Complete Solutions Manuals - Chapter 1 - 24 (All Chapters)
Chapter-by-Chapter Guide
Part I: Developing Perspective
The remainder of this Instructor Guide goes through the book chapter by chapter. Each
chapter is organized as follows:
• A brief introduction with general comments about the chapter.
• Teaching Notes: Organized section by section for the chapter, these are essentially
miscellaneous notes that may be of use to you when teaching your course.
• Answers/Discussion Points for Think About It and See It for Yourself Questions.
• Solutions to End-of-Chapter Problems.
Chapter 1. A Modern View of the Universe
The purpose of this first chapter is to provide students with the contextual framework
they need to learn the rest of the course material effectively: a general overview of the
scale of the universe (Section 1.1), the history of the universe and the scale of time
(Section 1.2), and an overview of motion in the universe (Section 1.3). We often tell
students that, after completing this first chapter, they have essentially learned all the
major ideas of astronomy, and the rest of their course will be building the detailed
scientific case for these general ideas.
As always, when you prepare to teach this chapter, be sure that you are familiar with the
online quizzes, interactive figures and tutorials, assignable homework, and other
resources available on the Mastering Astronomy Web site.
Key Changes for the 10th Edition: For those who have used earlier editions of our
textbook, please note the following significant changes in this chapter:
New Chapter Opening image: Using the first deep field released from JWST in
place of the Hubble Extreme Deep Field. This should provide a great opportunity
to discuss recent JWST discoveries that came after this edition went to press in
early fall 2022.
We have dropped the former short Section 1.4 (“The Human Adventure of
Astronomy”), based on comments that it was redundant with what we’ve already
stated in this chapter and discuss further in later chapters.
Clarifications on number of galaxies in the Local Group and universe to reflect
recent discoveries.
44 Instructor Guide
,Note on Mathematics: The MasteringAstronomy Web site has a set of Math Review
videos and brief, assignable tutorials that we created to cover basic topics like fractions,
scientific notation, and unit analysis. Those instructors who include some mathematical
work (such as covering the Mathematical Insight boxes or assigning end-of-chapter
quantitative exercises) may wish to assign these videos and tutorials along with the first
couple of chapters of the text.
Teaching Notes (by Section)
Section 1.1 The Scale of the Universe
This section provides a brief overview of our place in the universe, including the
hierarchical structure of the universe (our cosmic address) and the scale of the universe.
• Our emphasis on scale may seem unusual to those who have not taught from our
book previously. However, we believe it is an extraordinarily important topic that
generally is underappreciated by students. Most students enter our course without
any realistic view of the true scale of the universe, and without the context of
scale, they are likely to misinterpret much of the rest of the content and detail in
an astronomy course.
• Note that the section begins with a brief discussion of the JWST deep field image
in the Chapter Opening photo, which helps set the context for an overview of our
place in the universe.
• Note the box on “Basic Astronomical Definitions”: Although some of the terms in
this box are not discussed immediately, having them here in the beginning of the
book should be helpful to students. All these terms also appear in the Glossary, but
they are so basic and important that we want to emphasize them here in Chapter 1.
• This section introduces astronomical distance measurements in AU and light-years.
A couple of notes on our choices and definitions:
• There are several different ways to define an average distance between Earth
and the Sun (e.g., averaged over phase, over time, etc.). In defining an
astronomical unit (AU) as the average distance between Earth and the Sun,
we are using the term average to mean (perihelion + aphelion)/2, which is
equivalent to the semimajor axis. This has advantages when it comes to
discussing Kepler’s third law, as it is much easier for students to think of a in
the equation p 2 a3 as average than as semimajor axis.
• Note that we’ve chosen to use light-years rather than parsecs as our primary
unit for stellar and galactic distances for three reasons: (1) We have found that
light-years are more intuitive than parsecs to most students because light-years
require only an understanding of light travel times, and not of the more
complex trigonometry of parallax. (2) Lookback time is one of the most
important concepts in astronomy, and the use of light-years makes it far easier
to think about lookback times (e.g., when a student hears that a star is 100
light-years away, he/she can immediately recognize that we’re seeing light that
left the star 100 years ago). (3) Fortuitously, 1 light-year happens to be very
The Cosmic Perspective, Tenth Edition 45
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close to 10 kilometers (9.46 1012 kilometers), making approximate unit
conversions very easy, which by extension helps students remember that light-
years are a unit of distance, not of time.
• Note that in discussing distances to very distant galaxies, we give distances in
terms of lookback times. For example, when we say “7 billion light-years,” we
mean a lookback time of 7 billion years. With this definition, the radius of the
observable universe is about 14 billion light-years, corresponding to the age of the
universe. Note that some media reports instead quote distances as they would be
today with the ongoing expansion, for example, saying that the universe is 40+
billion light-years in radius. As a result, some students may be confused about
which is the “real” radius of the observable universe. To alleviate this confusion, it
is worth pointing out (and we discuss this further in Chapter 20) that
• “Distance” is ambiguous in an expanding universe; e.g., do you mean an
object’s distance at the time the light left, or now, or some time in between? The
choice is arbitrary, with no particular choice (such as “now”) being any better
than any other (such as “at the time the light left”).
• In contrast, “lookback time” is unambiguous—it is the actual amount of time
that the light has been traveling to reach us.
• Given the above, we feel that lookback time is a much better way to describe
distances.
• For our discussion of scale, we begin by making use of the 1-to-10-billion scale of
the Voyage scale model solar system in Washington, D.C., a project that was
proposed by The Cosmic Perspective author Jeff Bennett. Voyage replicas are
being developed for other science centers and universities; if you are interested in
learning more about how to get a Voyage replica in your town, please contact Jeff
by e-mail (jeff@bigkidscience.com).
• With regard to the count to 100 billion, it can be fun in lecture to describe what
happens when you ask children how long it would take. Young children inevitably
say they can count much faster than one per second. But what happens when they
get to, say, “twenty-four billion, six hundred ninety-seven million, five hundred
sixty-two thousand, nine hundred seventy-seven . . .”? How fast can they count
now? And can they remember what comes next?
• Regarding our statement that there are “more than 100 billion large galaxies in the
observable universe.” You have probably heard news reports suggesting that the
number of galaxies is more than 1 trillion. However, these reports are including
galaxy counts in different epochs (based on distant observations), and there were
more galaxies in the past than there are today, due to mergers. In addition, the
number of galaxies depends on the cutoff size used. That is why we qualify our
statement as “large” galaxies, meaning comparable in size to the Milky Way, for
which 100 to 200 billion remains a reasonable estimate.
• Regarding our claim that the number of stars in the observable universe is roughly
the same as the number of grains of sand on all the beaches on Earth, here are the
assumptions we’ve made:
46 Instructor Guide
, • We are using 1022 as the number of stars in the universe. Assuming that grains
of sand typically have a volume of 1 mm3 (correct within a factor of 2 or 3),
1022 grains of sand would occupy a volume of 1022 mm3 or 1013 m3 .
• We estimate the depth of sand on a typical beach to be about 2–5 meters (based
on beaches we’ve seen eroded by storms) and estimate the width of a typical
beach at 20–50 meters; thus, the cross-sectional area of a typical beach is
roughly 100 m 2 .
• With this 100 m 2 cross-sectional area, it would take a length of 1011 meters, or
108 kilometers, to make a volume of 1013 m3 . This is almost certainly greater
than the linear extent of sandy beaches on Earth.
Section 1.2 The History of the Universe
This section provides a brief overview of our place in time, including an overview of the
history of the universe (our cosmic origins) and the scale of time.
• As in the first section, we include a major emphasis on scale—in this case, the
scale of time. Be sure to point out the backside of the foldout in the front of the
book, which is called “You Are Here in Time” and is in some sense a summary of
this section.
• We give the age of the universe as “about 14 billion years”; we feel this rounding
to two significant digits makes it easier for students to understand, given that the
current best estimate age (from the Planck mission) is 13.82 billion years, with a 1
sigma error bar of about 0.1 billion years.
• The idea of a “cosmic calendar” was popularized by Carl Sagan. Now that we’ve
calibrated the cosmic calendar to a cosmic age of 14 billion years, note that 1
average month = 1.17 billion years.
Section 1.3 Spaceship Earth
This section completes our overview of the “big picture” of the universe by focusing on
motion in the context of the motions of Earth in space, using R. Buckminster Fuller’s
idea of Spaceship Earth.
• Note that the summary figure for this section comes at its end, in Figure 1.18.
• We use the term tilt rather than obliquity as part of our continuing effort to limit the
use of jargon.
• We note that universal expansion generally is not discussed until very late in other
books. However, it’s not difficult to understand through the raisin cake analogy;
most students have heard about it before (although few know what it means), and
it’s one of the most important aspects of the universe as we know it today. Given
all that, why wait to introduce it?
• Note: Students may have seen a demonstration of expansion using a balloon and
a marker. This illustration, however, is flawed in that the marks (usually
The Cosmic Perspective, Tenth Edition 47
