A "companion to Welcome to the Universe, a ... bestseller that was inspired by the ... introductory astronomy course for non-science majors that Neil deGrasse Tyson, Michael A. Strauss, and J. Richard Gott taught together at Princeton. [It] features more than one hundred problems and exercises used in the original course"--Amazon.com.
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.
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.
35 Tiny angles 21
Understanding the relationship between motions in space and in the plane of the sky.
36 Thinking about parallax 22
How nearby stars appear to move in the sky relative to more distant stars, due to the Earth's motion around the Sun.
37 Really small angles and distant stars 22
The Gaia spacecraft's ability to measure parallax of distant stars.
38 Brightness, distance, and luminosity 23
Exploring the relationship between brightness and luminosity of various stars.
39 Comparing stars 23
Relating the luminosity, radius, surface temperature, and distance of stars.
40 Hot and radiant 24
Exploring the relation between the properties of stars radiating as blackbodies.
41 A white dwarf star 24
Calculating the distance and size of a white dwarf star.
42 Orbiting a white dwarf 24
Using Kepler's third law to determine the orbit around a white dwarf star.
43 Hydrogen absorbs 25
Using the spectrum of an F star to understand the energy levels of a hydrogen atom. A challenge problem.
7-8 | THE LIVES AND DEATHS OF STARS 27
44 The shining Sun 27
Calculating the rate at which hydrogen fuses to helium in the core of the Sun.
45 Thermonuclear fusion and the Heisenberg uncertainty principle 27
Using quantum mechanics to determine the conditions under which thermonuclear fusion can take place in the core of a star. A challenge problem.
46 Properties of white dwarfs 29
Using direct observations of a white dwarf to determine its radius and density. A challenge problem.
47 Squeezing into a white dwarf 30
Determining how far apart the nuclei in a white dwarf star are.
48 Flashing in the night 30
Determining whether the gravity of a pulsar is adequate to hold it together as it spins.
49 Life on a neutron star 31
Calculating the effects of the extreme gravity of a neutron star.
50 Distance to a supernova 31
Watching a supernova remnant expand, and using this to determine how far away it is.
51 Supernovae are energetic! 32
Putting the luminosity of a supernova in context.
52 Supernovae are dangerous! 33
What would happen if a supernova were to explode within a few hundred light-years of Earth?
53 Neutrinos coursing through us 33
Calculating the flux and detectability of neutrinos emitted during a supernova explosion.
54 A really big explosion 34
Calculating the energy associated with a gamma-ray burst.
55 Kaboom! 36
Calculating the properties of one of the most powerful gamma-ray bursts ever seen.
56 Compact star 36
Calculating the distance between nuclei in a neutron star.
57 Orbiting a neutron star 37
Applying Kepler's third law for an orbit around a neutron star.
58 The Hertzsprung-Russell diagram 37
An essay about the relationship between surface temperature and luminosity of stars.
9 | WHY PLUTO IS NOT A PLANET 38
59 A rival to Pluto? 38
Calculating the properties of a large Kuiper Belt Object in the outer solar system, working directly from observations. A challenge problem.
60 Another Pluto rival 41
Exploring the properties of another large body in the outer solar system.
61 Effects of a planet on its parent star 43
Using observations of the motion of a star under the gravitational influence of an orbiting planet to infer the properties of that planet.
62 Catastrophic asteroid impacts 44
How the impact of an asteroid on the early Earth may have evaporated the oceans.
63 Tearing up planets 45
Calculating the tidal force of a planet on an orbiting moon. A challenge problem.
10 | THE SEARCH FOR LIFE IN THE GALAXY 47
64 Planetary orbits and temperatures 47
Calculating the orbits and equilibrium temperatures of planets orbiting other stars.
65 Water on other planets? 47
Determining whether liquid water can exist on the surface of planets orbiting other stars.
66 Oceans in the solar system 48
Exploring the properties of oceans on Earth, Mars and Europa.
67 Could photosynthetic life survive in Europa's ocean? 49
Determining how much life the sunlight that impinges on Europa could support.
68 An essay on liquid water 50
An essay describing the conditions under which liquid water, necessary for life as we know it, exists.
PART II. GALAXIES 51
11-13 | THE MILKY WAY AND THE UNIVERSE OF GALAXIES 53
69 How many stars are there? 53
Calculating the number of stars in the observable universe.
70 The distance between stars 54
Putting the distance between stars into perspective.
71 The emptiness of space 54
Calculating the density of the Milky Way and of the universe as a whole.
72 Squeezing the Milky Way 54
What would happen if you brought all the stars in the Milky Way into one big ball?
73 A star is born 55
How much interstellar gas do you need to bring together to make a star?
74 A massive black hole in the center of the Milky Way 55
Calculating the mass of the black hole at the center of our Galaxy, working directly from observations.
75 Supernovae and the Galaxy 55
How many supernovae are needed to create the heavy elements in the Milky Way?
76 Dark matter halos 56
Calculating the mass of the Milky Way from its observed rotation.
77 Orbiting Galaxy 57
The orbit of the Large Magellanic Cloud around the Milky Way, and what it says about the mass of our Galaxy.
78 Detecting dark matter 57
Calculating how many dark matter particles there are all around us, and how we plan to detect them. A challenge problem.
79 Rotating galaxies 60
Determining whether we can see the rotation of a galaxy on the sky.
80 Measuring the distance to a rotating galaxy 60
Using the apparent motion of stars in a galaxy in the plane of the sky and along the line of sight to determine its distance.
14 | THE EXPANSION OF THE UNIVERSE 61
81 The Hubble Constant 61
Measuring the expansion rate of the universe from the measured properties of galaxies.
82 Which expands faster: The universe or the Atlantic Ocean? 63
The answer may surprise you.
83 The third dimension in astronomy 63
An essay about how we measure distances in the universe.
84 Will the universe expand forever? 63
The relationship between the density of the universe and its future fate. A challenge problem.
85 The motion of the Local Group through space 64
Calculating the gravitational pull from the Virgo galaxy supercluster on our Local Group of galaxies. A challenge problem.
15-16 | THE EARLY UNIVERSE AND QUASARS 67
86 Neutrinos in the early universe 67
Calculating just how numerous the neutrinos produced soon after the Big Bang are.
87 No center to the universe 68
A brief essay explaining why the expanding universe has no center.
88 Luminous quasars 68
Calculating the properties of quasars, and the supermassive black holes that power them.
89 The origin of the elements 68
An essay describing how different elements are formed in the universe.
PART III. EINSTEIN AND THE UNIVERSE 69
17-18 | EINSTEIN'S ROAD TO SPECIAL RELATIVITY 71
90 Lorentz factor 71
Exploring the special relativistic relation between lengths as seen in different reference frames.
91 Speedy muons 72
How special relativity is important in understanding the formation and detection of muons created in the upper atmosphere.
92 Energetic cosmic rays 73
Determining relativistic effects for one of the highest-energy particles ever seen.
93 The Titanic is moving 73
Playing relativistic games with the great ship Titanic.
94 Aging astronaut 74
Understanding how the relativistic effects of moving an astronaut at close to the speed of light.
95 Reunions 74
How two friends can differ on the passage of time.
96 Traveling to another star 74
Calculating how time ticks slower for an astronaut traveling at close to the speed of light.
97 Clocks on Earth are slow 74
Calculating the difference between a clock in orbit around the Sun and one standing still.
98 Antimatter! 74
Should you run if trucks made of matter and antimatter collide with one another?
99 Energy in a glass of water 75
Calculating how much energy could be extracted from the fusion of the hydrogen in a glass of water.
100 Motion through spacetime 75
Drawing the path of the Earth's orbit around the Sun in spacetime.
101 Can you go faster than the speed of light? 75
Why the postulates of special relativity do not allow travel faster than the speed of light.
102 Short questions in special relativity 76
Quick questions which can be answered in a few sentences.
19 | EINSTEIN'S GENERAL THEORY OF RELATIVITY 77
103 Tin Can Land 77
Exploring the nature of geodesics on a familiar two-dimensional surface.
104 Negative mass 78
Would a dropped ball of negative mass fall down?
105 Aging in orbit 79
Exploring special and general relativistic effects on your clock while in orbit. A challenge problem.
106 Short questions in general relativity 80
Quick questions that can be answered in a few sentences.
20 | BLACK HOLES 82
107 A black hole at the center of the Milky Way 82
Calculating the properties of the supermassive black hole at the center of our Galaxy.
108 Quick questions about black holes 82
Short questions that can be answered in a few sentences.
109 Big black holes 83
Exploring the properties of the biggest black holes in the universe.
110 A Hitchhiker's challenge 83
The Hitchhiker's Guide to the Galaxy inspires a problem on black holes. A challenge problem.
111 Colliding black holes! 84
Measurements of gravitational waves from a pair of merging black holes allows us to determine their properties.
112 Extracting energy from a pair of black holes 85
Using ideas from Stephen Hawking to determine how much energy can be released when black holes collide.
21 | COSMIC STRINGS, WORMHOLES, AND TIME TRAVEL 87
113 Quick questions about time travel 87
Short questions that can be answered in a few sentences.
114 Time travel tennis 87
Playing a tennis game with yourself with the help of time travel. A challenge problem.
115 Science fiction 89
Writing a science fiction story that uses concepts from astrophysics: the challenge is to make it as scientifically realistic as possible.
22 | THE SHAPE OF THE UNIVERSE
AND THE BIG BANG 91
116 Mapping the universe 91
Ranking the distance of various astronomical objects from the Earth.
117 Gnomonic projections 91
Exploring the geometry of an unusual mapping of the night sky onto a flat piece of paper.
118 Doctor Who in Flatland 95
Using concepts from general relativity to understand the nature of Dr. Who's Tardis.
119 Quick questions about the shape of the universe 96
Short questions that can be answered in a few sentences.
23 | INFLATION AND RECENT
DEVELOPMENTS IN COSMOLOGY 97
120 The earliest possible time 97
Calculating it using both general relativity and quantum mechanics.
121 The worst approximation in all of physics 98
Can the Planck density give us a reasonable estimate for the density of dark energy? Hint: no.
122 Not a blunder after all? 99
Describing the relationship between Einstein's desire for a static universe and the accelerated expansion we now observe.
123 The Big Bang 99
An essay describing the empirical evidence that the universe started in a Big Bang.
24 | OUR FUTURE IN THE UNIVERSE 100
124 Getting to Mars 100
Calculating the most efficient orbit to get from Earth to Mars.
125 Interstellar travel: Solar sails 101
Using the pressure of light from the Sun to propel a spacecraft for interstellar travel.
126 Copernican arguments 102
Applied to time.
127 Copernicus in action 102
An essay about Copernican arguments in our understanding of the structure of the universe and our place in it.
128 Quick questions for our future in the universe 103
Short questions that can be answered in a few sentences.
129 Directed panspermia 103
Exploring how humankind could colonize the Milky Way with robotic probes.
Useful Numbers and Equations 107
Solutions 113
"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 "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 "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 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 "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 "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