, hydrogen) intermixed with tiny solid particles that we call interstellar dust. This gas and dust collect into enormous clouds in many places in the Galaxy, becoming the raw material for future generations of stars. Figure 1.10 shows an image of the disk of the Galaxy as seen from our vantage point.
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20 1 • Science and the Universe: A Brief Tour
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Figure 1.10 Milky Way Galaxy. Because we are inside the Milky Way Galaxy, we see its disk in cross-section flung across the sky like a great milky white avenue of stars with dark “rifts” of dust. In this dramatic image, part of it is seen above Trona Pinnacles in the California desert. (credit: Ian Norman)
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Typically, the interstellar material is so extremely sparse that the space between stars is a much better vacuum than anything we can produce in terrestrial laboratories. Yet, the dust in space, building up over thousands of light-years, can block the light of more distant stars. Like the distant buildings that disappear from our view on a smoggy day in Los Angeles, the more distant regions of the Milky Way cannot be seen behind the layers of interstellar smog. Luckily, astronomers have found that stars and raw material shine with various forms of light, some of which do penetrate the smog, and so we have been able to develop a pretty good map of the Galaxy. Recent observations, however, have also revealed a rather surprising and disturbing fact. There appears to be more—much more—to the Galaxy than meets the eye (or the telescope). From various investigations, we have evidence that much of our Galaxy is made of material we cannot currently observe directly with our instruments. We therefore call this component of the Galaxy dark matter. We know the dark matter is there by the pull its gravity exerts on the stars and raw material we can observe, but what this dark matter is made of and how much of it exists remain a mystery. Furthermore, this dark matter is not confined to our Galaxy; it appears to be an important part of other star groupings as well. By the way, not all stars live by themselves, as the Sun does. Many are born in double or triple systems with two, three, or more stars revolving about each other. Because the stars influence each other in such close systems, multiple stars allow us to measure characteristics that we cannot discern from observing single stars. In a number of places, enough stars have formed together that we recognized them as star clusters (Figure 1.11). Some of the largest of the star clusters that astronomers have cataloged contain hundreds of thousands of stars and take up volumes of space hundreds of light-years across.
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1.7 • The Universe on the Large Scale 21
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Figure 1.11 Star Cluster. This large star cluster is known by its catalog number, M9. It contains some 250,000 stars and is seen more clearly from space using the Hubble Space Telescope. It is located roughly 25,000 light-years away. (credit: NASA, ESA)
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You may hear stars referred to as “eternal,” but in fact no star can last forever. Since the “business” of stars is making energy, and energy production requires some sort of fuel to be used up, eventually all stars run out of fuel. This news should not cause you to panic, though, because our Sun still has at least 5 or 6 billion years to go. Ultimately, the Sun and all stars will die, and it is in their death throes that some of the most intriguing and important processes of the universe are revealed. For example, we now know that many of the atoms in our bodies were once inside stars. These stars exploded at the ends of their lives, recycling their material back into the reservoir of the Galaxy. In this sense, all of us are literally made of recycled “star dust.”
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1.7 The Universe on the Large Scale
|
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In a very rough sense, you could think of the solar system as your house or apartment and the Galaxy as your town, made up of many houses and buildings. In the twentieth century, astronomers were able to show that, just as our world is made up of many, many towns, so the universe is made up of enormous numbers of galaxies. (We define the universe to be everything that exists that is accessible to our observations.) Galaxies stretch as far into space as our telescopes can see, many billions of them within the reach of modern instruments. When they were first discovered, some astronomers called galaxies island universes, and the term is aptly descriptive; galaxies do look like islands of stars in the vast, dark seas of intergalactic space. The nearest galaxy, discovered in 1993, is a small one that lies 70,000 light-years from the Sun in the direction of the constellation Sagittarius, where the smog in our own Galaxy makes it especially difficult to discern. (A constellation, we should note, is one of the 88 sections into which astronomers divide the sky, each named after a prominent star pattern within it.) Beyond this Sagittarius dwarf galaxy lie two other small galaxies, about 160,000 light-years away. First recorded by Magellan’s crew as he sailed around the world, these are called the Magellanic Clouds (Figure 1.12). All three of these small galaxies are satellites of the Milky Way Galaxy, interacting with it through the force of gravity. Ultimately, all three may even be swallowed by our much larger Galaxy, as other small galaxies have been over the course of cosmic time.
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22 1 • Science and the Universe: A Brief Tour
|
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Figure 1.12 Neighbor Galaxies. This image shows both the Large Magellanic Cloud and the Small Magellanic Cloud above the telescopes of the Atacama Large Millimeter/Submillimeter Array (ALMA) in the Atacama Desert of northern Chile. (credit: ESO, C. Malin)
|
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The nearest large galaxy is a spiral quite similar to our own, located in the constellation of Andromeda, and is thus called the Andromeda galaxy; it is also known by one of its catalog numbers, M31 (Figure 1.13). M31 is a little more than 2 million light-years away and, along with the Milky Way, is part of a small cluster of more than 50 galaxies referred to as the Local Group.
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1.7 • The Universe on the Large Scale 23
|
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Figure 1.13 Closest Spiral Galaxy. The Andromeda galaxy (M31) is a spiral-shaped collection of stars similar to our own Milky Way. (credit: Adam Evans)
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At distances of 10 to 15 million light-years, we find other small galaxy groups, and then at about 50 million light-years there are more impressive systems with thousands of member galaxies. We have discovered that galaxies occur mostly in clusters, both large and small (Figure 1.14).
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24 1 • Science and the Universe: A Brief Tour
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Figure 1.14 Fornax Cluster of Galaxies. In this image, you can see part of a cluster of galaxies located about 60 million light-years away in the constellation of Fornax. All the objects that are not pinpoints of light in the picture are galaxies of billions of stars. (credit: ESO, J. Emerson, VISTA. Acknowledgment: Cambridge Astronomical Survey Unit)
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Some of the clusters themselves form into larger groups called superclusters. The Local Group is part of a supercluster of galaxies, called the Virgo Supercluster, which stretches over a diameter of 110 million lightyears. We are just beginning to explore the structure of the universe at these enormous scales and are already encountering some unexpected findings. At even greater distances, where many ordinary galaxies are too dim to see, we find quasars. These are brilliant centers of galaxies, glowing with the light of an extraordinarily energetic process. The enormous energy of the quasars is produced by gas that is heated to a temperature of millions of degrees as it falls toward a massive black hole and swirls around it. The brilliance of quasars makes them the most distant beacons we can see in the dark oceans of space. They allow us to probe the universe 10 billion light-years away or more, and thus 10 billion years or more in the past. With quasars we can see way back close to the Big Bang explosion that marks the beginning of time. Beyond the quasars and the most distant visible galaxies, we have detected the feeble glow of the explosion itself, filling the universe and thus coming to us from all directions in space. The discovery of this “afterglow of creation” is considered to be one of the most significant events in twentieth-century science, and we are still exploring the many things it has to tell us about the earliest times of the universe. Measurements of the properties of galaxies and quasars in remote locations require large telescopes, sophisticated light-amplifying devices, and painstaking labor. Every clear night, at observatories around the world, astronomers and students are at work on such mysteries as the birth of new stars and the large-scale structure of the universe, fitting their results into the tapestry of our understanding.
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1.8 The Universe of the Very Small
|
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The foregoing discussion has likely impressed on you that the universe is extraordinarily large and extraordinarily empty. On average, it is 10,000 times more empty than our Galaxy. Yet, as we have seen, even
|
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1.8 • The Universe of the Very Small 25
|
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the Galaxy is mostly empty space. The air we breathe has about 1019 atoms in each cubic centimeter—and we usually think of air as empty space. In the interstellar gas of the Galaxy, there is about one atom in every cubic centimeter. Intergalactic space is filled so sparsely that to find one atom, on average, we must search through a cubic meter of space. Most of the universe is fantastically empty; places that are dense, such as the human body, are tremendously rare.
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Even our most familiar solids are mostly space. If we could take apart such a solid, piece by piece, we would eventually reach the tiny molecules from which it is formed. Molecules are the smallest particles into which any matter can be divided while still retaining its chemical properties. A molecule of water (H2O), for example, consists of two hydrogen atoms and one oxygen atom bonded together.
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Molecules, in turn, are built of atoms, which are the smallest particles of an element that can still be identified as that element. For example, an atom of gold is the smallest possible piece of gold. Nearly 100 different kinds of atoms (elements) exist in nature. Most of them are rare, and only a handful account for more than 99% of everything with which we come in contact. The most abundant elements in the cosmos today are listed in Table 1.1; think of this table as the “greatest hits” of the universe when it comes to elements. Note that the list includes the four elements most common in life on Earth—hydrogen, carbon, nitrogen, and oxygen.
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The Cosmically Abundant Elements
|
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Element1
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Symbol Number of Atoms per Million Hydrogen Atoms
|
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Hydrogen H
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1,000,000
|
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Helium
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He
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80,000
|
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Carbon
|
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C
|
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450
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Nitrogen
|
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N
|
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92
|
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Oxygen
|
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O
|
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740
|
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Neon
|
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Ne
|
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130
|
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Magnesium Mg
|
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40
|
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Silicon
|
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Si
|
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37
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Sulfur
|
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S
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19
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Iron
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Fe
|
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32
|
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Table 1.1
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All atoms consist of a central, positively charged nucleus surrounded by negatively charged electrons. The bulk of the matter in each atom is found in the nucleus, which consists of positive protons and electrically neutral neutrons all bound tightly together in a very small space. Each element is defined by the number of protons in its atoms. Thus, any atom with 6 protons in its nucleus is called carbon, any with 50 protons is called tin, and
|
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1 This list of elements is arranged in order of the atomic number, which is the number of protons in each nucleus.
|
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26 1 • Science and the Universe: A Brief Tour
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any with 70 protons is called ytterbium. (For a list of the elements, see Appendix K.) The distance from an atomic nucleus to its electrons is typically 100,000 times the size of the nucleus itself. This is why we say that even solid matter is mostly space. The typical atom is far emptier than the solar system out to Neptune. (The distance from Earth to the Sun, for example, is only 100 times the size of the Sun.) This is one reason atoms are not like miniature solar systems. Remarkably, physicists have discovered that everything that happens in the universe, from the smallest atomic nucleus to the largest superclusters of galaxies, can be explained through the action of only four forces: gravity, electromagnetism (which combines the actions of electricity and magnetism), and two forces that act at the nuclear level. The fact that there are four forces (and not a million, or just one) has puzzled physicists and astronomers for many years and has led to a quest for a unified picture of nature.
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LINK TO LEARNING
|
|||
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To construct an atom, particle by particle, check out this guided animation (https://openstax.org/l/ 30buildanatom) for building an atom.
|
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1.9 A Conclusion and a Beginning
|
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If you are new to astronomy, you have probably reached the end of our brief tour in this chapter with mixed emotions. On the one hand, you may be fascinated by some of the new ideas you’ve read about and you may be eager to learn more. On the other hand, you may be feeling a bit overwhelmed by the number of topics we have covered, and the number of new words and ideas we have introduced. Learning astronomy is a little like learning a new language: at first it seems there are so many new expressions that you’ll never master them all, but with practice, you soon develop facility with them. At this point you may also feel a bit small and insignificant, dwarfed by the cosmic scales of distance and time. But, there is another way to look at what you have learned from our first glimpses of the cosmos. Let us consider the history of the universe from the Big Bang to today and compress it, for easy reference, into a single year. (We have borrowed this idea from Carl Sagan’s 1977 Pulitzer Prize-winning book, The Dragons of Eden.) On this scale, the Big Bang happened at the first moment of January 1, and this moment, when you are reading this chapter would be the end of the very last second of December 31. When did other events in the development of the universe happen in this “cosmic year?” Our solar system formed around September 10, and the oldest rocks we can date on Earth go back to the third week in September (Figure 1.15).
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1.9 • A Conclusion and a Beginning 27
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Figure 1.15 Charting Cosmic Time. On a cosmic calendar, where the time since the Big Bang is compressed into 1 year, creatures we would call human do not emerge on the scene until the evening of December 31. (credit: February: modification of work by NASA, JPL-Caltech, W. Reach (SSC/Caltech); March: modification of work by ESA, Hubble and NASA, Acknowledgement: Giles Chapdelaine; April: modification of work by NASA, ESA, CFHT, CXO, M.J. Jee (University of California, Davis), A. Mahdavi (San Francisco State University); May: modification of work by NASA, JPL-Caltech; June: modification of work by NASA/ESA; July: modification of work by NASA, JPL-Caltech, Harvard-Smithsonian; August: modification of work by NASA, JPL-Caltech, R. Hurt (SSC-Caltech); September: modification of work by NASA; October: modification of work by NASA; November: modification of work by Dénes Emőke)
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Where does the origin of human beings fall during the course of this cosmic year? The answer turns out to be the evening of December 31. The invention of the alphabet doesn’t occur until the fiftieth second of 11:59 p.m. on December 31. And the beginnings of modern astronomy are a mere fraction of a second before the New Year. Seen in a cosmic context, the amount of time we have had to study the stars is minute, and our success in piecing together as much of the story as we have is remarkable. Certainly our attempts to understand the universe are not complete. As new technologies and new ideas allow us to gather more and better data about the cosmos, our present picture of astronomy will very likely undergo many changes. Still, as you read our current progress report on the exploration of the universe, take a few minutes every once in a while just to savor how much you have already learned.
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28 1 • For Further Exploration
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For Further Exploration
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Books Miller, Ron, and William Hartmann. The Grand Tour: A Traveler’s Guide to the Solar System. 3rd ed. Workman, 2005. This volume for beginners is a colorfully illustrated voyage among the planets. Sagan, Carl. Cosmos. Ballantine, 2013 [1980]. This tome presents a classic overview of astronomy by an astronomer who had a true gift for explaining things clearly. (You can also check out Sagan’s television series Cosmos: A Personal Voyage and Neil DeGrasse Tyson’s current series Cosmos: A Spacetime Odyssey.) Tyson, Neil DeGrasse, and Don Goldsmith. Origins: Fourteen Billion Years of Cosmic Evolution. Norton, 2004. This book provides a guided tour through the beginnings of the universe, galaxies, stars, planets, and life. Websites If you enjoyed the beautiful images in this chapter (and there are many more fabulous photos to come in other chapters), you may want to know where you can obtain and download such pictures for your own enjoyment. (Many astronomy images are from government-supported instruments or projects, paid for by tax dollars, and therefore are free of copyright laws.) Here are three resources we especially like: • Astronomy Picture of the Day: apod.nasa.gov/apod/astropix.html (https://apod.nasa.gov/apod/astropix.html). Two space scientists scour the Internet and select one beautiful astronomy image to feature each day. Their archives range widely, from images of planets and nebulae to rockets and space instruments; they also have many photos of the night sky. The search function (see the menu on the bottom of the page) works quite well for finding something specific among the many years’ worth of daily images. • Hubble Space Telescope Images: https://www.spacetelescope.org/images/ (https://www.spacetelescope.org/ images/). Here you can browse some of the remarkable images, select a particular subject in the menu boxes, or search for the name of an object that intrigues you in this book. • National Aeronautics and Space Administration’s (NASA’s) Planetary Photojournal: photojournal.jpl.nasa.gov (https://photojournal.jpl.nasa.gov). This site features thousands of images from planetary exploration, with captions of varied length. You can select images by world, feature name, date, or catalog number, and download images in a number of popular formats. However, only NASA mission images are included. Note the Photojournal Search option on the menu at the top of the homepage to access ways to search their archives. Videos Powers of Ten: www.youtube.com/watch?v=0fKBhvDjuy0 (https://www.youtube.com/watch?v=0fKBhvDjuy0). This classic short video is a much earlier version of Powers of Ten, narrated by Philip Morrison (9:00). The Known Universe: www.youtube.com/watch?v=17jymDn0W6U (https://www.youtube.com/ watch?v=17jymDn0W6U). This video tour from the American Museum of Natural History has realistic animation, music, and captions (6:30). Wanderers: apod.nasa.gov/apod/ap141208.html (https://apod.nasa.gov/apod/ap141208.html). This video provides a tour of the solar system, with narrative by Carl Sagan, imagining other worlds with dramatically realistic paintings (3:50).
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2 • Thinking Ahead
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29
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2 Observing the Sky: The Birth of Astronomy
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Figure 2.1 Night Sky. In this panoramic photograph of the night sky from the Atacama Desert in Chile, we can see the central
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portion of the Milky Way Galaxy arcing upward in the center of the frame. On the left, the Large Magellanic Cloud and the Small Magellanic Cloud (smaller galaxies that orbit the Milky Way Galaxy) are easily visible from the Southern Hemisphere. (credit: modification of work by ESO/Y. Beletsky)
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Chapter Outline
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2.1 The Sky Above 2.2 Ancient Astronomy 2.3 Astrology and Astronomy 2.4 The Birth of Modern Astronomy
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Thinking Ahead
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Much to your surprise, a member of the Flat Earth Society moves in next door. He believes that Earth is flat and all the NASA images of a spherical Earth are either faked or simply show the round (but flat) disk of Earth from above. How could you prove to your new neighbor that Earth really is a sphere? (When you’ve thought about this on your own, you can check later in the chapter for some suggested answers.)
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Today, few people really spend much time looking at the night sky. In ancient days, before electric lights robbed so many people of the beauty of the sky, the stars and planets were an important aspect of everyone’s daily life. All the records that we have—on paper and in stone—show that ancient civilizations around the world noticed, worshipped, and tried to understand the lights in the sky and fit them into their own view of the world. These ancient observers found both majestic regularity and never-ending surprise in the motions of the heavens. Through their careful study of the planets, the Greeks and later the Romans laid the foundation of the science of astronomy.
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30 2 • Observing the Sky: The Birth of Astronomy
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2.1 The Sky Above
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Learning Objectives
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By the end of this section, you will be able to: Define the main features of the celestial sphere Explain the system astronomers use to describe the sky Describe how motions of the stars appear to us on Earth Describe how motions of the Sun, Moon, and planets appear to us on Earth Understand the modern meaning of the term constellation
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Our senses suggest to us that Earth is the center of the universe—the hub around which the heavens turn. This geocentric (Earth-centered) view was what almost everyone believed until the European Renaissance. After all, it is simple, logical, and seemingly self-evident. Furthermore, the geocentric perspective reinforced those philosophical and religious systems that taught the unique role of human beings as the central focus of the cosmos. However, the geocentric view happens to be wrong. One of the great themes of our intellectual history is the overthrow of the geocentric perspective. Let us, therefore, take a look at the steps by which we reevaluated the place of our world in the cosmic order.
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The Celestial Sphere
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If you go on a camping trip or live far from city lights, your view of the sky on a clear night is pretty much identical to that seen by people all over the world before the invention of the telescope. Gazing up, you get the impression that the sky is a great hollow dome with you at the center (Figure 2.2), and all the stars are an equal distance from you on the surface of the dome. The top of that dome, the point directly above your head, is called the zenith, and where the dome meets Earth is called the horizon. From the sea or a flat prairie, it is easy to see the horizon as a circle around you, but from most places where people live today, the horizon is at least partially hidden by mountains, trees, buildings, or smog.
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Figure 2.2 The Sky around Us. The horizon is where the sky meets the ground; an observer’s zenith is the point directly overhead.
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If you lie back in an open field and observe the night sky for hours, as ancient shepherds and travelers regularly did, you will see stars rising on the eastern horizon (just as the Sun and Moon do), moving across the dome of the sky in the course of the night, and setting on the western horizon. Watching the sky turn like this night after night, you might eventually get the idea that the dome of the sky is really part of a great sphere that is turning around you, bringing different stars into view as it turns. The early Greeks regarded the sky as
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2.1 • The Sky Above 31
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just such a celestial sphere (Figure 2.3). Some thought of it as an actual sphere of transparent crystalline material, with the stars embedded in it like tiny jewels.
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Figure 2.3 Circles on the Celestial Sphere. Here we show the (imaginary) celestial sphere around Earth, on which objects are fixed, and which rotates around Earth on an axis. In reality, it is Earth that turns around this axis, creating the illusion that the sky revolves around us. Note that Earth in this picture has been tilted so that your location is at the top and the North Pole is where the N is. The apparent motion of celestial objects in the sky around the pole is shown by the circular arrow.
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Today, we know that it is not the celestial sphere that turns as night and day proceed, but rather the planet on which we live. We can put an imaginary stick through Earth’s North and South Poles, representing our planet’s axis. It is because Earth turns on this axis every 24 hours that we see the Sun, Moon, and stars rise and set with clockwork regularity. Today, we know that these celestial objects are not really on a dome, but at greatly varying distances from us in space. Nevertheless, it is sometimes still convenient to talk about the celestial dome or sphere to help us keep track of objects in the sky. There is even a special theater, called a planetarium, in which we project a simulation of the stars and planets onto a white dome. As the celestial sphere rotates, the objects on it maintain their positions with respect to one another. A grouping of stars such as the Big Dipper has the same shape during the course of the night, although it turns with the sky. During a single night, even objects we know to have significant motions of their own, such as the nearby planets, seem fixed relative to the stars. Only meteors—brief “shooting stars” that flash into view for just a few seconds—move appreciably with respect to other objects on the celestial sphere. (This is because they are not stars at all. Rather, they are small pieces of cosmic dust, burning up as they hit Earth’s atmosphere.) We can use the fact that the entire celestial sphere seems to turn together to help us set up systems for keeping track of what things are visible in the sky and where they happen to be at a given time.
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Celestial Poles and Celestial Equator
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To help orient us in the turning sky, astronomers use a system that extends Earth’s axis points into the sky.
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32 2 • Observing the Sky: The Birth of Astronomy
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Imagine a line going through Earth, connecting the North and South Poles. This is Earth’s axis, and Earth rotates about this line. If we extend this imaginary line outward from Earth, the points where this line intersects the celestial sphere are called the north celestial pole and the south celestial pole. As Earth rotates about its axis, the sky appears to turn in the opposite direction around those celestial poles (Figure 2.4). We also (in our imagination) throw Earth’s equator onto the sky and call this the celestial equator. It lies halfway between the celestial poles, just as Earth’s equator lies halfway between our planet’s poles.
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Figure 2.4 Circling the South Celestial Pole. This long-exposure photo shows trails left by stars as a result of the apparent rotation of the celestial sphere around the south celestial pole. (In reality, it is Earth that rotates.) (Credit: ESO/Iztok Bončina)
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Now let’s imagine how riding on different parts of our spinning Earth affects our view of the sky. The apparent motion of the celestial sphere depends on your latitude (position north or south of the equator). First of all, notice that Earth’s axis is pointing at the celestial poles, so these two points in the sky do not appear to turn. If you stood at the North Pole of Earth, for example, you would see the north celestial pole overhead, at your zenith. The celestial equator, 90° from the celestial poles, would lie along your horizon. As you watched the stars during the course of the night, they would all circle around the celestial pole, with none rising or setting. Only that half of the sky north of the celestial equator is ever visible to an observer at the North Pole. Similarly, an observer at the South Pole would see only the southern half of the sky. If you were at Earth’s equator, on the other hand, you see the celestial equator (which, after all, is just an “extension” of Earth’s equator) pass overhead through your zenith. The celestial poles, being 90° from the celestial equator, must then be at the north and south points on your horizon. As the sky turns, all stars rise and set; they move straight up from the east side of the horizon and set straight down on the west side. During a 24-hour period, all stars are above the horizon exactly half the time. (Of course, during some of those hours, the Sun is too bright for us to see them.) What would an observer in the latitudes of the United States or Europe see? Remember, we are neither at Earth’s pole nor at the equator, but in between them. For those in the continental United States and Europe, the north celestial pole is neither overhead nor on the horizon, but in between. It appears above the northern horizon at an angular height, or altitude, equal to the observer’s latitude. In San Francisco, for example, where the latitude is 38° N, the north celestial pole is 38° above the northern horizon. For an observer at 38° N latitude, the south celestial pole is 38° below the southern horizon and, thus, never visible. As Earth turns, the whole sky seems to pivot about the north celestial pole. For this observer, stars within 38° of the North Pole can never set. They are always above the horizon, day and night. This part of the
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2.1 • The Sky Above 33
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sky is called the north circumpolar zone. For observers in the continental United States, the Big Dipper, Little Dipper, and Cassiopeia are examples of star groups in the north circumpolar zone. On the other hand, stars within 38° of the south celestial pole never rise. That part of the sky is the south circumpolar zone. To most U.S. observers, the Southern Cross is in that zone. (Don’t worry if you are not familiar with the star groups just mentioned; we will introduce them more formally later on.)
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At this particular time in Earth’s history, there happens to be a star very close to the north celestial pole. It is called Polaris, the pole star, and has the distinction of being the star that moves the least amount as the northern sky turns each day. Because it moved so little while the other stars moved much more, it played a special role in the mythology of several Native American tribes, for example (some called it the “fastener of the sky”).
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ASTRONOMY BASICS
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What’s Your Angle?
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Astronomers measure how far apart objects appear in the sky by using angles. By definition, there are 360° in a circle, so a circle stretching completely around the celestial sphere contains 360°. The half-sphere or dome of the sky then contains 180° from horizon to opposite horizon. Thus, if two stars are 18° apart, their separation spans about 1/10 of the dome of the sky. To give you a sense of how big a degree is, the full Moon is about half a degree across. This is about the width of your smallest finger (pinkie) seen at arm’s length.
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Rising and Setting of the Sun
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We described the movement of stars in the night sky, but what about during the daytime? The stars continue to circle during the day, but the brilliance of the Sun makes them difficult to see. (The Moon can often be seen in the daylight, however.) On any given day, we can think of the Sun as being located at some position on the hypothetical celestial sphere. When the Sun rises—that is, when the rotation of Earth carries the Sun above the horizon—sunlight is scattered by the molecules of our atmosphere, filling our sky with light and hiding the stars above the horizon.
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For thousands of years, astronomers have been aware that the Sun does more than just rise and set. It changes position gradually on the celestial sphere, moving each day about 1° to the east relative to the stars. Very reasonably, the ancients thought this meant the Sun was slowly moving around Earth, taking a period of time we call 1 year to make a full circle. Today, of course, we know it is Earth that is going around the Sun, but the effect is the same: the Sun’s position in our sky changes day to day. We have a similar experience when we walk around a campfire at night; we see the flames appear in front of each person seated about the fire in turn.
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The path the Sun appears to take around the celestial sphere each year is called the ecliptic (Figure 2.6). Because of its motion on the ecliptic, the Sun rises about 4 minutes later each day with respect to the stars. Earth must make just a bit more than one complete rotation (with respect to the stars) to bring the Sun up again.
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34 2 • Observing the Sky: The Birth of Astronomy
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Figure 2.5 Star Circles at Different Latitudes. The turning of the sky looks different depending on your latitude on Earth. The red circle in each case is your horizon. Your zenith is the point above your head. (a) At the North Pole, the stars circle the zenith and do not rise and set. (b) At the equator, the celestial poles are on the horizon, and the stars rise straight up and set straight down. (c) At intermediate latitudes, the north celestial pole is at some position between overhead and the horizon. Its angle above the horizon turns out to be equal to the observer’s latitude. Stars rise and set at an angle to the horizon.
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As the months go by and we look at the Sun from different places in our orbit, we see it projected against different places in our orbit, and thus against different stars in the background (Figure 2.6 and Table 2.1)—or we would, at least, if we could see the stars in the daytime. In practice, we must deduce which stars lie behind and beyond the Sun by observing the stars visible in the opposite direction at night. After a year, when Earth has completed one trip around the Sun, the Sun will appear to have completed one circuit of the sky along the ecliptic.
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Figure 2.6 Constellations on the Ecliptic. As Earth revolves around the Sun, we sit on “platform Earth” and see the Sun moving Access for free at openstax.org
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2.1 • The Sky Above 35
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around the sky. The circle in the sky that the Sun appears to make around us in the course of a year is called the ecliptic. This circle (like all circles in the sky) goes through a set of constellations. The ancients thought these constellations, which the Sun (and the Moon and planets) visited, must be special and incorporated them into their system of astrology. Note that at any given time of the year, some of the constellations crossed by the ecliptic are visible in the night sky; others are in the day sky and are thus hidden by the brilliance of the Sun. (The term constellation will be defined more precisely in the next subsection.)
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Constellations on the Ecliptic
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Constellation on the Ecliptic Dates When the Sun Crosses It
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Capricornus
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January 21–February 16
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Aquarius
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February 16–March 11
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Pisces
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March 11–April 18
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Aries
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April 18–May 13
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Taurus
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May 13–June 22
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Gemini
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June 22–July 21
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Cancer
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July 21–August 10
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Leo
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August 10–September 16
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Virgo
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September 16–October 31
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Libra
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October 31–November 23
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Scorpius
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November 23–November 29
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Ophiuchus
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November 29–December 18
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Sagittarius
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December 18–January 21
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Table 2.1
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The ecliptic does not lie along the celestial equator but is inclined to it at an angle of about 23.5°. In other words, the Sun’s annual path in the sky is not linked with Earth’s equator. This is because our planet’s axis of rotation is tilted by about 23.5° from a vertical line sticking out of the plane of the ecliptic (Figure 2.7). Being tilted from “straight up” is not at all unusual among celestial bodies; Uranus and Pluto are actually tilted so much that they orbit the Sun “on their side.”
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36 2 • Observing the Sky: The Birth of Astronomy
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Figure 2.7 The Celestial Tilt. The celestial equator is tilted by 23.5° to the ecliptic. As a result, North Americans and Europeans see the Sun north of the celestial equator and high in our sky in June, and south of the celestial equator and low in the sky in December.
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The inclination of the ecliptic is the reason the Sun moves north and south in the sky as the seasons change. In Earth, Moon, and Sky, we discuss the progression of the seasons in more detail.
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Fixed and Wandering Stars
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The Sun is not the only object that moves among the fixed stars. The Moon and each of the planets that are visible to the unaided eye—Mercury, Venus, Mars, Jupiter, Saturn, and Uranus (although just barely)—also change their positions slowly from day to day. During a single day, the Moon and planets all rise and set as Earth turns, just as the Sun and stars do. But like the Sun, they have independent motions among the stars, superimposed on the daily rotation of the celestial sphere. Noticing these motions, the Greeks of 2000 years ago distinguished between what they called the fixed stars—those that maintain fixed patterns among themselves through many generations—and the wandering stars, or planets. The word “planet,” in fact, means “wanderer” in ancient Greek. Today, we do not regard the Sun and Moon as planets, but the ancients applied the term to all seven of the moving objects in the sky. Much of ancient astronomy was devoted to observing and predicting the motions of these celestial wanderers. They even dedicated a unit of time, the week, to the seven objects that move on their own; that’s why there are 7 days in a week. The Moon, being Earth’s nearest celestial neighbor, has the fastest apparent motion; it completes a trip around the sky in about 1 month (or moonth). To do this, the Moon moves about 12°, or 24 times its own apparent width on the sky, each day.
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2.1 • The Sky Above 37
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EXAMPLE 2.1
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Angles in the Sky
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A circle consists of 360 degrees (°). When we measure the angle in the sky that something moves, we can use this formula:
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This is true whether the motion is measured in kilometers per hour or degrees per hour; we just need to use consistent units.
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As an example, let’s say you notice the bright star Sirius due south from your observing location in the Northern Hemisphere. You note the time, and then later, you note the time that Sirius sets below the horizon. You find that Sirius has traveled an angular distance of about 75° in 5 h. About how many hours will it take for Sirius to return to its original location?
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Solution
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The speed of Sirius is
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If we want to know the time required for Sirius to return to its original
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location, we need to wait until it goes around a full circle, or 360°. Rearranging the formula for speed we
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were originally given, we find:
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The actual time is a few minutes shorter than this, and we will explore why in a later chapter.
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Check Your Learning
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The Moon moves in the sky relative to the background stars (in addition to moving with the stars as a result of Earth’s rotation.) Go outside at night and note the position of the Moon relative to nearby stars. Repeat the observation a few hours later. How far has the Moon moved? (For reference, the diameter of the Moon is about 0.5°.) Based on your estimate of its motion, how long will it take for the Moon to return to the position relative to the stars in which you first observed it?
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Answer:
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The speed of the moon is 0.5°/1 h. To move a full 360°, the moon needs 720 h:
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720 h by the conversion factor of 24 h/day reveals the lunar cycle is about 30 days.
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Dividing
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The individual paths of the Moon and planets in the sky all lie close to the ecliptic, although not exactly on it. This is because the paths of the planets about the Sun, and of the Moon about Earth, are all in nearly the same plane, as if they were circles on a huge sheet of paper. The planets, the Sun, and the Moon are thus always found in the sky within a narrow 18-degree-wide belt, centered on the ecliptic, called the zodiac (Figure 2.6). (The root of the term “zodiac” is the same as that of the word “zoo” and means a collection of animals; many of the patterns of stars within the zodiac belt reminded the ancients of animals, such as a fish or a goat.)
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How the planets appear to move in the sky as the months pass is a combination of their actual motions plus the motion of Earth about the Sun; consequently, their paths are somewhat complex. As we will see, this complexity has fascinated and challenged astronomers for centuries.
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Constellations
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The backdrop for the motions of the “wanderers” in the sky is the canopy of stars. If there were no clouds in the sky and we were on a flat plain with nothing to obstruct our view, we could see about 3000 stars with the
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38 2 • Observing the Sky: The Birth of Astronomy
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unaided eye. To find their way around such a multitude, the ancients found groupings of stars that made some familiar geometric pattern or (more rarely) resembled something they knew. Each civilization found its own patterns in the stars, much like a modern Rorschach test in which you are asked to discern patterns or pictures in a set of inkblots. The ancient Chinese, Egyptians, and Greeks, among others, found their own groupings—or constellations—of stars. These were helpful in navigating among the stars and in passing their star lore on to their children. You may be familiar with some of the old star patterns we still use today, such as the Big Dipper, Little Dipper, and Orion the hunter, with his distinctive belt of three stars (Figure 2.8). However, many of the stars we see are not part of a distinctive star pattern at all, and a telescope reveals millions of stars too faint for the eye to see. Therefore, during the early decades of the 20th century, astronomers from many countries decided to establish a more formal system for organizing the sky.
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Figure 2.8 Orion. (a) The winter constellation of Orion, the hunter, is surrounded by neighboring constellations, as illustrated in the seventeenth-century atlas by Hevelius. (b) A photograph shows the Orion region in the sky. Note the three blue stars that make up the belt of the hunter. The bright red star above the belt denotes his armpit and is called Betelgeuse (pronounced “Beetel-juice”). The bright blue star below the belt is his foot and is called Rigel. (credit a: modification of work by Johannes Hevelius; b: modification of work by Matthew Spinelli)
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Today, we use the term constellation to mean one of 88 sectors into which we divide the sky, much as the United States is divided into 50 states. The modern boundaries between the constellations are imaginary lines in the sky running north–south and east–west, so that each point in the sky falls in a specific constellation, although, like the states, not all constellations are the same size. All the constellations are listed in Appendix L. Whenever possible, we have named each modern constellation after the Latin translations of one of the ancient Greek star patterns that lies within it. Thus, the modern constellation of Orion is a kind of box on the sky, which includes, among many other objects, the stars that made up the ancient picture of the hunter. Some people use the term asterism to denote an especially noticeable star pattern within a constellation (or sometimes spanning parts of several constellations). For example, the Big Dipper is an asterism within the constellation of Ursa Major, the Big Bear. Students are sometimes puzzled because the constellations seldom resemble the people or animals for which they were named. In all likelihood, the Greeks themselves did not name groupings of stars because they looked like actual people or subjects (any more than the outline of Washington state resembles George Washington). Rather, they named sections of the sky in honor of the characters in their mythology and then fit the star configurations to the animals and people as best they could.
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2.2 • Ancient Astronomy 39
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LINK TO LEARNING
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This website about objects in the sky (https://openstax.org/l/30heavensabove) allows users to construct a detailed sky map showing the location and information about the Sun, Moon, planets, stars, constellations, and even satellites orbiting Earth. Begin by setting your observing location using the option in the menu in the upper right corner of the screen. An excellent website called Figures in the Sky (https://openstax.org/l/ 30constel) shows the constellation figures imagined by cultures around the world.
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2.2 Ancient Astronomy
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Learning Objectives
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By the end of this section, you will be able to: Describe early examples of astronomy around the world Explain how Greek astronomers were able to deduce that Earth is spherical Explain how Greek astronomers were able to calculate Earth’s size Describe the motion of Earth called precession Describe Ptolemy’s geocentric system of planetary motion
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Let us now look briefly back into history. Much of modern Western civilization is derived in one way or another from the ideas of the ancient Greeks and Romans, and this is true in astronomy as well. However, many other ancient cultures also developed sophisticated systems for observing and interpreting the sky.
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Astronomy around the World
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Ancient Babylonian, Assyrian, and Egyptian astronomers knew the approximate length of the year. The Egyptians of 3000 years ago, for example, adopted a calendar based on a 365-day year. They kept careful track of the rising time of the bright star Sirius in the predawn sky, which has a yearly cycle that corresponded with the flooding of the Nile River. The Chinese also had a working calendar; they determined the length of the year at about the same time as the Egyptians. The Chinese also recorded comets, bright meteors, and dark spots on the Sun. (Many types of astronomical objects were introduced in Science and the Universe: A Brief Tour. If you are not familiar with terms like comets and meteors, you may want to review that chapter.) Later, Chinese astronomers kept careful records of “guest stars”—those that are normally too faint to see but suddenly flare up to become visible to the unaided eye for a few weeks or months. We still use some of these records in studying stars that exploded a long time ago.
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The Mayan culture in Mexico and Central America developed a sophisticated calendar based on the planet Venus, and they made astronomical observations from sites dedicated to this purpose a thousand years ago. The Polynesians learned to navigate by the stars over hundreds of kilometers of open ocean—a skill that enabled them to colonize new islands far away from where they began.
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In Britain, before the widespread use of writing, ancient people used stones to keep track of the motions of the Sun and Moon. We still find some of the great stone circles they built for this purpose, dating from as far back as 2800 BCE. The best known of these is Stonehenge, which is discussed in Earth, Moon, and Sky.1
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Early Greek and Roman Cosmology
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Our concept of the cosmos—its basic structure and origin—is called cosmology, a word with Greek roots. Before the invention of telescopes, humans had to depend on the simple evidence of their senses for a picture of the universe. The ancients developed cosmologies that combined their direct view of the heavens with a
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1 For resources providing more information about the astronomy of diverse cultures around the world, please see http://bit.ly/ astrocultures (http://bit.ly/astrocultures).
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40 2 • Observing the Sky: The Birth of Astronomy
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rich variety of philosophical and religious symbolism.
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At least 2000 years before Columbus, educated people in the eastern Mediterranean region knew Earth was round. Belief in a spherical Earth may have stemmed from the time of Pythagoras, a philosopher and mathematician who lived 2500 years ago. He believed circles and spheres to be “perfect forms” and suggested that Earth should therefore be a sphere. As evidence that the gods liked spheres, the Greeks cited the fact that the Moon is a sphere, using evidence we describe later.
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The writings of Aristotle (384–322 BCE), the tutor of Alexander the Great, summarize many of the ideas of his day. They describe how the progression of the Moon’s phases—its apparent changing shape—results from our seeing different portions of the Moon’s sunlit hemisphere as the month goes by (see Earth, Moon, and Sky). Aristotle also knew that the Sun has to be farther away from Earth than is the Moon because occasionally the Moon passed exactly between Earth and the Sun and hid the Sun temporarily from view. We call this a solar eclipse.
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Aristotle cited convincing arguments that Earth must be round. First is the fact that as the Moon enters or emerges from Earth’s shadow during an eclipse of the Moon, the shape of the shadow seen on the Moon is always round (Figure 2.9). Only a spherical object always produces a round shadow. If Earth were a disk, for example, there would be some occasions when the sunlight would strike it edge-on and its shadow on the Moon would be a line.
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Figure 2.9 Earth’s Round Shadow. A lunar eclipse occurs when the Moon moves into and out of Earth’s shadow. Note the curved shape of the shadow—evidence for a spherical Earth that has been recognized since antiquity. (credit: modification of work by Brian Paczkowski)
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As a second argument, Aristotle explained that travelers who go south a significant distance are able to observe stars that are not visible farther north. And the height of the North Star—the star nearest the north celestial pole—decreases as a traveler moves south. On a flat Earth, everyone would see the same stars overhead. The only possible explanation is that the traveler must have moved over a curved surface on Earth, showing stars from a different angle. (See the How Do We Know Earth Is Round? feature for more ideas on proving Earth is round.)
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One Greek thinker, Aristarchus of Samos (310–230 BCE), even suggested that Earth was moving around the Sun, but Aristotle and most of the ancient Greek scholars rejected this idea. One of the reasons for their conclusion was the thought that if Earth moved about the Sun, they would be observing the stars from different places along Earth’s orbit. As Earth moved along, nearby stars should shift their positions in the sky relative to more distant stars. In a similar way, we see foreground objects appear to move against a more distant background whenever we are in motion. When we ride on a train, the trees in the foreground appear to shift their position relative to distant hills as the train rolls by. Unconsciously, we use this phenomenon all of the time to estimate distances around us.
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The apparent shift in the direction of an object as a result of the motion of the observer is called parallax. We call the shift in the apparent direction of a star due to Earth’s orbital motion stellar parallax. The Greeks made dedicated efforts to observe stellar parallax, even enlisting the aid of Greek soldiers with the clearest vision, but to no avail. The brighter (and presumably nearer) stars just did not seem to shift as the Greeks observed them in the spring and then again in the fall (when Earth is on the opposite side of the Sun).
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This meant either that Earth was not moving or that the stars had to be so tremendously far away that the parallax shift was immeasurably small. A cosmos of such enormous extent required a leap of imagination that most ancient philosophers were not prepared to make, so they retreated to the safety of the Earth-centered view, which would dominate Western thinking for nearly two millennia.
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Access for free at openstax.org
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2.2 • Ancient Astronomy 41
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ASTRONOMY BASICS
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How Do We Know Earth Is Round?
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In addition to the two ways (from Aristotle’s writings) discussed in this chapter, you might also reason as follows: 1. Let’s watch a ship leave its port and sail into the distance on a clear day. On a flat Earth, we would just
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see the ship get smaller and smaller as it sails away. But this isn’t what we actually observe. Instead, ships sink below the horizon, with the hull disappearing first and the mast remaining visible for a while longer. Eventually, only the top of the mast can be seen as the ship sails around the curvature of Earth. Finally, the ship disappears under the horizon. 2. The International Space Station circles Earth once every 90 minutes or so. Photographs taken from the shuttle and other satellites show that Earth is round from every perspective. 3. Suppose you made a friend in each time zone of Earth. You call all of them at the same hour and ask, “Where is the Sun?” On a flat Earth, each caller would give you roughly the same answer. But on a round Earth you would find that, for some friends, the Sun would be high in the sky whereas for others it would be rising, setting, or completely out of sight (and this last group of friends would be upset with you for waking them up).
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Measurement of Earth by Eratosthenes
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The Greeks not only knew Earth was round, but also they were able to measure its size. The first fairly accurate determination of Earth’s diameter was made in about 200 BCE by Eratosthenes (276–194 BCE), a Greek living in Alexandria, Egypt. His method was a geometric one, based on observations of the Sun. The Sun is so distant from us that all the light rays that strike our planet approach us along essentially parallel lines. To see why, look at Figure 2.10. Take a source of light near Earth—say, at position A. Its rays strike different parts of Earth along diverging paths. From a light source at B, or at C (which is still farther away), the angle between rays that strike opposite parts of Earth is smaller. The more distant the source, the smaller the angle between the rays. For a source infinitely distant, the rays travel along parallel lines.
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Figure 2.10 Light Rays from Space. The more distant an object, the more nearly parallel the rays of light coming from it.
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Of course, the Sun is not infinitely far away, but given its distance of 150 million kilometers, light rays striking Earth from a point on the Sun diverge from one another by an angle far too small to be observed with the unaided eye. As a consequence, if people all over Earth who could see the Sun were to point at it, their fingers would, essentially, all be parallel to one another. (The same is also true for the planets and stars—an idea we will use in our discussion of how telescopes work.) Eratosthenes was told that on the first day of summer at Syene, Egypt (near modern Aswan), sunlight struck
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42 2 • Observing the Sky: The Birth of Astronomy
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the bottom of a vertical well at noon. This indicated that the Sun was directly over the well—meaning that Syene was on a direct line from the center of Earth to the Sun. At the corresponding time and date in Alexandria, Eratosthenes observed the shadow a column made and saw that the Sun was not directly overhead, but was slightly south of the zenith, so that its rays made an angle with the vertical equal to about 1/50 of a circle (7°). Because the Sun’s rays striking the two cities are parallel to one another, why would the two rays not make the same angle with Earth’s surface? Eratosthenes reasoned that the curvature of the round Earth meant that “straight up” was not the same in the two cities. And the measurement of the angle in Alexandria, he realized, allowed him to figure out the size of Earth. Alexandria, he saw, must be 1/50 of Earth’s circumference north of Syene (Figure 2.11). Alexandria had been measured to be 5000 stadia north of Syene. (The stadium was a Greek unit of length, derived from the length of the racetrack in a stadium.) Eratosthenes thus found that Earth’s circumference must be 50 × 5000, or 250,000 stadia.
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Figure 2.11 How Eratosthenes Measured the Size of Earth. Eratosthenes measured the size of Earth by observing the angle at which the Sun’s rays hit our planet’s surface. The Sun’s rays come in parallel, but because Earth’s surface curves, a ray at Syene comes straight down whereas a ray at Alexandria makes an angle of 7° with the vertical. That means, in effect, that at Alexandria, Earth’s surface has curved away from Syene by 7° of 360°, or 1/50 of a full circle. Thus, the distance between the two cities must be 1/ 50 the circumference of Earth. (credit: modification of work by NOAA Ocean Service Education)
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It is not possible to evaluate precisely the accuracy of Eratosthenes solution because there is doubt about which of the various kinds of Greek stadia he used as his unit of distance. If it was the common Olympic stadium, his result is about 20% too large. According to another interpretation, he used a stadium equal to about 1/6 kilometer, in which case his figure was within 1% of the correct value of 40,000 kilometers. Even if his measurement was not exact, his success at measuring the size of our planet by using only shadows, sunlight, and the power of human thought was one of the greatest intellectual achievements in history.
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Hipparchus and Precession
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Perhaps the greatest astronomer of antiquity was Hipparchus, born in Nicaea in what is present-day Turkey.
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Access for free at openstax.org
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2.2 • Ancient Astronomy 43
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He erected an observatory on the island of Rhodes around 150 BCE, when the Roman Republic was expanding its influence throughout the Mediterranean region. There he measured, as accurately as possible, the positions of objects in the sky, compiling a pioneering star catalog with about 850 entries. He designated celestial coordinates for each star, specifying its position in the sky, just as we specify the position of a point on Earth by giving its latitude and longitude. He also divided the stars into apparent magnitudes according to their apparent brightness. He called the brightest ones “stars of the first magnitude”; the next brightest group, “stars of the second magnitude”; and so forth. This rather arbitrary system, in modified form, still remains in use today (although it is less and less useful for professional astronomers). By observing the stars and comparing his data with older observations, Hipparchus made one of his most remarkable discoveries: the position in the sky of the north celestial pole had altered over the previous century and a half. Hipparchus deduced correctly that this had happened not only during the period covered by his observations, but was in fact happening all the time: the direction around which the sky appears to rotate changes slowly but continuously. Recall from the section on celestial poles and the celestial equator that the north celestial pole is just the projection of Earth’s North Pole into the sky. If the north celestial pole is wobbling around, then Earth itself must be doing the wobbling. Today, we understand that the direction in which Earth’s axis points does indeed change slowly but regularly—a motion we call precession. If you have ever watched a spinning top wobble, you observed a similar kind of motion. The top’s axis describes a path in the shape of a cone, as Earth’s gravity tries to topple it (Figure 2.12).
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Figure 2.12 Precession. Just as the axis of a rapidly spinning top wobbles slowly in a circle, so the axis of Earth wobbles in a 26,000-year cycle. Today the north celestial pole is near the star Polaris, but about 5000 years ago it was close to a star called Thuban, and in 14,000 years it will be closest to the star Vega.
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Because our planet is not an exact sphere, but bulges a bit at the equator, the pulls of the Sun and Moon cause it to wobble like a top. It takes about 26,000 years for Earth’s axis to complete one circle of precession. As a result of this motion, the point where our axis points in the sky changes as time goes on. While Polaris is the star closest to the north celestial pole today (it will reach its closest point around the year 2100), the star Vega in the constellation of Lyra will be the North Star in 14,000 years.
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44 2 • Observing the Sky: The Birth of Astronomy
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Ptolemy’s Model of the Solar System
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The last great astronomer of the Roman era was Claudius Ptolemy (or Ptolemaeus), who flourished in Alexandria in about the year 140. He wrote a mammoth compilation of astronomical knowledge, which today is called by its Arabic name, Almagest (meaning “The Greatest”). Almagest does not deal exclusively with Ptolemy’s own work; it includes a discussion of the astronomical achievements of the past, principally those of Hipparchus. Today, it is our main source of information about the work of Hipparchus and other Greek astronomers. Ptolemy’s most important contribution was a geometric representation of the solar system that predicted the positions of the planets for any desired date and time. Hipparchus, not having enough data on hand to solve the problem himself, had instead amassed observational material for posterity to use. Ptolemy supplemented this material with new observations of his own and produced a cosmological model that endured more than a thousand years, until the time of Copernicus. The complicating factor in explaining the motions of the planets is that their apparent wandering in the sky results from the combination of their own motions with Earth’s orbital revolution. As we watch the planets from our vantage point on the moving Earth, it is a little like watching a car race while you are competing in it. Sometimes opponents’ cars pass you, but at other times you pass them, making them appear to move backward for a while with respect to you. Figure 2.13 shows the motion of Earth and a planet farther from the Sun—in this case, Mars. Earth travels around the Sun in the same direction as the other planet and in nearly the same plane, but its orbital speed is faster. As a result, it overtakes the planet periodically, like a faster race car on the inside track. The figure shows where we see the planet in the sky at different times. The path of the planet among the stars is illustrated in the star field on the right side of the figure.
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Figure 2.13 Retrograde Motion of a Planet beyond Earth’s Orbit. The letters on the diagram show where Earth and Mars are at different times. By following the lines from each Earth position through each corresponding Mars position, you can see how the retrograde path of Mars looks against the background stars.
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2.2 • Ancient Astronomy 45
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LINK TO LEARNING
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The planetary configurations simulator from Foothill AstroSims (https://openstax.org/l/30planetconfig) allows you to see the usual prograde and occasional retrograde motion of other planets. You can switch back and forth between viewing motion from Earth and Mars (as well as other planets).
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Normally, planets move eastward in the sky over the weeks and months as they orbit the Sun, but from positions B to D in Figure 2.13, as Earth passes the planets in our example, it appears to drift backward, moving west in the sky. Even though it is actually moving to the east, the faster-moving Earth has overtaken it and seems, from our perspective, to be leaving it behind. As Earth rounds its orbit toward position E, the planet again takes up its apparent eastward motion in the sky. The temporary apparent westward motion of a planet as Earth swings between it and the Sun is called retrograde motion. Such backward motion is much easier for us to understand today, now that we know Earth is one of the moving planets and not the unmoving center of all creation. But Ptolemy was faced with the far more complex problem of explaining such motion while assuming a stationary Earth. Furthermore, because the Greeks believed that celestial motions had to be circles, Ptolemy had to construct his model using circles alone. To do it, he needed dozens of circles, some moving around other circles, in a complex structure that makes a modern viewer dizzy. But we must not let our modern judgment cloud our admiration for Ptolemy’s achievement. In his day, a complex universe centered on Earth was perfectly reasonable and, in its own way, quite beautiful. However, as Alfonso X, the King of Castile, was reported to have said after having the Ptolemaic system of planet motions explained to him, “If the Lord Almighty had consulted me before embarking upon Creation, I should have recommended something simpler.” Ptolemy solved the problem of explaining the observed motions of planets by having each planet revolve in a small orbit called an epicycle. The center of the epicycle then revolved about Earth on a circle called a deferent (Figure 2.14). When the planet is at position x in Figure 2.14 on the epicycle orbit, it is moving in the same direction as the center of the epicycle; from Earth, the planet appears to be moving eastward. When the planet is at y, however, its motion is in the direction opposite to the motion of the epicycle’s center around Earth. By choosing the right combination of speeds and distances, Ptolemy succeeded in having the planet moving westward at the correct speed and for the correct interval of time, thus replicating retrograde motion with his model.
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Figure 2.14 Ptolemy’s Complicated Cosmological System. Each planet orbits around a small circle called an epicycle. Each epicycle orbits on a larger circle called the deferent. This system is not centered exactly on Earth but on an offset point called the equant. The
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46 2 • Observing the Sky: The Birth of Astronomy
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Greeks needed all this complexity to explain the actual motions in the sky because they believed that Earth was stationary and that all sky motions had to be circular.
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LINK TO LEARNING
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Use the Ptolemaic System simulator from Foothill AstroSims (https://openstax.org/l/30ptolemaic) to explore how Ptolemy's system of deferents and epicycles explained the apparent motion of the planets.
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However, we shall see in Orbits and Gravity that the planets, like Earth, travel about the Sun in orbits that are ellipses, not circles. Their actual behavior cannot be represented accurately by a scheme of uniform circular motions. In order to match the observed motions of the planets, Ptolemy had to center the deferent circles, not on Earth, but at points some distance from Earth. In addition, he introduced uniform circular motion around yet another axis, called the equant point. All of these considerably complicated his scheme.
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It is a tribute to the genius of Ptolemy as a mathematician that he was able to develop such a complex system to account successfully for the observations of planets. It may be that Ptolemy did not intend for his cosmological model to describe reality, but merely to serve as a mathematical representation that allowed him to predict the positions of the planets at any time. Whatever his thinking, his model, with some modifications, was eventually accepted as authoritative in the Muslim world and (later) in Christian Europe.
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2.3 Astrology and Astronomy
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Learning Objectives
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By the end of this section, you will be able to: Explain the origins of astrology Explain what a horoscope is Summarize the arguments that invalidate astrology as a scientific practice
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Many ancient cultures regarded the planets and stars as representatives or symbols of the gods or other supernatural forces that controlled their lives. For them, the study of the heavens was not an abstract subject; it was connected directly to the life-and-death necessity of understanding the actions of the gods and currying favor with them. Before the time of our scientific perspectives, everything that happened in nature—from the weather, to diseases and accidents, to celestial surprises such as eclipses or new comets—was thought to be an expression of the whims or displeasure of the gods. Any signs that helped people understand what these gods had in mind were considered extremely important.
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The movements of the seven objects that had the power to “wander” through the realm of the sky—the Sun, the Moon, and five planets visible to the unaided eye—clearly must have special significance in such a system of thinking.
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Most ancient cultures associated these seven objects with various supernatural rulers in their pantheon and kept track of them for religious reasons. Even in the comparatively sophisticated Greece of antiquity, the planets had the names of gods and were credited with having the same powers and influences as the gods whose names they bore. From such ideas was born the ancient system called astrology, still practiced by some people today, in which the positions of these bodies among the stars of the zodiac are thought to hold the key to understanding what we can expect from life.
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The Beginnings of Astrology
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Astrology began in Babylonia about two and half millennia ago. The Babylonians, believing the planets and their motions influenced the fortunes of kings and nations, used their knowledge of astronomy to guide their rulers. When the Babylonian culture was absorbed by the Greeks, astrology gradually came to influence the
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2.3 • Astrology and Astronomy 47
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entire Western world and eventually spread to Asia as well. By the 2nd century BCE the Greeks democratized astrology by developing the idea that the planets influence every individual. In particular, they believed that the configuration of the Sun, Moon, and planets at the moment of birth affected a person’s personality and fortune—a doctrine called natal astrology. Natal astrology reached its peak with Ptolemy 400 years later. As famous for his astrology as for his astronomy, Ptolemy compiled the Tetrabiblos, a treatise on astrology that remains the “bible” of the subject. It is essentially this ancient religion, older than Christianity or Islam, that is still practiced by today’s astrologers.
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The Horoscope
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The key to natal astrology is the horoscope, a chart showing the positions of the planets in the sky at the moment of an individual’s birth. The word “horoscope” comes from the Greek words hora (meaning “time”) and skopos (meaning a “watcher” or “marker”), so “horoscope” can literally be translated as “marker of the hour.” When a horoscope is charted, the planets (including the Sun and Moon, classed as wanderers by the ancients) must first be located in the zodiac. At the time astrology was set up, the zodiac was divided into 12 sectors called signs (Figure 2.15), each 30° long. Each sign was named after a constellation in the sky through which the Sun, Moon, and planets were seen to pass—the sign of Virgo after the constellation of Virgo, for example.
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Figure 2.15 Zodiac Signs. The signs of the zodiac are shown in a medieval woodcut.
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When someone today casually asks you your “sign,” they are asking for your “sun sign”—which zodiac sign the Sun was in at the moment you were born. However, more than 2000 years have passed since the signs received their names from the constellations. Because of precession, the constellations of the zodiac slide westward along the ecliptic, going once around the sky in about 26,000 years. Thus, today the real stars have slipped around by about 1/12 of the zodiac—about the width of one sign. In most forms of astrology, however, the signs have remained assigned to the dates of the year they had when astrology was first set up. This means that the astrological signs and the real constellations are out of step; the sign of Aries, for example, now occupies the constellation of Pisces. When you look up your sun sign in a newspaper astrology column, the name of the sign associated with your birthday is no longer the name of the constellation in which the Sun was actually located when you were born. To know that constellation, you must
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48 2 • Observing the Sky: The Birth of Astronomy
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look for the sign before the one that includes your birthday.
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A complete horoscope shows the location of not only the Sun, but also the Moon and each planet in the sky by indicating its position in the appropriate sign of the zodiac. However, as the celestial sphere turns (owing to the rotation of Earth), the entire zodiac moves across the sky to the west, completing a circuit of the heavens each day. Thus, the position in the sky (or “house” in astrology) must also be calculated. There are more or less standardized rules for the interpretation of the horoscope, most of which (at least in Western schools of astrology) are derived from the Tetrabiblos of Ptolemy. Each sign, each house, and each planet—the last acting as a center of force—is supposed to be associated with particular matters in a person’s life.
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The detailed interpretation of a horoscope is a very complicated business, and there are many schools of astrological thought on how it should be done. Although some of the rules may be standardized, how each rule is to be weighed and applied is a matter of judgment—and “art.” It also means that it is very difficult to tie down astrology to specific predictions or to get the same predictions from different astrologers.
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Astrology Today
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Astrologers today use the same basic principles laid down by Ptolemy nearly 2000 years ago. They cast horoscopes (a process much simplified by the development of appropriate computer programs) and suggest interpretations. Sun sign astrology (which you read in the newspapers and many magazines) is a recent, simplified variant of natal astrology. Although even professional astrologers do not place much trust in such a limited scheme, which tries to fit everyone into just 12 groups, sun sign astrology is taken seriously by many people (perhaps because it is discussed so commonly in the media).
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Today, we know much more about the nature of the planets as physical bodies, as well as about human genetics, than the ancients could. It is hard to imagine how the positions of the Sun, Moon, or planets in the sky at the moment of our birth could have anything to do with our personality or future. There are no known forces, not gravity or anything else, that could cause such effects. (For example, a straightforward calculation shows that the gravitational pull of the obstetrician delivering a newborn baby is greater than that of Mars.) Astrologers thus have to argue there must be unknown forces exerted by the planets that depend on their configurations with respect to one another and that do not vary according to the distance of the planet—forces for which there is no shred of evidence.
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Another curious aspect of astrology is its emphasis on planet configurations at birth. What about the forces that might influence us at conception? Isn’t our genetic makeup more important for determining our personality than the circumstances of our birth? Would we really be a different person if we had been born a few hours earlier or later, as astrology claims? (Back when astrology was first conceived, birth was thought of as a moment of magic significance, but today we understand a lot more about the long process that precedes it.)
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Actually, very few well-educated people today buy the claim that our entire lives are predetermined by astrological influences at birth, but many people apparently believe that astrology has validity as an indicator of affinities and personality. A surprising number of Americans make judgments about people—whom they will hire, associate with, and even marry—on the basis of astrological information. To be sure, these are difficult decisions, and you might argue that we should use any relevant information that might help us to make the right choices. But does astrology actually provide any useful information on human personality? This is the kind of question that can be tested using the scientific method (see Testing Astrology).
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The results of hundreds of tests are all the same: there is no evidence that natal astrology has any predictive power, even in a statistical sense. Why, then, do people often seem to have anecdotes about how well their own astrologer advised them? Effective astrologers today use the language of the zodiac and the horoscope only as the outward trappings of their craft. Mostly they work as amateur therapists, offering simple truths that clients like or need to hear. (Recent studies have shown that just about any sort of short-term therapy makes people feel a little better because the very act of talking about our problems with someone who listens
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2.3 • Astrology and Astronomy 49
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attentively is, in itself, beneficial.)
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The scheme of astrology has no basis in scientific fact, however; at best, it can be described as a pseudoscience. It is an interesting historical system, left over from prescientific days and best remembered for the impetus it gave people to learn the cycles and patterns of the sky. From it grew the science of astronomy, which is our main subject for discussion.
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MAKING CONNECTIONS
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Testing Astrology
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In response to modern public interest in astrology, scientists have carried out a wide range of statistical tests to assess its predictive power. The simplest of these examine sun sign astrology to determine whether—as astrologers assert—some signs are more likely than others to be associated with some objective measure of success, such as winning Olympic medals, earning high corporate salaries, or achieving elective office or high military rank. (You can devise such a test yourself by looking up the birth dates of all members of Congress, for example, or all members of the U.S. Olympic team.) Are our political leaders somehow selected at birth by their horoscopes and thus more likely to be Leos, say, than Scorpios?
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You do not even need to be specific about your prediction in such tests. After all, many practitioners of astrology disagree about which signs go with which personality characteristics. To demonstrate the validity of the astrological hypothesis, it would be sufficient if the birthdays of all our leaders clustered in any one or two signs in some statistically significant way. Dozens of such tests have been performed, and all have come up completely negative: the birth dates of leaders in all fields tested have been found to be distributed randomly among all the signs. Sun sign astrology does not predict anything about a person’s future occupation or strong personality traits.
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In a fine example of such a test, two statisticians examined the reenlistment records of the United States Marine Corps. We suspect you will agree that it takes a certain kind of personality not only to enlist, but also to reenlist in the Marines. If sun signs can predict strong personality traits—as astrologers claim—then those who reenlisted (with similar personalities) should have been distributed preferentially in those one or few signs that matched the personality of someone who loves being a Marine. However, the reenlisted were distributed randomly among all the signs.
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More sophisticated studies have also been done, involving full horoscopes calculated for thousands of individuals. The results of all these studies are also negative: none of the systems of astrology has been shown to be at all effective in connecting astrological aspects to personality, success, or finding the right person to love.
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Other tests show that it hardly seems to matter what a horoscope interpretation says, as long as it is vague enough, and as long as each subject feels it was prepared personally just for him or her. The French statistician Michel Gauquelin, for example, sent the horoscope interpretation for one of the worst mass murderers in history to 150 people, but told each recipient that it was a “reading” prepared exclusively for him or her. Ninety-four percent of the readers said they recognized themselves in the interpretation of the mass murderer’s horoscope.
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Geoffrey Dean, an Australian researcher, reversed the astrological readings of 22 subjects, substituting phrases that were the opposite of what the horoscope actually said. Yet, his subjects said that the resulting readings applied to them just as often (95%) as the people to whom the original phrases were given.
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50 2 • Observing the Sky: The Birth of Astronomy
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LINK TO LEARNING
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For more on astrology and science from an astronomer’s point of view, read this article (https://openstax.org/l/30astrosociety) that shines light on the topic through an accessible Q&A.
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2.4 The Birth of Modern Astronomy
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Learning Objectives
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By the end of this section, you will be able to: Explain how Copernicus developed the heliocentric model of the solar system Explain the Copernican model of planetary motion and describe evidence or arguments in favor of it Describe Galileo’s discoveries concerning the study of motion and forces Explain how Galileo’s discoveries tilted the balance of evidence in favor of the Copernican model
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Astronomy made no major advances in strife-torn medieval Europe. The birth and expansion of Islam after the seventh century led to a flowering of Arabic and Jewish cultures that preserved, translated, and added to many of the astronomical ideas of the Greeks. Many of the names of the brightest stars, for example, are today taken from the Arabic, as are such astronomical terms as “zenith.” As European culture began to emerge from its long, dark age, trading with Arab countries led to a rediscovery of ancient texts such as Almagest and to a reawakening of interest in astronomical questions. This time of rebirth (in French, “renaissance”) in astronomy was embodied in the work of Copernicus (Figure 2.16).
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Figure 2.16 Nicolaus Copernicus (1473–1543). Copernicus was a cleric and scientist who played a leading role in the emergence of modern science. Although he could not prove that Earth revolves about the Sun, he presented such compelling arguments for this idea that he turned the tide of cosmological thought and laid the foundations upon which Galileo and Kepler so effectively built in the following century.
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Copernicus
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One of the most important events of the Renaissance was the displacement of Earth from the center of the universe, an intellectual revolution initiated by a Polish cleric in the sixteenth century. Nicolaus Copernicus was born in Torun, a mercantile town along the Vistula River. His training was in law and medicine, but his main interests were astronomy and mathematics. His great contribution to science was a critical reappraisal of the existing theories of planetary motion and the development of a new Sun-centered, or heliocentric, model of the solar system. Copernicus concluded that Earth is a planet and that all the planets circle the Sun. Only the Moon orbits Earth (Figure 2.17).
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2.4 • The Birth of Modern Astronomy 51
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Figure 2.17 Copernicus’ System. Copernicus developed a heliocentric plan of the solar system. This system was published in the first edition of De Revolutionibus Orbium Coelestium. Notice the word Sol for “Sun” in the middle. (credit: Nicolai Copernici)
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Copernicus described his ideas in detail in his book De Revolutionibus Orbium Coelestium (On the Revolution of Celestial Orbs), published in 1543, the year of his death. By this time, the old Ptolemaic system needed significant adjustments to predict the positions of the planets correctly. Copernicus wanted to develop an improved theory from which to calculate planetary positions, but in doing so, he was himself not free of all traditional prejudices. He began with several assumptions that were common in his time, such as the idea that the motions of the heavenly bodies must be made up of combinations of uniform circular motions. But he did not assume (as most people did) that Earth had to be in the center of the universe, and he presented a defense of the heliocentric system that was elegant and persuasive. His ideas, although not widely accepted until more than a century after his death, were much discussed among scholars and, ultimately, had a profound influence on the course of world history. One of the objections raised to the heliocentric theory was that if Earth were moving, we would all sense or feel this motion. Solid objects would be ripped from the surface, a ball dropped from a great height would not strike the ground directly below it, and so forth. But a moving person is not necessarily aware of that motion. We have all experienced seeing an adjacent train, bus, or ship appear to move, only to discover that it is we who are moving. Copernicus argued that the apparent motion of the Sun about Earth during the course of a year could be represented equally well by a motion of Earth about the Sun. He also reasoned that the apparent rotation of the celestial sphere could be explained by assuming that Earth rotates while the celestial sphere is stationary. To the objection that if Earth rotated about an axis it would fly into pieces, Copernicus answered that if such motion would tear Earth apart, the still faster motion of the much larger celestial sphere required by the geocentric hypothesis would be even more devastating.
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The Heliocentric Model
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The most important idea in Copernicus’ De Revolutionibus is that Earth is one of six (then-known) planets that revolve about the Sun. Using this concept, he was able to work out the correct general picture of the solar system. He placed the planets, starting nearest the Sun, in the correct order: Mercury, Venus, Earth, Mars, Jupiter, and Saturn. Further, he deduced that the nearer a planet is to the Sun, the greater its orbital speed.
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52 2 • Observing the Sky: The Birth of Astronomy
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With his theory, he was able to explain the complex retrograde motions of the planets without epicycles and to work out a roughly correct scale for the solar system. Copernicus could not prove that Earth revolves about the Sun. In fact, with some adjustments, the old Ptolemaic system could have accounted, as well, for the motions of the planets in the sky. But Copernicus pointed out that the Ptolemaic cosmology was clumsy and lacking the beauty and symmetry of its successor. In Copernicus’ time, in fact, few people thought there were ways to prove whether the heliocentric or the older geocentric system was correct. A long philosophical tradition, going back to the Greeks and defended by the Catholic Church, held that pure human thought combined with divine revelation represented the path to truth. Nature, as revealed by our senses, was suspect. For example, Aristotle had reasoned that heavier objects (having more of the quality that made them heavy) must fall to Earth faster than lighter ones. This is absolutely incorrect, as any simple experiment dropping two balls of different weights shows. However, in Copernicus’ day, experiments did not carry much weight (if you will pardon the expression); Aristotle’s reasoning was more convincing. In this environment, there was little motivation to carry out observations or experiments to distinguish between competing cosmological theories (or anything else). It should not surprise us, therefore, that the heliocentric idea was debated for more than half a century without any tests being applied to determine its validity. (In fact, in the North American colonies, the older geocentric system was still taught at Harvard University in the first years after it was founded in 1636.) Contrast this with the situation today, when scientists rush to test each new hypothesis and do not accept any ideas until the results are in. For example, when two researchers at the University of Utah announced in 1989 that they had discovered a way to achieve nuclear fusion (the process that powers the stars) at room temperature, other scientists at more than 25 laboratories around the United States attempted to duplicate “cold fusion” within a few weeks—without success, as it turned out. The cold fusion theory soon went down in flames. How would we look at Copernicus’ model today? When a new hypothesis or theory is proposed in science, it must first be checked for consistency with what is already known. Copernicus’ heliocentric idea passes this test, for it allows planetary positions to be calculated at least as well as does the geocentric theory. The next step is to determine which predictions the new hypothesis makes that differ from those of competing ideas. In the case of Copernicus, one example is the prediction that, if Venus circles the Sun, the planet should go through the full range of phases just as the Moon does, whereas if it circles Earth, it should not (Figure 2.18). Also, we should not be able to see the full phase of Venus from Earth because the Sun would then be between Venus and Earth. But in those days, before the telescope, no one imagined testing these predictions.
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2.4 • The Birth of Modern Astronomy 53
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Figure 2.18 Phases of Venus. As Venus moves around the Sun, we see changing illumination of its surface, just as we see the face of the Moon illuminated differently in the course of a month.
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LINK TO LEARNING
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This animation (https://openstax.org/l/30venusphases) shows the phases of Venus. You can also see its distance from Earth as it orbits the Sun.
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Galileo and the Beginning of Modern Science
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Many of the modern scientific concepts of observation, experimentation, and the testing of hypotheses through careful quantitative measurements were pioneered by a man who lived nearly a century after Copernicus. Galileo Galilei (Figure 2.19), a contemporary of Shakespeare, was born in Pisa. Like Copernicus, he began training for a medical career, but he had little interest in the subject and later switched to mathematics. He held faculty positions at the University of Pisa and the University of Padua, and eventually became mathematician to the Grand Duke of Tuscany in Florence.
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Figure 2.19 Galileo Galilei (1564–1642). Galileo advocated that we perform experiments or make observations to ask nature its ways. When Galileo turned the telescope to the sky, he found things were not the way philosophers had supposed.
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54 2 • Observing the Sky: The Birth of Astronomy
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Galileo’s greatest contributions were in the field of mechanics, the study of motion and the actions of forces on bodies. It was familiar to all persons then, as it is to us now, that if something is at rest, it tends to remain at rest and requires some outside influence to start it in motion. Rest was thus generally regarded as the natural state of matter. Galileo showed, however, that rest is no more natural than motion. If an object is slid along a rough horizontal floor, it soon comes to rest because friction between it and the floor acts as a retarding force. However, if the floor and the object are both highly polished, the object, given the same initial speed, will slide farther before stopping. On a smooth layer of ice, it will slide farther still. Galileo reasoned that if all resisting effects could be removed, the object would continue in a steady state of motion indefinitely. He argued that a force is required not only to start an object moving from rest but also to slow down, stop, speed up, or change the direction of a moving object. You will appreciate this if you have ever tried to stop a rolling car by leaning against it, or a moving boat by tugging on a line. Galileo also studied the way objects accelerate—change their speed or direction of motion. Galileo watched objects as they fell freely or rolled down a ramp. He found that such objects accelerate uniformly; that is, in equal intervals of time they gain equal increments in speed. Galileo formulated these newly found laws in precise mathematical terms that enabled future experimenters to predict how far and how fast objects would move in various lengths of time.
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LINK TO LEARNING
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In theory, if Galileo is right, a feather and a hammer, dropped at the same time from a height, should land at the same moment. On Earth, this experiment is not possible because air resistance and air movements make the feather flutter, instead of falling straight down, accelerated only by the force of gravity. For generations, physics teachers had said that the place to try this experiment is somewhere where there is no air, such as the Moon. In 1971, Apollo 15 astronaut David Scott took a hammer and feather to the Moon and tried it, to the delight of physics nerds everywhere. NASA provides the video of the hammer and feather (https://openstax.org/l/30HamVsFeath) as well as a brief explanation.
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Sometime in the 1590s, Galileo adopted the Copernican hypothesis of a heliocentric solar system. In Roman Catholic Italy, this was not a popular philosophy, for Church authorities still upheld the ideas of Aristotle and Ptolemy, and they had powerful political and economic reasons for insisting that Earth was the center of creation. Galileo not only challenged this thinking but also had the audacity to write in Italian rather than scholarly Latin, and to lecture publicly on those topics. For him, there was no contradiction between the authority of the Church in matters of religion and morality, and the authority of nature (revealed by experiments) in matters of science. It was primarily because of Galileo and his “dangerous” opinions that, in 1616, the Church issued a prohibition decree stating that the Copernican doctrine was “false and absurd” and not to be held or defended.
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Galileo’s Astronomical Observations
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It is not certain who first conceived of the idea of combining two or more pieces of glass to produce an instrument that enlarged images of distant objects, making them appear nearer. The first such “spyglasses” (now called telescopes) that attracted much notice were made in 1608 by the Dutch spectacle maker Hans Lippershey (1570–1619). Galileo heard of the discovery and, without ever having seen an assembled telescope, constructed one of his own with a three-power magnification (3×), which made distant objects appear three times nearer and larger (Figure 2.20).
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2.4 • The Birth of Modern Astronomy 55
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Figure 2.20 Telescope Used by Galileo. The telescope has a wooden tube covered with paper and a lens 26 millimeters across.
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On August 25, 1609, Galileo demonstrated a telescope with a magnification of 9× to government officials of the city-state of Venice. By a magnification of 9×, we mean the linear dimensions of the objects being viewed appeared nine times larger or, alternatively, the objects appeared nine times closer than they really were. There were obvious military advantages associated with a device for seeing distant objects. For his invention, Galileo’s salary was nearly doubled, and he was granted lifetime tenure as a professor. (His university colleagues were outraged, particularly because the invention was not even original.)
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Others had used the telescope before Galileo to observe things on Earth. But in a flash of insight that changed the history of astronomy, Galileo realized that he could turn the power of the telescope toward the heavens. Before using his telescope for astronomical observations, Galileo had to devise a stable mount and improve the optics. He increased the magnification to 30×. Galileo also needed to acquire confidence in the telescope.
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At that time, human eyes were believed to be the final arbiter of truth about size, shape, and color. Lenses, mirrors, and prisms were known to distort distant images by enlarging, reducing, or inverting them, or spreading the light into a spectrum (rainbow of colors). Galileo undertook repeated experiments to convince himself that what he saw through the telescope was identical to what he saw up close. Only then could he begin to believe that the miraculous phenomena the telescope revealed in the heavens were real.
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Beginning his astronomical work late in 1609, Galileo found that many stars too faint to be seen with the unaided eye became visible with his telescope. In particular, he found that some nebulous blurs resolved into many stars, and that the Milky Way—the strip of whiteness across the night sky—was also made up of a multitude of individual stars.
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Examining the planets, Galileo found four moons revolving about Jupiter in times ranging from just under 2 days to about 17 days. This discovery was particularly important because it showed that not everything has to revolve around Earth. Furthermore, it demonstrated that there could be centers of motion that are themselves in motion. Defenders of the geocentric view had argued that if Earth was in motion, then the Moon would be left behind because it could hardly keep up with a rapidly moving planet. Yet, here were Jupiter’s moons doing exactly that. (To recognize this discovery and honor his work, NASA named a spacecraft that explored the Jupiter system Galileo.)
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With his telescope, Galileo was able to carry out the test of the Copernican theory mentioned earlier, based on the phases of Venus. Within a few months, he had found that Venus goes through phases like the Moon, showing that it must revolve about the Sun, so that we see different parts of its daylight side at different times (see Figure 2.18.) These observations could not be reconciled with Ptolemy’s model, in which Venus circled about Earth. In Ptolemy’s model, Venus could also show phases, but they were the wrong phases in the wrong order from what Galileo observed.
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Galileo also observed the Moon and saw craters, mountain ranges, valleys, and flat, dark areas that he thought might be water. These discoveries showed that the Moon might be not so dissimilar to Earth—suggesting that Earth, too, could belong to the realm of celestial bodies.
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LINK TO LEARNING
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For more information about the life and work of Galileo, see the Galileo Project (https://openstax.org/l/ 30GalProj) at Rice University.
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56 2 • Observing the Sky: The Birth of Astronomy
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After Galileo’s work, it became increasingly difficult to deny the Copernican view, and Earth was slowly dethroned from its central position in the universe and given its rightful place as one of the planets attending the Sun. Initially, however, Galileo met with a great deal of opposition. The Roman Catholic Church, still reeling from the Protestant Reformation, was looking to assert its authority and chose to make an example of Galileo. He had to appear before the Inquisition to answer charges that his work was heretical, and he was ultimately condemned to house arrest. His books were on the Church’s forbidden list until 1836, although in countries where the Roman Catholic Church held less sway, they were widely read and discussed. Not until 1992 did the Catholic Church admit publicly that it had erred in the matter of censoring Galileo’s ideas.
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The new ideas of Copernicus and Galileo began a revolution in our conception of the cosmos. It eventually became evident that the universe is a vast place and that Earth’s role in it is relatively unimportant. The idea that Earth moves around the Sun like the other planets raised the possibility that they might be worlds themselves, perhaps even supporting life. As Earth was demoted from its position at the center of the universe, so, too, was humanity. The universe, despite what we may wish, does not revolve around us.
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Most of us take these things for granted today, but four centuries ago such concepts were frightening and heretical for some, immensely stimulating for others. The pioneers of the Renaissance started the European world along the path toward science and technology that we still tread today. For them, nature was rational and ultimately knowable, and experiments and observations provided the means to reveal its secrets.
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SEEING FOR YOURSELF
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Observing the Planets
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At most any time of the night, and at any season, you can spot one or more bright planets in the sky. All five of the planets known to the ancients—Mercury, Venus, Mars, Jupiter, and Saturn—are more prominent than any but the brightest stars, and they can be seen even from urban locations if you know where and when to look. One way to tell planets from bright stars is that planets twinkle less.
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Venus, which stays close to the Sun from our perspective, appears either as an “evening star” in the west after sunset or as a “morning star” in the east before sunrise. It is the brightest object in the sky after the Sun and Moon. It far outshines any real star, and under the most favorable circumstances, it can even cast a visible shadow. Some young military recruits have tried to shoot Venus down as an approaching enemy craft or UFO.
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Mars, with its distinctive red color, can be nearly as bright as Venus is when close to Earth, but normally it remains much less conspicuous. Jupiter is most often the second-brightest planet, approximately equaling in brilliance the brightest stars. Saturn is dimmer, and it varies considerably in brightness, depending on whether its large rings are seen nearly edge-on (faint) or more widely opened (bright).
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Mercury is quite bright, but few people ever notice it because it never moves very far from the Sun (it’s never more than 28° away in the sky) and is always seen against bright twilight skies.
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True to their name, the planets “wander” against the background of the “fixed” stars. Although their apparent motions are complex, they reflect an underlying order upon which the heliocentric model of the solar system, as described in this chapter, was based. The positions of the planets are often listed in newspapers (sometimes on the weather page), and clear maps and guides to their locations can be found each month in such magazines as Sky & Telescope and Astronomy (available at most libraries and online). There are also a number of computer programs and phone and tablet apps that allow you to display where the planets are on any night.
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2 • Key Terms 57
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Key Terms
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accelerate to change velocity; to speed up, slow down, or change direction. apparent magnitude a measure of how bright a star looks in the sky; the larger the number, the dimmer
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the star appears to us astrology the pseudoscience that deals with the supposed influences on human destiny of the
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configurations and locations in the sky of the Sun, Moon, and planets celestial equator a great circle on the celestial sphere 90° from the celestial poles; where the celestial sphere
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intersects the plane of Earth’s equator celestial poles points about which the celestial sphere appears to rotate; intersections of the celestial sphere
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with Earth’s polar axis celestial sphere the apparent sphere of the sky; a sphere of large radius centered on the observer;
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directions of objects in the sky can be denoted by their position on the celestial sphere circumpolar zone those portions of the celestial sphere near the celestial poles that are either always above
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or always below the horizon cosmology the study of the organization and evolution of the universe ecliptic the apparent annual path of the Sun on the celestial sphere epicycle the circular orbit of a body in the Ptolemaic system, the center of which revolves about another
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circle (the deferent) geocentric centered on Earth heliocentric centered on the Sun horizon (astronomical) a great circle on the celestial sphere 90° from the zenith; more popularly, the circle
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around us where the dome of the sky meets Earth horoscope a chart used by astrologers that shows the positions along the zodiac and in the sky of the Sun,
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Moon, and planets at some given instant and as seen from a particular place on Earth—usually corresponding to the time and place of a person’s birth parallax the apparent displacement of a nearby star that results from the motion of Earth around the Sun planet today, any of the larger objects revolving about the Sun or any similar objects that orbit other stars; in ancient times, any object that moved regularly among the fixed stars precession (of Earth) the slow, conical motion of Earth’s axis of rotation caused principally by the gravitational pull of the Moon and Sun on Earth’s equatorial bulge retrograde motion the apparent westward motion of a planet on the celestial sphere or with respect to the stars year the period of revolution of Earth around the Sun zenith the point on the celestial sphere opposite the direction of gravity; point directly above the observer zodiac a belt around the sky about 18° wide centered on the ecliptic
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Summary
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2.1 The Sky Above
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The direct evidence of our senses supports a geocentric perspective, with the celestial sphere pivoting on the celestial poles and rotating about a stationary Earth. We see only half of this sphere at one time, limited by the horizon; the point directly overhead is our zenith. The Sun’s annual path on the celestial sphere is the ecliptic—a line that runs through the center of the zodiac, which is the 18-degree-wide strip of the sky within which we always find the Moon and planets. The celestial sphere is organized into 88 constellations, or sectors.
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2.2 Ancient Astronomy
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Ancient Greeks such as Aristotle recognized that Earth and the Moon are spheres, and understood the phases of the Moon, but because of their inability to detect stellar parallax, they rejected the idea that Earth moves. Eratosthenes measured the size of Earth with surprising precision. Hipparchus carried out many astronomical
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58 2 • For Further Exploration
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observations, making a star catalog, defining the system of stellar magnitudes, and discovering precession from the apparent shift in the position of the north celestial pole. Ptolemy of Alexandria summarized classic astronomy in his Almagest; he explained planetary motions, including retrograde motion, with remarkably good accuracy using a model centered on Earth. This geocentric model, based on combinations of uniform circular motion using epicycles, was accepted as authority for more than a thousand years.
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2.3 Astrology and Astronomy
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The ancient religion of astrology, with its main contribution to civilization a heightened interest in the heavens, began in Babylonia. It reached its peak in the Greco-Roman world, especially as recorded in the Tetrabiblos of Ptolemy. Natal astrology is based on the assumption that the positions of the planets at the time of our birth, as described by a horoscope, determine our future. However, modern tests clearly show that there is no evidence for this, even in a broad statistical sense, and there is no verifiable theory to explain what might cause such an astrological influence.
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2.4 The Birth of Modern Astronomy
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Nicolaus Copernicus introduced the heliocentric cosmology to Renaissance Europe in his book De Revolutionibus. Although he retained the Aristotelian idea of uniform circular motion, Copernicus suggested that Earth is a planet and that the planets all circle about the Sun, dethroning Earth from its position at the center of the universe. Galileo was the father of both modern experimental physics and telescopic astronomy. He studied the acceleration of moving objects and, in 1610, began telescopic observations, discovering the nature of the Milky Way, the large-scale features of the Moon, the phases of Venus, and four moons of Jupiter. Although he was accused of heresy for his support of heliocentric cosmology, Galileo is credited with observations and brilliant writings that convinced most of his scientific contemporaries of the reality of the Copernican theory.
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For Further Exploration
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Articles Ancient Astronomy Gingerich, O. “From Aristarchus to Copernicus.” Sky & Telescope (November 1983): 410. Gingerich, O. “Islamic Astronomy.” Scientific American (April 1986): 74. Astronomy and Astrology Fraknoi, A. “Your Astrology Defense Kit.” Sky & Telescope (August 1989): 146. Copernicus and Galileo Gingerich, O. “Galileo and the Phases of Venus.” Sky & Telescope (December 1984): 520. Gingerich, O. “How Galileo Changed the Rules of Science.” Sky & Telescope (March 1993): 32. Maran, S., and Marschall, L. “The Moon, the Telescope, and the Birth of the Modern World.” Sky & Telescope
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(February 2009): 28. Sobel, D. “The Heretic’s Daughter: A Startling Correspondence Reveals a New Portrait of Galileo.” The New
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Yorker (September 13, 1999): 52. Websites Ancient Astronomy Aristarchos of Samos: http://adsabs.harvard.edu//full/seri/JRASC/0075//0000029.000.html
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(http://adsabs.harvard.edu//full/seri/JRASC/0075//0000029.000.html). By Dr. Alan Batten.
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Access for free at openstax.org
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2 • Collaborative Group Activities 59
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Claudius Ptolemy: http://www-history.mcs.st-and.ac.uk/Biographies/Ptolemy.html (http://www-history.mcs.stand.ac.uk/Biographies/Ptolemy.html). An interesting biography.
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Hipparchus of Rhodes: http://www-history.mcs.st-andrews.ac.uk/Biographies/Hipparchus.html (http://wwwhistory.mcs.st-andrews.ac.uk/Biographies/Hipparchus.html). An interesting biography.
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Astronomy and Astrology
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Astrology and Science: http://www.astrology-and-science.com/hpage.htm (http://www.astrology-andscience.com/hpage.htm). The best site for a serious examination of the issues with astrology and the research on whether it works.
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Real Romance in the Stars: http://www.independent.co.uk/voices/the-real-romance-in-the-stars-1527970.html (http://www.independent.co.uk/voices/the-real-romance-in-the-stars-1527970.html). 1995 newspaper commentary attacking astrology.
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Copernicus and Galileo
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Galileo Galilei: http://www-history.mcs.st-andrews.ac.uk/Biographies/Galileo.html (http://www-history.mcs.standrews.ac.uk/Biographies/Galileo.html). A good biography with additional links.
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Galileo Project: http://galileo.rice.edu/ (http://galileo.rice.edu/). Rice University’s repository of information on Galileo.
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Nicolaus Copernicus: http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Copernicus.html (http://wwwgroups.dcs.st-and.ac.uk/~history/Biographies/Copernicus.html). A biography including links to photos about his life.
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Videos
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Astronomy and Astrology
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Astrology Debunked: https://www.youtube.com/watch?v=y84HX2pMo5U (https://www.youtube.com/ watch?v=y84HX2pMo5U). A compilation of scientists and magicians commenting skeptically on astrology (9:09).
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Copernicus and Galileo
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Galileo: http://www.biography.com/people/galileo-9305220 (http://www.biography.com/people/ galileo-9305220). A brief biography (2:51).
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Galileo’s Battle for the Heavens: https://www.youtube.com/playlist?list=PL28AF597A9C90E18E (https://www.youtube.com/playlist?list=PL28AF597A9C90E18E). A NOVA episode on PBS (1:48:55)
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Nicolaus Copernicus: http://www.biography.com/people/nicolaus-copernicus-9256984 (http://www.biography.com/people/nicolaus-copernicus-9256984). An overview of his life and work (2:41).
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Collaborative Group Activities
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A. With your group, consider the question with which we began this chapter. How many ways can you think of to prove to a member of the “Flat Earth Society” that our planet is, indeed, round?
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B. Make a list of ways in which a belief in astrology (the notion that your life path or personality is controlled by the position of the Sun, Moon, and planets at the time of your birth) might be harmful to an individual or to society at large.
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C. Have members of the group compare their experiences with the night sky. Did you see the Milky Way? Can you identify any constellations? Make a list of reasons why you think so many fewer people know the night sky today than at the time of the ancient Greeks. Discuss reasons for why a person, today, may want
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60 2 • Exercises
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to be acquainted with the night sky. D. Constellations commemorate great heroes, dangers, or events in the legends of the people who name
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them. Suppose we had to start from scratch today, naming the patterns of stars in the sky. Whom or what would you choose to commemorate by naming a constellation after it, him, or her and why (begin with people from history; then if you have time, include living people as well)? Can the members of your group agree on any choices? E. Although astronomical mythology no longer holds a powerful sway over the modern imagination, we still find proof of the power of astronomical images in the number of products in the marketplace that have astronomical names. How many can your group come up with? (Think of things like Milky Way candy bars, Eclipse and Orbit gum, or Comet cleanser.)
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Exercises
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Review Questions
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1. From where on Earth could you observe all of the stars during the course of a year? What fraction of the sky can be seen from the North Pole?
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2. Give four ways to demonstrate that Earth is spherical. 3. Explain, according to both geocentric and heliocentric cosmologies, why we see retrograde motion of the
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planets. 4. In what ways did the work of Copernicus and Galileo differ from the views of the ancient Greeks and of
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their contemporaries? 5. What were four of Galileo’s discoveries that were important to astronomy? 6. Explain the origin of the magnitude designation for determining the brightness of stars. Why does it seem
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to go backward, with smaller numbers indicating brighter stars? 7. Ursa Minor contains the pole star, Polaris, and the asterism known as the Little Dipper. From most locations
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in the Northern Hemisphere, all of the stars in Ursa Minor are circumpolar. Does that mean these stars are also above the horizon during the day? Explain. 8. How many degrees does the Sun move per day relative to the fixed stars? How many days does it take for the Sun to return to its original location relative to the fixed stars? 9. How many degrees does the Moon move per day relative to the fixed stars? How many days does it take for the Moon to return to its original location relative to the fixed stars? 10. Explain how the zodiacal constellations are different from the other constellations. 11. The Sun was once thought to be a planet. Explain why. 12. Is the ecliptic the same thing as the celestial equator? Explain. 13. What is an asterism? Can you name an example? 14. Why did Pythagoras believe that Earth should be spherical? 15. How did Aristotle deduce that the Sun is farther away from Earth than the Moon? 16. What are two ways in which Aristotle deduced that Earth is spherical? 17. How did Hipparchus discover the wobble of Earth’s axis, known as precession? 18. Why did Ptolemy have to introduce multiple circles of motion for the planets instead of a single, simple
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circle to represent the planet’s motion around the Earth?
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Access for free at openstax.org
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2 • Exercises 61
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19. Why did Copernicus want to develop a completely new system for predicting planetary positions? Provide two reasons.
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20. What two factors made it difficult, at first, for astronomers to choose between the Copernican heliocentric model and the Ptolemaic geocentric model?
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21. What phases would Venus show if the geocentric model were correct?
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Thought Questions
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22. Describe a practical way to determine in which constellation the Sun is found at any time of the year.
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23. What is a constellation as astronomers define it today? What does it mean when an astronomer says, “I saw a comet in Orion last night”?
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24. Draw a picture that explains why Venus goes through phases the way the Moon does, according to the heliocentric cosmology. Does Jupiter also go through phases as seen from Earth? Why?
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25. Show with a simple diagram how the lower parts of a ship disappear first as it sails away from you on a spherical Earth. Use the same diagram to show why lookouts on old sailing ships could see farther from the masthead than from the deck. Would there be any advantage to posting lookouts on the mast if Earth were flat? (Note that these nautical arguments for a spherical Earth were quite familiar to Columbus and other mariners of his time.)
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26. Parallaxes of stars were not observed by ancient astronomers. How can this fact be reconciled with the heliocentric hypothesis?
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27. Why do you think so many people still believe in astrology and spend money on it? What psychological needs does such a belief system satisfy?
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28. Consider three cosmological perspectives—the geocentric perspective, the heliocentric perspective, and the modern perspective—in which the Sun is a minor star on the outskirts of one galaxy among billions. Discuss some of the cultural and philosophical implications of each point of view.
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29. The north celestial pole appears at an altitude above the horizon that is equal to the observer’s latitude. Identify Polaris, the North Star, which lies very close to the north celestial pole. Measure its altitude. (This can be done with a protractor. Alternatively, your fist, extended at arm’s length, spans a distance approximately equal to 10°.) Compare this estimate with your latitude. (Note that this experiment cannot be performed easily in the Southern Hemisphere because Polaris itself is not visible in the south and no bright star is located near the south celestial pole.)
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30. What were two arguments or lines of evidence in support of the geocentric model?
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31. Although the Copernican system was largely correct to place the Sun at the center of all planetary motion, the model still gave inaccurate predictions for planetary positions. Explain the flaw in the Copernican model that hindered its accuracy.
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32. During a retrograde loop of Mars, would you expect Mars to be brighter than usual in the sky, about average in brightness, or fainter than usual in the sky? Explain.
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33. The Great Pyramid of Giza was constructed nearly 5000 years ago. Within the pyramid, archaeologists discovered a shaft leading from the central chamber out of the pyramid, oriented for favorable viewing of the bright star Thuban at that time. Thinking about Earth’s precession, explain why Thuban might have been an important star to the ancient Egyptians.
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34. Explain why more stars are circumpolar for observers at higher latitudes.
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62 2 • Exercises
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35. What is the altitude of the north celestial pole in the sky from your latitude? If you do not know your latitude, look it up. If you are in the Southern Hemisphere, answer this question for the south celestial pole, since the north celestial pole is not visible from your location.
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36. If you were to drive to some city south of your current location, how would the altitude of the celestial pole in the sky change?
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37. Hipparchus could have warned us that the dates associated with each of the natal astrology sun signs would eventually be wrong. Explain why.
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38. Explain three lines of evidence that argue against the validity of astrology. 39. What did Galileo discover about the planet Jupiter that cast doubt on exclusive geocentrism? 40. What did Galileo discover about Venus that cast doubt on geocentrism?
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Figuring for Yourself
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41. Suppose Eratosthenes had found that, in Alexandria, at noon on the first day of summer, the line to the Sun makes an angle 30° with the vertical. What, then, would he have found for Earth’s circumference?
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42. Suppose Eratosthenes’ results for Earth’s circumference were quite accurate. If the diameter of Earth is 12,740 km, what is the length of his stadium in kilometers?
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43. Suppose you are on a strange planet and observe, at night, that the stars do not rise and set, but circle parallel to the horizon. Next, you walk in a constant direction for 8000 miles, and at your new location on the planet, you find that all stars rise straight up in the east and set straight down in the west, perpendicular to the horizon. How could you determine the circumference of the planet without any further observations? What is the circumference, in miles, of the planet?
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Access for free at openstax.org
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3 • Thinking Ahead
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63
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3 Orbits and Gravity
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Figure 3.1 International Space Station. This space habitat and laboratory orbits Earth once every 90 minutes. (credit:
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modification of work by NASA)
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Chapter Outline
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3.1 The Laws of Planetary Motion 3.2 Newton’s Great Synthesis 3.3 Newton’s Universal Law of Gravitation 3.4 Orbits in the Solar System 3.5 Motions of Satellites and Spacecraft 3.6 Gravity with More Than Two Bodies
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Thinking Ahead
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How would you find a new planet at the outskirts of our solar system that is too dim to be seen with the unaided eye and is so far away that it moves very slowly among the stars? This was the problem confronting astronomers during the nineteenth century as they tried to pin down a full inventory of our solar system.
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If we could look down on the solar system from somewhere out in space, interpreting planetary motions would be much simpler. But the fact is, we must observe the positions of all the other planets from our own moving planet. Scientists of the Renaissance did not know the details of Earth’s motions any better than the motions of the other planets. Their problem, as we saw in Observing the Sky: The Birth of Astronomy, was that they had to deduce the nature of all planetary motion using only their earthbound observations of the other planets’ positions in the sky. To solve this complex problem more fully, better observations and better models of the planetary system were needed.
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64 3 • Orbits and Gravity
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3.1 The Laws of Planetary Motion
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Learning Objectives
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By the end of this section, you will be able to: Describe how Tycho Brahe and Johannes Kepler contributed to our understanding of how planets move
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around the Sun Explain Kepler’s three laws of planetary motion
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At about the time that Galileo was beginning his experiments with falling bodies, the efforts of two other scientists dramatically advanced our understanding of the motions of the planets. These two astronomers were the observer Tycho Brahe and the mathematician Johannes Kepler. Together, they placed the speculations of Copernicus on a sound mathematical basis and paved the way for the work of Isaac Newton in the next century.
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Tycho Brahe’s Observatory
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Three years after the publication of Copernicus’ De Revolutionibus, Tycho Brahe was born to a family of Danish nobility. He developed an early interest in astronomy and, as a young man, made significant astronomical observations. Among these was a careful study of what we now know was an exploding star that flared up to great brilliance in the night sky. His growing reputation gained him the patronage of the Danish King Frederick II, and at the age of 30, Brahe was able to establish a fine astronomical observatory on the North Sea island of Hven (Figure 3.2). Brahe was the last and greatest of the pre-telescopic observers in Europe.
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Figure 3.2 Tycho Brahe (1546–1601) and Johannes Kepler (1571–1630). (a) A stylized engraving shows Tycho Brahe using his instruments to measure the altitude of celestial objects above the horizon. The large curved instrument in the foreground allowed him to measure precise angles in the sky. Note that the scene includes hints of the grandeur of Brahe’s observatory at Hven. (b) Kepler was a German mathematician and astronomer. His discovery of the basic laws that describe planetary motion placed the heliocentric cosmology of Copernicus on a firm mathematical basis.
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At Hven, Brahe made a continuous record of the positions of the Sun, Moon, and planets for almost 20 years. His extensive and precise observations enabled him to note that the positions of the planets varied from those
|
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Access for free at openstax.org
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3.1 • The Laws of Planetary Motion 65
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given in published tables, which were based on the work of Ptolemy. These data were extremely valuable, but Brahe didn’t have the ability to analyze them and develop a better model than what Ptolemy had published. He was further inhibited because he was an extravagant and cantankerous fellow, and he accumulated enemies among government officials. When his patron, Frederick II, died in 1597, Brahe lost his political base and decided to leave Denmark. He took up residence in Prague, where he became court astronomer to Emperor Rudolf of Bohemia. There, in the year before his death, Brahe found a most able young mathematician, Johannes Kepler, to assist him in analyzing his extensive planetary data.
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Johannes Kepler
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Johannes Kepler was born into a poor family in the German province of Württemberg and lived much of his life amid the turmoil of the Thirty Years’ War (see Figure 3.2). He attended university at Tubingen and studied for a theological career. There, he learned the principles of the Copernican system and became converted to the heliocentric hypothesis. Eventually, Kepler went to Prague to serve as an assistant to Brahe, who set him to work trying to find a satisfactory theory of planetary motion—one that was compatible with the long series of observations made at Hven. Brahe was reluctant to provide Kepler with much material at any one time for fear that Kepler would discover the secrets of the universal motion by himself, thereby robbing Brahe of some of the glory. Only after Brahe’s death in 1601 did Kepler get full possession of the priceless records. Their study occupied most of Kepler’s time for more than 20 years. Through his analysis of the motions of the planets, Kepler developed a series of principles, now known as Kepler’s three laws, which described the behavior of planets based on their paths through space. The first two laws of planetary motion were published in 1609 in The New Astronomy. Their discovery was a profound step in the development of modern science.
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The First Two Laws of Planetary Motion
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The path of an object through space is called its orbit. Kepler initially assumed that the orbits of planets were circles, but doing so did not allow him to find orbits that were consistent with Brahe’s observations. Working with the data for Mars, he eventually discovered that the orbit of that planet had the shape of a somewhat flattened circle, or ellipse. Next to the circle, the ellipse is the simplest kind of closed curve, belonging to a family of curves known as conic sections (Figure 3.3).
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Figure 3.3 Conic Sections. The circle, ellipse, parabola, and hyperbola are all formed by the intersection of a plane with a cone. This is why such curves are called conic sections.
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You might recall from math classes that in a circle, the center is a special point. The distance from the center to anywhere on the circle is exactly the same. In an ellipse, the sum of the distance from two special points inside the ellipse to any point on the ellipse is always the same. These two points inside the ellipse are called its foci (singular: focus), a word invented for this purpose by Kepler. This property suggests a simple way to draw an ellipse (Figure 3.4). We wrap the ends of a loop of string
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66 3 • Orbits and Gravity
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around two tacks pushed through a sheet of paper into a drawing board, so that the string is slack. If we push a pencil against the string, making the string taut, and then slide the pencil against the string all around the tacks, the curve that results is an ellipse. At any point where the pencil may be, the sum of the distances from the pencil to the two tacks is a constant length—the length of the string. The tacks are at the two foci of the ellipse. The widest diameter of the ellipse is called its major axis. Half this distance—that is, the distance from the center of the ellipse to one end—is the semimajor axis, which is usually used to specify the size of the ellipse. For example, the semimajor axis of the orbit of Mars, which is also the planet’s average distance from the Sun, is 228 million kilometers.
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Figure 3.4 Drawing an Ellipse. (a) We can construct an ellipse by pushing two tacks (the white objects) into a piece of paper on a drawing board, and then looping a string around the tacks. Each tack represents a focus of the ellipse, with one of the tacks being the Sun. Stretch the string tight using a pencil, and then move the pencil around the tacks. The length of the string remains the same, so that the sum of the distances from any point on the ellipse to the foci is always constant. (b) In this illustration, each semimajor axis is denoted by a. The distance 2a is called the major axis of the ellipse.
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The shape (roundness) of an ellipse depends on how close together the two foci are, compared with the major axis. The ratio of the distance between the foci to the length of the major axis is called the eccentricity of the ellipse. If the foci (or tacks) are moved to the same location, then the distance between the foci would be zero. This means that the eccentricity is zero and the ellipse is just a circle; thus, a circle can be called an ellipse of zero eccentricity. In a circle, the semimajor axis would be the radius. Next, we can make ellipses of various elongations (or extended lengths) by varying the spacing of the tacks (as long as they are not farther apart than the length of the string). The greater the eccentricity, the more elongated is the ellipse, up to a maximum eccentricity of 1.0, when the ellipse becomes “flat,” the other extreme from a circle. The size and shape of an ellipse are completely specified by its semimajor axis and its eccentricity. Using Brahe’s data, Kepler found that Mars has an elliptical orbit, with the Sun at one focus (the other focus is empty). The eccentricity of the orbit of Mars is only about 0.1; its orbit, drawn to scale, would be practically indistinguishable from a circle, but the difference turned out to be critical for understanding planetary motions. Kepler generalized this result in his first law and said that the orbits of all the planets are ellipses. Here was a decisive moment in the history of human thought: it was not necessary to have only circles in order to have an acceptable cosmos. The universe could be a bit more complex than the Greek philosophers had wanted it to be. Kepler’s second law deals with the speed with which each planet moves along its ellipse, also known as its orbital speed. Working with Brahe’s observations of Mars, Kepler discovered that the planet speeds up as it comes closer to the Sun and slows down as it pulls away from the Sun. He expressed the precise form of this relationship by imagining that the Sun and Mars are connected by a straight, elastic line. When Mars is closer to the Sun (positions 1 and 2 in Figure 3.5), the elastic line is not stretched as much, and the planet moves rapidly. Farther from the Sun, as in positions 3 and 4, the line is stretched a lot, and the planet does not move
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3.1 • The Laws of Planetary Motion 67
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so fast. As Mars travels in its elliptical orbit around the Sun, the elastic line sweeps out areas of the ellipse as it moves (the colored regions in our figure). Kepler found that in equal intervals of time (t), the areas swept out in space by this imaginary line are always equal; that is, the area of the region B from 1 to 2 is the same as that of region A from 3 to 4. If a planet moves in a circular orbit, the elastic line is always stretched the same amount and the planet moves at a constant speed around its orbit. But, as Kepler discovered, in most orbits that speed of a planet orbiting its star (or moon orbiting its planet) tends to vary because the orbit is elliptical.
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Figure 3.5 Kepler’s Second Law: The Law of Equal Areas. The orbital speed of a planet traveling around the Sun (the circular object inside the ellipse) varies in such a way that in equal intervals of time (t), a line between the Sun and a planet sweeps out equal areas (A and B). Note that the eccentricities of the planets’ orbits in our solar system are substantially less than shown here.
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LINK TO LEARNING
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The Kepler's Second Law demonstrator (https://openstax.org/l/30kepsecond) from CCNY's ScienceSims project shows how an orbiting planet sweeps out the same area in the same time.
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Kepler’s Third Law
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Kepler’s first two laws of planetary motion describe the shape of a planet’s orbit and allow us to calculate the speed of its motion at any point in the orbit. Kepler was pleased to have discovered such fundamental rules, but they did not satisfy his quest to fully understand planetary motions. He wanted to know why the orbits of the planets were spaced as they are and to find a mathematical pattern in their movements—a “harmony of the spheres” as he called it. For many years he worked to discover mathematical relationships governing planetary spacing and the time each planet took to go around the Sun. In 1619, Kepler discovered a basic relationship to relate the planets’ orbits to their relative distances from the Sun. We define a planet’s orbital period, (P), as the time it takes a planet to travel once around the Sun. Also, recall that a planet’s semimajor axis, a, is equal to its average distance from the Sun. The relationship, now known as Kepler’s third law, says that a planet’s orbital period squared is proportional to the semimajor axis of its orbit cubed, or
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When P (the orbital period) is measured in years, and a is expressed in a quantity known as an astronomical unit (AU), the two sides of the formula are not only proportional but equal. One AU is the average distance between Earth and the Sun and is approximately equal to 1.5 × 108 kilometers. In these units,
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68 3 • Orbits and Gravity
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Kepler’s third law applies to all objects orbiting the Sun, including Earth, and provides a means for calculating their relative distances from the Sun from the time they take to orbit. Let’s look at a specific example to illustrate how useful Kepler’s third law is. For instance, suppose you time how long Mars takes to go around the Sun (in Earth years). Kepler’s third law can then be used to calculate Mars’ average distance from the Sun. Mars’ orbital period (1.88 Earth years) squared, or P2, is 1.882 = 3.53, and according to the equation for Kepler’s third law, this equals the cube of its semimajor axis, or a3. So what number must be cubed to give 3.53? The answer is 1.52 (since 1.52 × 1.52 × 1.52 = 3.53). Thus, Mars’ semimajor axis in astronomical units must be 1.52 AU. In other words, to go around the Sun in a little less than two years, Mars must be about 50% (half again) as far from the Sun as Earth is.
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EXAMPLE 3.1
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Calculating Periods
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Imagine an object is traveling around the Sun. What would be the orbital period of the object if its orbit has a semimajor axis of 50 AU?
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Solution
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From Kepler’s third law, we know that (when we use units of years and AU)
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If the object’s orbit has a semimajor axis of 50 AU (a = 50), we can cube 50 and then take the square root of the result to get P:
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Therefore, the orbital period of the object is about 350 years. This would place our hypothetical object beyond the orbit of Pluto.
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Check Your Learning
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What would be the orbital period of an asteroid (a rocky chunk between Mars and Jupiter) with a semimajor axis of 3 AU?
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Answer:
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Kepler’s three laws of planetary motion can be summarized as follows: • Kepler’s first law: Each planet moves around the Sun in an orbit that is an ellipse, with the Sun at one focus of the ellipse. • Kepler’s second law: The straight line joining a planet and the Sun sweeps out equal areas in space in equal intervals of time. • Kepler’s third law: The square of a planet’s orbital period is directly proportional to the cube of the semimajor axis of its orbit.
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Kepler’s three laws provide a precise geometric description of planetary motion within the framework of the Copernican system. With these tools, it was possible to calculate planetary positions with greatly improved precision. Still, Kepler’s laws are purely descriptive: they do not help us understand what forces of nature constrain the planets to follow this particular set of rules. That step was left to Isaac Newton.
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Access for free at openstax.org
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3.2 • Newton’s Great Synthesis 69
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EXAMPLE 3.2
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Applying Kepler’s Third Law
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Using the orbital periods and semimajor axes for Venus and Earth that are provided here, calculate P2 and a3, and verify that they obey Kepler’s third law. Venus’ orbital period is 0.62 year, and its semimajor axis is 0.72 AU. Earth’s orbital period is 1.00 year, and its semimajor axis is 1.00 AU.
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Solution
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We can use the equation for Kepler’s third law, P2 ∝ a3. For Venus, P2 = 0.62 × 0.62 = 0.38 and a3 = 0.72 × 0.72 × 0.72 = 0.37 (rounding numbers sometimes causes minor discrepancies like this). The square of the orbital period (0.38) approximates the cube of the semimajor axis (0.37). Therefore, Venus obeys Kepler’s third law. For Earth, P2 = 1.00 × 1.00 = 1.00 and a3 = 1.00 × 1.00 × 1.00 = 1.00. The square of the orbital period (1.00) approximates (in this case, equals) the cube of the semimajor axis (1.00). Therefore, Earth obeys Kepler’s third law.
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Check Your Learning
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Using the orbital periods and semimajor axes for Saturn and Jupiter that are provided here, calculate P2 and a3, and verify that they obey Kepler’s third law. Saturn’s orbital period is 29.46 years, and its semimajor axis is 9.54 AU. Jupiter’s orbital period is 11.86 years, and its semimajor axis is 5.20 AU.
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Answer:
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For Saturn, P2 = 29.46 × 29.46 = 867.9 and a3 = 9.54 × 9.54 × 9.54 = 868.3. The square of the orbital period (867.9) approximates the cube of the semimajor axis (868.3). Therefore, Saturn obeys Kepler’s third law.
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LINK TO LEARNING
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In honor of the scientist who first devised the laws that govern the motions of planets, the team that built the first spacecraft to search for planets orbiting other stars decided to name the probe “Kepler.” Visit NASA's Kepler website to learn more about Johannes Kepler’s life and his laws of planetary motion. NASA’s Kepler website (https://openstax.org/l/30nasakepmiss) and follow the links that interest you.
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3.2 Newton’s Great Synthesis
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Learning Objectives
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By the end of this section, you will be able to: Describe Newton’s three laws of motion Explain how Newton’s three laws of motion relate to momentum Define mass, volume, and density and how they differ Define angular momentum
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It was the genius of Isaac Newton that found a conceptual framework that completely explained the observations and rules assembled by Galileo, Brahe, Kepler, and others. Newton was born in Lincolnshire, England, in the year after Galileo’s death (Figure 3.6). Against the advice of his mother, who wanted him to stay home and help with the family farm, he entered Trinity College at Cambridge in 1661 and eight years later was appointed professor of mathematics. Among Newton’s contemporaries in England were architect Christopher Wren, authors Aphra Behn and Daniel Defoe, and composer G. F. Handel.
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70 3 • Orbits and Gravity
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Figure 3.6 Isaac Newton (1643–1727), 1689 Portrait by Sir Godfrey Kneller. Isaac Newton’s work on the laws of motion, gravity, optics, and mathematics laid the foundations for much of physical science.
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Newton’s Laws of Motion
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As a young man in college, Newton became interested in natural philosophy, as science was then called. He worked out some of his first ideas on machines and optics during the plague years of 1665 and 1666, when students were sent home from college. Newton, a moody and often difficult man, continued to work on his ideas in private, even inventing new mathematical tools to help him deal with the complexities involved. Eventually, his friend Edmund Halley (profiled in Comets and Asteroids: Debris of the Solar System) prevailed on him to collect and publish the results of his remarkable investigations on motion and gravity. The result was a volume that set out the underlying system of the physical world, Philosophiae Naturalis Principia Mathematica. The Principia, as the book is generally known, was published at Halley’s expense in 1687. At the very beginning of the Principia, Newton proposes three laws that would govern the motions of all objects:
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• Newton’s first law: Every object will continue to be in a state of rest or move at a constant speed in a straight line unless it is compelled to change by an outside force.
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• Newton’s second law: The change of motion of a body is proportional to and in the direction of the force acting on it.
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• Newton’s third law: For every action there is an equal and opposite reaction (or: the mutual actions of two bodies upon each other are always equal and act in opposite directions).
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In the original Latin, the three laws contain only 59 words, but those few words set the stage for modern science. Let us examine them more carefully.
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Interpretation of Newton’s Laws
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Newton’s first law is a restatement of one of Galileo’s discoveries, called the conservation of momentum. The law states that in the absence of any outside influence, there is a measure of a body’s motion, called its momentum, that remains unchanged. You may have heard the term momentum used in everyday expressions, such as “This bill in Congress has a lot of momentum; it’s going to be hard to stop.” Newton’s first law is sometimes called the law of inertia, where inertia is the tendency of objects (and legislatures) to keep doing what they are already doing. In other words, a stationary object stays put, and a moving object keeps moving unless some force intervenes. Let’s define the precise meaning of momentum—it depends on three factors: (1) speed—how fast a body
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Access for free at openstax.org
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3.2 • Newton’s Great Synthesis 71
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moves (zero if it is stationary), (2) the direction of its motion, and (3) its mass—a measure of the amount of matter in a body, which we will discuss later. Scientists use the term velocity to describe the speed and direction of motion. For example, 20 kilometers per hour due south is velocity, whereas 20 kilometers per hour just by itself is speed. Momentum then can be defined as an object’s mass times its velocity.
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It’s not so easy to see this rule in action in the everyday world because of the many forces acting on a body at any one time. One important force is friction, which generally slows things down. If you roll a ball along the sidewalk, it eventually comes to a stop because the sidewalk exerts a rubbing force on the ball. But in the space between the stars, where there is so little matter that friction is insignificant, objects can in fact continue to move (to coast) indefinitely.
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The momentum of a body can change only under the action of an outside influence. Newton’s second law expresses force in terms of its ability to change momentum with time. A force (a push or a pull) has both size and direction. When a force is applied to a body, the momentum changes in the direction of the applied force. This means that a force is required to change either the speed or the direction of a body, or both—that is, to start it moving, to speed it up, to slow it down, to stop it, or to change its direction.
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As you learned in Observing the Sky: The Birth of Astronomy, the rate of change in an object’s velocity is called acceleration. Newton showed that the acceleration of a body was proportional to the force being applied to it. Suppose that after a long period of reading, you push an astronomy book away from you on a long, smooth table. (We use a smooth table so we can ignore friction.) If you push the book steadily, it will continue to speed up as long as you are pushing it. The harder you push the book, the larger its acceleration will be. How much a force will accelerate an object is also determined by the object’s mass. If you kept pushing a pen with the same force with which you pushed the textbook, the pen—having less mass—would be accelerated to a greater speed.
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Newton’s third law is perhaps the most profound of the rules he discovered. Basically, it is a generalization of the first law, but it also gives us a way to define mass. If we consider a system of two or more objects isolated from outside influences, Newton’s first law says that the total momentum of the objects should remain constant. Therefore, any change of momentum within the system must be balanced by another change that is equal and opposite so that the momentum of the entire system is not changed.
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This means that forces in nature do not occur alone: we find that in each situation there is always a pair of forces that are equal to and opposite each other. If a force is exerted on an object, it must be exerted by something else, and the object will exert an equal and opposite force back on that something. We can look at a simple example to demonstrate this.
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Suppose that a daredevil astronomy student—and avid skateboarder—wants to jump from his second-story dorm window onto his board below (we don’t recommend trying this!). The force pulling him down after jumping (as we will see in the next section) is the force of gravity between him and Earth. Both he and Earth must experience the same total change of momentum because of the influence of these mutual forces. So, both the student and Earth are accelerated by each other’s pull. However, the student does much more of the moving. Because Earth has enormously greater mass, it can experience the same change of momentum by accelerating only a very small amount. Things fall toward Earth all the time, but the acceleration of our planet as a result is far too small to be measured.
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A more obvious example of the mutual nature of forces between objects is familiar to all who have batted a baseball. The recoil you feel as you swing your bat shows that the ball exerts a force on it during the impact, just as the bat does on the ball. Similarly, when a rifle you are bracing on your shoulder is discharged, the force pushing the bullet out of the muzzle is equal to the force pushing backward upon the gun and your shoulder.
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This is the principle behind jet engines and rockets: the force that discharges the exhaust gases from the rear of the rocket is accompanied by the force that pushes the rocket forward. The exhaust gases need not push
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72 3 • Orbits and Gravity
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against air or Earth; a rocket actually operates best in a vacuum (Figure 3.7).
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Figure 3.7 Demonstrating Newton’s Third Law. The U.S. Space Shuttle (here launching Discovery), powered by three fuel engines burning liquid oxygen and liquid hydrogen, with two solid fuel boosters, demonstrates Newton’s third law. (credit: modification of work by NASA)
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LINK TO LEARNING
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For more about Isaac Newton’s life and work, check out this timeline page (https://openstax.org/l/ 30IsaacNewTime) with snapshots from his career, produced by the British Broadcasting Corporation (BBC).
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Mass, Volume, and Density
|
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Before we go on to discuss Newton’s other work, we want to take a brief look at some terms that will be important to sort out clearly. We begin with mass, which is a measure of the amount of material within an object. The volume of an object is the measure of the physical space it occupies. Volume is measured in cubic units, such as cubic centimeters or liters. The volume is the “size” of an object. A penny and an inflated balloon may both have the same mass, but they have very different volumes. The reason is that they also have very different densities, which is a measure of how much mass there is per unit volume. Specifically, density is the mass divided by the volume. Note that in everyday language we often use “heavy” and “light” as indications of density (rather than weight) as, for instance, when we say that iron is heavy or that whipped cream is light. The units of density that will be used in this book are grams per cubic centimeter (g/cm3).1 If a block of some material has a mass of 300 grams and a volume of 100 cm3, its density is 3 g/cm3. Familiar materials span a considerable range in density, from artificial materials such as plastic insulating foam (less than 0.1 g/cm3) to gold (19.3 g/cm3). Table 3.1 gives the densities of some familiar materials. In the astronomical universe, much more remarkable densities can be found, all the way from a comet’s tail (10–16 g/cm3) to a collapsed “star corpse” called a neutron star (1015 g/cm3).
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1 Generally we use standard metric (or SI) units in this book. The proper metric unit of density in that system is kg/m3. But to most people, g/cm3 provides a more meaningful unit because the density of water is exactly 1 g/cm3, and this is useful information for comparison. Density expressed in g/cm3 is sometimes called specific density or specific weight.
|
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Access for free at openstax.org
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3.2 • Newton’s Great Synthesis 73
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Densities of Common Materials
|
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Material
|
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Density (g/cm3)
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Gold
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19.3
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Lead
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11.3
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Iron
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7.9
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Earth (bulk)
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5.5
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Rock (typical)
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2.5
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Water
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1
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Wood (typical) 0.8
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Insulating foam 0.1
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Silica gel
|
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0.02
|
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Table 3.1
|
|||
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|
|||
|
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To sum up, mass is how much, volume is how big, and density is how tightly packed.
|
|||
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LINK TO LEARNING
|
|||
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|
|||
|
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You can play with a simple animation (https://openstax.org/l/30phetsimdenmas) demonstrating the relationship between the concepts of density, mass, and volume, and find out why objects like wood float in water.
|
|||
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Angular Momentum
|
|||
|
|
A concept that is a bit more complex, but important for understanding many astronomical objects, is angular momentum, which is a measure of the rotation of a body as it revolves around some fixed point (an example is a planet orbiting the Sun). The angular momentum of an object is defined as the product of its mass, its velocity, and its distance from the fixed point around which it revolves.
|
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If these three quantities remain constant—that is, if the motion of a particular object takes place at a constant velocity at a fixed distance from the spin center—then the angular momentum is also a constant. Kepler’s second law is a consequence of the conservation of angular momentum. As a planet approaches the Sun on its elliptical orbit and the distance to the spin center decreases, the planet speeds up to conserve the angular momentum. Similarly, when the planet is farther from the Sun, it moves more slowly.
|
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The conservation of angular momentum is illustrated by figure skaters, who bring their arms and legs in to spin more rapidly, and extend their arms and legs to slow down (Figure 3.8). You can duplicate this yourself on a well-oiled swivel stool by starting yourself spinning slowly with your arms extended and then pulling your arms in. Another example of the conservation of angular momentum is a shrinking cloud of dust or a star
|
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74 3 • Orbits and Gravity
|
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collapsing on itself (both are situations that you will learn about as you read on). As material moves to a lesser distance from the spin center, the speed of the material increases to conserve angular momentum.
|
|||
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|
Figure 3.8 Conservation of Angular Momentum. When a spinning figure skater brings in her arms, their distance from her spin center is smaller, so her speed increases. When her arms are out, their distance from the spin center is greater, so she slows down.
|
|||
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3.3 Newton’s Universal Law of Gravitation
|
|||
|
|
Learning Objectives
|
|||
|
|
By the end of this section, you will be able to: Explain what determines the strength of gravity Describe how Newton’s universal law of gravitation extends our understanding of Kepler’s laws
|
|||
|
|
Newton’s laws of motion show that objects at rest will stay at rest and those in motion will continue moving uniformly in a straight line unless acted upon by a force. Thus, it is the straight line that defines the most natural state of motion. But the planets move in ellipses, not straight lines; therefore, some force must be bending their paths. That force, Newton proposed, was gravity. In Newton’s time, gravity was something associated with Earth alone. Everyday experience shows us that Earth exerts a gravitational force upon objects at its surface. If you drop something, it accelerates toward Earth as it falls. Newton’s insight was that Earth’s gravity might extend as far as the Moon and produce the force required to curve the Moon’s path from a straight line and keep it in its orbit. He further hypothesized that gravity is not limited to Earth, but that there is a general force of attraction between all material bodies. If so, the attractive force between the Sun and each of the planets could keep them in their orbits. (This may seem part of our everyday thinking today, but it was a remarkable insight in Newton’s time.) Once Newton boldly hypothesized that there was a universal attraction among all bodies everywhere in space, he had to determine the exact nature of the attraction. The precise mathematical description of that gravitational force had to dictate that the planets move exactly as Kepler had described them to (as expressed in Kepler’s three laws). Also, that gravitational force had to predict the correct behavior of falling bodies on Earth, as observed by Galileo. How must the force of gravity depend on distance in order for these conditions to be met? The answer to this question required mathematical tools that had not yet been developed, but this did not deter Isaac Newton, who invented what we today call calculus to deal with this problem. Eventually he was able to conclude that the magnitude of the force of gravity must decrease with increasing distance between
|
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Access for free at openstax.org
|
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3.3 • Newton’s Universal Law of Gravitation 75
|
|||
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the Sun and a planet (or between any two objects) in proportion to the inverse square of their separation. In other words, if a planet were twice as far from the Sun, the force would be (1/2)2, or 1/4 as large. Put the planet three times farther away, and the force is (1/3)2, or 1/9 as large.
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Newton also concluded that the gravitational attraction between two bodies must be proportional to their masses. The more mass an object has, the stronger the pull of its gravitational force. The gravitational attraction between any two objects is therefore given by one of the most famous equations in all of science:
|
|||
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where Fgravity is the gravitational force between two objects, M1 and M2 are the masses of the two objects, and R is their separation. G is a constant number known as the universal gravitational constant, and the equation itself symbolically summarizes Newton’s universal law of gravitation. With such a force and the laws of motion, Newton was able to show mathematically that the only orbits permitted were exactly those described by Kepler’s laws.
|
|||
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Newton’s universal law of gravitation works for the planets, but is it really universal? The gravitational theory should also predict the observed acceleration of the Moon toward Earth as it orbits Earth, as well as of any object (say, an apple) dropped near Earth’s surface. The falling of an apple is something we can measure quite easily, but can we use it to predict the motions of the Moon?
|
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Recall that according to Newton’s second law, forces cause acceleration. Newton’s universal law of gravitation says that the force acting upon (and therefore the acceleration of) an object toward Earth should be inversely proportional to the square of its distance from the center of Earth. Objects like apples at the surface of Earth, at a distance of one Earth-radius from the center of Earth, are observed to accelerate downward at 9.8 meters per second per second (9.8 m/s2).
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It is this force of gravity on the surface of Earth that gives us our sense of weight. Unlike your mass, which would remain the same on any planet or moon, your weight depends on the local force of gravity. So you would weigh less on Mars and the Moon than on Earth, even though there is no change in your mass. (Which means you would still have to go easy on the desserts in the college cafeteria when you got back!)
|
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The Moon is 60 Earth radii away from the center of Earth. If gravity (and the acceleration it causes) gets weaker with distance squared, the acceleration the Moon experiences should be a lot less than for the apple. The acceleration should be (1/60)2 = 1/3600 (or 3600 times less—about 0.00272 m/s2). This is precisely the observed acceleration of the Moon in its orbit. (As we shall see, the Moon does not fall to Earth with this acceleration, but falls around Earth.) Imagine the thrill Newton must have felt to realize he had discovered, and verified, a law that holds for Earth, apples, the Moon, and, as far as he knew, everything in the universe.
|
|||
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EXAMPLE 3.3
|
|||
|
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Calculating Weight
|
|||
|
|
By what factor would a person’s weight at the surface of Earth change if Earth had its present mass but eight times its present volume?
|
|||
|
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Solution
|
|||
|
|
With eight times the volume, Earth’s radius would double. This means the gravitational force at the surface would reduce by a factor of (1/2)2 = 1/4, so a person would weigh only one-fourth as much.
|
|||
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Check Your Learning
|
|||
|
|
By what factor would a person’s weight at the surface of Earth change if Earth had its present size but only one-third its present mass?
|
|||
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76 3 • Orbits and Gravity
|
|||
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Answer:
|
|||
|
|
With one-third its present mass, the gravitational force at the surface would reduce by a factor of 1/3, so a person would weight only one-third as much.
|
|||
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Gravity is a “built-in” property of mass. Whenever there are masses in the universe, they will interact via the force of gravitational attraction. The more mass there is, the greater the force of attraction. Here on Earth, the largest concentration of mass is, of course, the planet we stand on, and its pull dominates the gravitational interactions we experience. But everything with mass attracts everything else with mass anywhere in the universe. Newton’s law also implies that gravity never becomes zero. It quickly gets weaker with distance, but it continues to act to some degree no matter how far away you get. The pull of the Sun is stronger at Mercury than at Pluto, but it can be felt far beyond Pluto, where astronomers have good evidence that it continuously makes enormous numbers of smaller icy bodies move around huge orbits. And the Sun’s gravitational pull joins with the pull of billions of others stars to create the gravitational pull of our Milky Way Galaxy. That force, in turn, can make other smaller galaxies orbit around the Milky Way, and so on. Why is it then, you may ask, that the astronauts aboard the Space Shuttle appear to have no gravitational forces acting on them when we see images on television of the astronauts and objects floating in the spacecraft? After all, the astronauts in the shuttle are only a few hundred kilometers above the surface of Earth, which is not a significant distance compared to the size of Earth, so gravity is certainly not a great deal weaker that much farther away. The astronauts feel “weightless” (meaning that they don’t feel the gravitational force acting on them) for the same reason that passengers in an elevator whose cable has broken or in an airplane whose engines no longer work feel weightless: they are falling (Figure 3.9).2
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Figure 3.9 Astronauts in Free Fall. While in space, astronauts are falling freely, so they experience “weightlessness.” Clockwise from top left: Tracy Caldwell Dyson (NASA), Naoko Yamazaki (JAXA), Dorothy Metcalf-Lindenburger (NASA), and Stephanie Wilson 2 In the film Apollo 13, the scenes in which the astronauts were “weightless” were actually filmed in a falling airplane. As you might imagine, the plane fell for only short periods before the engines engaged again.
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Access for free at openstax.org
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3.3 • Newton’s Universal Law of Gravitation 77
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(NASA). (credit: NASA)
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When falling, they are in free fall and accelerate at the same rate as everything around them, including their spacecraft or a camera with which they are taking photographs of Earth. When doing so, astronauts experience no additional forces and therefore feel “weightless.” Unlike the falling elevator passengers, however, the astronauts are falling around Earth, not to Earth; as a result they will continue to fall and are said to be “in orbit” around Earth (see the next section for more about orbits).
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Orbital Motion and Mass
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Kepler’s laws describe the orbits of the objects whose motions are described by Newton’s laws of motion and the law of gravity. Knowing that gravity is the force that attracts planets toward the Sun, however, allowed Newton to rethink Kepler’s third law. Recall that Kepler had found a relationship between the orbital period of a planet’s revolution and its distance from the Sun. But Newton’s formulation introduces the additional factor of the masses of the Sun (M1) and the planet (M2), both expressed in units of the Sun’s mass. Newton’s universal law of gravitation can be used to show mathematically that this relationship is actually
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where a is the semimajor axis and P is the orbital period.
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How did Kepler miss this factor? In units of the Sun’s mass, the mass of the Sun is 1, and in units of the Sun’s mass, the mass of a typical planet is a negligibly small factor. This means that the sum of the Sun’s mass and a planet’s mass, (M1 + M2), is very, very close to 1. This makes Newton’s formula appear almost the same as Kepler’s; the tiny mass of the planets compared to the Sun is the reason that Kepler did not realize that both masses had to be included in the calculation. There are many situations in astronomy, however, in which we do need to include the two mass terms—for example, when two stars or two galaxies orbit each other.
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Including the mass term allows us to use this formula in a new way. If we can measure the motions (distances and orbital periods) of objects acting under their mutual gravity, then the formula will permit us to deduce their masses. For example, we can calculate the mass of the Sun by using the distances and orbital periods of the planets, or the mass of Jupiter by noting the motions of its moons.
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Indeed, Newton’s reformulation of Kepler’s third law is one of the most powerful concepts in astronomy. Our ability to deduce the masses of objects from their motions is key to understanding the nature and evolution of many astronomical bodies. We will use this law repeatedly throughout this text in calculations that range from the orbits of comets to the interactions of galaxies.
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EXAMPLE 3.4
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Calculating the Effects of Gravity
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A planet like Earth is found orbiting its star at a distance of 1 AU in 0.71 Earth-year. Can you use Newton’s version of Kepler’s third law to find the mass of the star? (Remember that compared to the mass of a star, the mass of an earthlike planet can be considered negligible.)
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Solution
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In the formula a3 = (M1 + M2) × P2, the factor M1 + M2 would now be approximately equal to M1 (the mass of the star), since the planet’s mass is so small by comparison. Then the formula becomes a3 = M1 × P2, and we can solve for M1:
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Since a = 1, a3 = 1, so
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78 3 • Orbits and Gravity
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So the mass of the star is twice the mass of our Sun. (Remember that this way of expressing the law has units in terms of Earth and the Sun, so masses are expressed in units of the mass of our Sun.)
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Check Your Learning
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Suppose a star with twice the mass of our Sun had an earthlike planet that took 4 years to orbit the star. At what distance (semimajor axis) would this planet orbit its star?
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Answer:
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Again, we can neglect the mass of the planet. So M1 = 2 and P = 4 years. The formula is a3 = M1 × P2, so a3 = 2 × 42 = 2 × 16 = 32. So a is the cube root of 32. To find this, you can just ask Google, “What is the cube root of 32?” and get the answer 3.2 AU.
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LINK TO LEARNING
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You might like to try a simulation (https://openstax.org/l/30phetsimsunear) that lets you move the Sun, Earth, Moon, and space station to see the effects of changing their distances on their gravitational forces and orbital paths. You can even turn off gravity and see what happens.
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3.4 Orbits in the Solar System
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Learning Objectives
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By the end of this section, you will be able to: Compare the orbital characteristics of the planets in the solar system Compare the orbital characteristics of asteroids and comets in the solar system
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Recall that the path of an object under the influence of gravity through space is called its orbit, whether that object is a spacecraft, planet, star, or galaxy. An orbit, once determined, allows the future positions of the object to be calculated. Two points in any orbit in our solar system have been given special names. The place where the planet is closest to the Sun (helios in Greek) and moves the fastest is called the perihelion of its orbit, and the place where it is farthest away and moves the most slowly is the aphelion. For the Moon or a satellite orbiting Earth (gee in Greek), the corresponding terms are perigee and apogee. (In this book, we use the word moon for a natural object that goes around a planet and the word satellite to mean a human-made object that revolves around a planet.)
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Orbits of the Planets
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Today, Newton’s work enables us to calculate and predict the orbits of the planets with marvelous precision. We know eight planets, beginning with Mercury closest to the Sun and extending outward to Neptune. The average orbital data for the planets are summarized in Table 3.2. (Ceres is the largest of the asteroids, now considered a dwarf planet.) According to Kepler’s laws, Mercury must have the shortest orbital period (88 Earth-days); thus, it has the highest orbital speed, averaging 48 kilometers per second. At the opposite extreme, Neptune has a period of 165 years and an average orbital speed of just 5 kilometers per second. All the planets have orbits of rather low eccentricity. The most eccentric orbit is that of Mercury (0.21); the rest
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Access for free at openstax.org
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3.4 • Orbits in the Solar System 79
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have eccentricities smaller than 0.1. It is fortunate that among the rest, Mars has an eccentricity greater than that of many of the other planets. Otherwise the pre-telescopic observations of Brahe would not have been sufficient for Kepler to deduce that its orbit had the shape of an ellipse rather than a circle. The planetary orbits are also confined close to a common plane, which is near the plane of Earth’s orbit (called the ecliptic). The strange orbit of the dwarf planet Pluto is inclined about 17° to the ecliptic, and that of the dwarf planet Eris (orbiting even farther away from the Sun than Pluto) by 44°, but all the major planets lie within 10° of the common plane of the solar system.
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LINK TO LEARNING
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JavaLab’s solar system simulator (https://openstax.org/l/30solarsim) allows you to explore the size and speed of the planets’ orbits, and view the orbits from different perspectives.
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Orbits of Asteroids and Comets
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In addition to the eight planets, there are many smaller objects in the solar system. Some of these are moons (natural satellites) that orbit all the planets except Mercury and Venus. In addition, there are two classes of smaller objects in heliocentric orbits: asteroids and comets. Both asteroids and comets are believed to be small chunks of material left over from the formation process of the solar system. In general, asteroids have orbits with smaller semimajor axes than do comets (Figure 3.10). The majority of them lie between 2.2 and 3.3 AU, in the region known as the asteroid belt (see Comets and Asteroids: Debris of the Solar System). As you can see in Table 3.2, the asteroid belt (represented by its largest member, Ceres) is in the middle of a gap between the orbits of Mars and Jupiter. It is because these two planets are so far apart that stable orbits of small bodies can exist in the region between them.
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80 3 • Orbits and Gravity
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Figure 3.10 Solar System Orbits. We see the orbits of typical comets and asteroids compared with those of the planets Mercury, Venus, Earth, Mars, and Jupiter (black circles). Shown in red are three comets: Halley, Kopff, and Encke. In blue are the four largest asteroids: Ceres, Pallas, Vesta, and Hygeia.
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Orbital Data for the Planets
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Planet Semimajor Axis (AU) Period (y) Eccentricity
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Mercury 0.39
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0.24
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0.21
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Venus
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0.72
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0.6
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0.01
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Earth
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1
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1.00
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0.02
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Mars
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1.52
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1.88
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0.09
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(Ceres) 2.77
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4.6
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0.08
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Jupiter 5.20
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11.86
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0.05
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Saturn 9.54
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29.46
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0.06
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Uranus 19.19
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84.01
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0.05
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Table 3.2
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Access for free at openstax.org
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3.5 • Motions of Satellites and Spacecraft 81
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Planet Semimajor Axis (AU) Period (y) Eccentricity
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Neptune 30.06
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164.82
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0.01
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Table 3.2
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Comets generally have orbits of larger size and greater eccentricity than those of the asteroids. Typically, the eccentricity of their orbits is 0.8 or higher. According to Kepler’s second law, therefore, they spend most of their time far from the Sun, moving very slowly. As they approach perihelion, the comets speed up and whip through the inner parts of their orbits more rapidly.
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3.5 Motions of Satellites and Spacecraft
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Learning Objectives
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By the end of this section, you will be able to: Explain how an object (such as a satellite) can be put into orbit around Earth Explain how an object (such as a planetary probe) can escape from orbit
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Newton’s universal law of gravitation and Kepler’s laws describe the motions of Earth satellites and interplanetary spacecraft as well as the planets. Sputnik, the first artificial Earth satellite, was launched by what was then called the Soviet Union on October 4, 1957. Since that time, thousands of satellites have been placed into orbit around Earth, and spacecraft have also orbited the Moon, Venus, Mars, Jupiter, Saturn, and a number of asteroids and comets.
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Once an artificial satellite is in orbit, its behavior is no different from that of a natural satellite, such as our Moon. If the satellite is high enough to be free of atmospheric friction, it will remain in orbit forever. However, although there is no difficulty in maintaining a satellite once it is in orbit, a great deal of energy is required to lift the spacecraft off Earth and accelerate it to orbital speed.
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To illustrate how a satellite is launched, imagine a gun firing a bullet horizontally from the top of a high mountain, as in Figure 3.11, which has been adapted from a similar diagram by Newton. Imagine, further, that the friction of the air could be removed and that nothing gets in the bullet’s way. Then the only force that acts on the bullet after it leaves the muzzle is the gravitational force between the bullet and Earth.
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82 3 • Orbits and Gravity
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Figure 3.11 Firing a Bullet into Orbit. (a) For paths a and b, the velocity is not enough to prevent gravity from pulling the bullet back to Earth; in case c, the velocity allows the bullet to fall completely around Earth. (b) This diagram by Newton in his De Mundi Systemate, 1731 edition, illustrates the same concept shown in (a).
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If the bullet is fired with a velocity we can call va, the gravitational force acting upon it pulls it downward toward Earth, where it strikes the ground at point a. However, if it is given a higher muzzle velocity, vb, its higher speed carries it farther before it hits the ground at point b. If our bullet is given a high enough muzzle velocity, vc, the curved surface of Earth causes the ground to remain the same distance from the bullet so that the bullet falls around Earth in a complete circle. The speed needed to do this—called the circular satellite velocity—is about 8 kilometers per second, or about 17,500 miles per hour in more familiar units.
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LINK TO LEARNING
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Use the Newton’s Mountain simulator (https://openstax.org/l/30newmtnsim) to see for yourself the effects of increasing an object’s speed. You can raise the speed until you find the speed that is just fast enough for an object to orbit the Earth, the circular satellite velocity, and also the speed at which an object leaves the Earth forever, or the escape speed.
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Each year, more than 50 new satellites are launched into orbit by such nations as Russia, the United States, China, Japan, India, and Israel, as well as by the European Space Agency (ESA), a consortium of European nations (Figure 3.12). Today, these satellites are used for weather tracking, ecology, global positioning systems, communications, and military purposes, to name a few uses. Most satellites are launched into low Earth orbit, since this requires the minimum launch energy. At the orbital speed of 8 kilometers per second, they circle the planet in about 90 minutes. Some of the very low Earth orbits are not indefinitely stable because, as Earth’s atmosphere swells from time to time, a frictional drag is generated by the atmosphere on these satellites, eventually leading to a loss of energy and “decay” of the orbit.
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Access for free at openstax.org
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