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Welcome to the Universe: The Problem Book

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Here is the essential companion to Welcome to the Universe, a New York Times bestseller that was inspired by the enormously popular introductory astronomy course for non science majors that Neil deGrasse Tyson, Michael A. Strauss, and J. Richard Gott taught together at Princeton. This problem book features more than one hundred problems and exercises used in the original course—ideal for anyone who wants to deepen their understanding of the original material and to learn to think like an astrophysicist.

Whether you’re a student or teacher, citizen scientist or science enthusiast, your guided tour of the cosmos just got even more hands-on with Welcome to the Universe: The Problem Book.

. The essential companion book to the acclaimed bestseller

. Features the problems used in the original introductory astronomy course for non science majors at Princeton University

. Organized according to the structure of Welcome to the Universe, empowering readers to explore real astrophysical problems that are conceptually introduced in each chapter

. Problems are designed to stimulate physical insight into the frontier of astrophysics

. Problems develop quantitative skills, yet use math no more advanced than high school algebra

. Problems are often multipart, building critical thinking and quantitative skills and developing readers’ insight into what astrophysicists do

. Ideal for course use—either in tandem with Welcome to the Universe or as a supplement to courses using standard astronomy textbooks—or self-study

. Tested in the classroom over numerous semesters for more than a decade

. Prefaced with a review of relevant concepts and equations

. Full solutions and explanations are provided, allowing students and other readers to check their own understanding

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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
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.
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.
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 o

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