Welcome to the Universe

"This book provides a very valuable resource for anyone who wants to acquire a reasonably quantitative understanding of introductory astronomy. The questions cover a broad range of interesting topics, and the solutions are thorough and often enlightening, providing additional insights into the subject matter."-Alex Filippenko, University of California, Berkeley "The difference between a good astronomy course and a great astronomy course is great problems. This book is a gold mine of great problems for introductory astronomy, problems that can be solved with high school algebra and run the gamut from earth-smashing asteroids to neutron stars, black holes, the fate of the universe, and the search for life on other worlds. It will be a valuable resource for anyone teaching introductory astronomy and an exhilarating challenge for students who want to sharpen their wits against the cosmos."-David Weinberg, Ohio State University "A fantastic asset. The hardest part of teaching introductory astronomy courses is writing engaging, informative problems at the appropriate level. This book provides a treasure trove of wonderfully instructive material that is much better than anything else out there. I will be using Tyson, Strauss, and Gott for a long time to come."-James H. Applegate, Columbia University "A marvelous compendium. This companion book demonstrates in a playful manner how, with no more than high school algebra, we can obtain a deeper appreciation of the properties of the infinitely large and small, and deepen our conversation with the cosmos."-Trinh X. Thuan, University of Virginia "A wonderful collection of introductory problems that convey the wonders of the universe and fundamental concepts in astronomy through specific examples and numbers. A fantastic resource for the classroom and aspiring astronomers."-Abraham Loeb, Harvard University "Microorganisms on Europa, colliding black holes, cosmic inflation, and much more are covered in this expansive and thoughtfully selected collection of exciting problems in astrophysics-even a two-dimensional Tardis appears! Both students and experienced astronomers should come away enriched through study of these problems and the techniques presented to crack them."-W. Niel Brandt, Pennsylvania State University

Neil deGrasse Tyson is director of the Hayden Planetarium at the American Museum of Natural History. He is the author of many books, including Space Chronicles: Facing the Ultimate Frontier, and the host of the Emmy-winning documentary Cosmos: A Spacetime Odyssey. Michael A. Strauss is professor of astrophysics at Princeton University. J. Richard Gott is professor emeritus of astrophysics at Princeton University. His other books include The Cosmic Web: Mysterious Architecture of the Universe (Princeton).

Preface xvii Math Tips xxi PART I. STARS, PLANETS, AND LIFE 1 1 | THE SIZE AND SCALE OF THE UNIVERSE 3 1 Scientific notation review 3 Writing numbers in scientific notation. 2 How long is a year? 3 Calculating the number of seconds in a year. 3 How fast does light travel? 3 Calculating the number of kilometers in a light-year. 4 Arcseconds in a radian 3 Calculating the number of arcseconds in a radian, a number used whenever applying the small-angle formula. 5 How far is a parsec? 3 Converting from parsecs to light-years and astronomical units. 6 Looking out in space and back in time 4 Exploring the relationship between distance and time when traveling at the speed of light. 7 Looking at Neptune 4 The time for light to travel from Earth to the planet Neptune depends on where it and we are in our respective orbits. 8 Far, far away; long, long ago 5 There is an intrinsic time delay in communicating with spacecraft elsewhere in the solar system or elsewhere in the Milky Way galaxy. 9 Interstellar travel 6 Calculating how long it takes to travel various distances at various speeds. 10 Traveling to the stars 6 Calculating how long it would take to travel to the nearest stars. 11 Earth's atmosphere 7 Calculating the mass of the air in Earth's atmosphere, and comparing it with the mass of the oceans. 2 | FROM THE DAY AND NIGHT SKY TO PLANETARY ORBITS 8 12 Movements of the Sun, Moon, and stars 8 Exploring when and where one can see various celestial bodies. 13 Looking at the Moon 8 There is a lot you can infer by just looking at the Moon! 14 Rising and setting 9 Questions about when various celestial bodies rise and set. 15 Objects in the sky 9 More questions about what you can learn by looking at objects in the sky. 16 Aristarchus and the Moon 10 Determining the relative distance to the Moon and the Sun using high-school geometry. 17 The distance to Mars 11 Using parallax to determine how far away Mars is. 18 The distance to the Moon 11 Using parallax to determine how far away the Moon is. 19 Masses and densities in the solar system 11 Calculating the density of the Sun and of the solar system. 3 | NEWTON'S LAWS 13 20 Forces on a book 13 Using Newton's laws to understand the forces on a book resting on a table. 21 Going ballistic 13 Calculating the speed of a satellite in low Earth orbit. 22 Escaping Earth's gravity? 14 Calculating the distance at which the gravitational force from Earth and the Moon are equal. 23 Geosynchronous orbits 14 Calculating the radius of the orbit around Earth that is synchronized with Earth's rotation. 24 Centripetal acceleration and kinetic energy in Earth orbit 14 Calculating the damage done by a collision with space debris. 25 Centripetal acceleration of the Moon and the law of universal gravitation 15 Comparing the acceleration of the Moon in its orbit to that of a dropped apple at Earth's surface. 26 Kepler at Jupiter 16 Applying Kepler's laws to the orbits of Jupiter's moons. 27 Neptune and Pluto 17 Calculating the relationship of the orbits of Neptune and Pluto. 28 Is there an asteroid with our name on it? 17 How to deflect an asteroid that is on a collision course with Earth. 29 Halley's comet and the limits of Kepler's third law 18 Applying Kepler's third law to the orbit of Halley's comet. 30 You cannot touch without being touched 19 The motion of the Sun due to the gravitational pull of Jupiter. 31 Aristotle and Copernicus 19 An essay about ancient and modern views of the heavens. 4-6 | HOW STARS RADIATE ENERGY 20 32 Distant supernovae 20 Using the inverse square law relating brightness and luminosity. 33 Spacecraft solar power 20 Calculating how much power solar panels on a spacecraft can generate. 34 You glow! 21 Calculating how much blackbody radiation our bodies give off.