Astronomy & Astrophysics Chapter 1 Homework The Observable Universe One Way Get Sense

Instructor Guide for The Essential Cosmic Perspective, Eighth Edition 21

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.

22 Bennett, Donahue, Schneider, Voit

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 the course will

build the detailed scientific case for these general ideas.

Key Changes for the 8th Edition: For those who have used earlier editions of

our textbook, please note the following significant changes in this chapter:

Updated definition of galaxies to reflect recent discoveries.

Added emphasis on dark matter and dark energy, so students will be

prepared for the fact that we will be making more use of these ideas in our

discussion of galaxy evolution.

Added clarification on how the age of the universe is related to the

expansion rate of the universe, along with two new end-of-chapter

questions to reinforce this connection. Our classroom experience has shown

that students are less likely to over-think this idea this early in the course,

so introducing it in Chapter 1 aids their understanding when expansion is

covered in more detail later in the book.

Note on Mathematics: The MasteringAstronomy website 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

Instructor Guide for The Essential Cosmic Perspective, Eighth Edition 23

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

Note the box titled

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 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, or over time). In defining

an astronomical unit (AU) as the average distance between Earth and the

24 Bennett, Donahue, Schneider, Voit

Note that in discussing distances to very distant galaxies, we give

distances in terms of lookback times; for example, when

light-

definition, the radius of the observable universe is about 14 billion light–

years, corresponding to the age of the universe. Unfortunately, some

media reports instead quote distances as they would be today with the

ongoing expansion, hence saying that the universe is 40+ billion light–

years in radius. As a result, some students may be confused about which is

confusion,

we point out that:

the number of

galaxies in the Local Group, much has been learned about the Local

Group in recent years, and numerous dwarf galaxies have been discovered.

Some of these push the boundaries of our definition: Should they really

, are they groups of stars that have been tidally

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

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.

Instructor Guide for The Essential Cosmic Perspective, Eighth Edition 25

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

made:

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

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 back side of the foldout in the

front of the book,

Section 1.3 Spaceship Earth

focusing on motion in the context of the motions of Earth in space, using R.

Spaceship Earth.

Note that the summary figure for this section, Figure 1.16, comes at the

end.

We use the term tilt, rather than obliquity, as part of our continuing effort

to limit the use of jargon.

26 Bennett, Donahue, Schneider, Voit

the literature offers values over a fairly wide range, for example:

Answers/Discussion Points for Think About It/See It for Yourself

Questions

The Think About It and See It for Yourself questions are not numbered in the

book, so we list them in the order in which they appear, keyed by section number.

Section 1.1

(p. 4) This question is, of course, very subjective, but it can make for a

lively in-class debate.

(p. 6, SIFY) The main goal of this activity is for students to go out and

Section 1.2

(p. 15) This is another very subjective question, similar to the one at the

end of Section 1.1 but focused on our place in time rather than in space.

Section 1.3

Instructor Guide for The Essential Cosmic Perspective, Eighth Edition 27

Solutions to End-of-Chapter Problems (Chapter 1)

(Note: Solutions provided in the Instructor Guide are intended as samples

only; individual answers may vary.)

Visual Skills Check

Review Questions

1. The largest scale is the universe itself, which is the sum total of all matter

and energy. The largest-known organized structures are superclusters of

2. Astronomical unit: the average distance between Earth and Sun, which is

3. Because light travels at a fixed speed, it takes time for it to go between two

points in space. Although light travels very quickly, the distances in the

4. The observable universe is the portion of the entire universe that we can in

principle see; it is about 14 billion light-years in radius, because light from

5. Solar system: On the 1-to-10-billion scale, the Sun is about the size of a

grapefruit, and the planets are the sizes of marbles or smaller. The distances

between the planets are a few meters for the inner solar system to many tens

28 Bennett, Donahue, Schneider, Voit

6. When we say that the universe is expanding, we mean that the average

distance between galaxies is increasing with time. If the universe is

niverse

7. s

except for hydrogen, since our bodies generally do not contain helium) were

8. There are numerous ways to describe how humanity fits into cosmic time,

but here is one straight from the cosmic calendar: If the entire history of the

9. Earth rotates once each day on its axis and orbits the Sun once each year.

The ecliptic plane is the plane d

10. The Milky Way Galaxy is a spiral galaxy, which means that it is disk-

shaped with a large bulge in the center. The galactic disk includes a few

11. Dark matter is matter that does not emit light, and is therefore invisible to our

telescopes, but that we can detect because it has gravity that affects other

12. Edwin Hubble discovered that most galaxies are moving away from our

galaxy, and the farther away they are located, the faster they are moving

away. While at first this might seem to suggest that we are at the center of

13. The expansion rate tells us the age of the universe because it allows us to

Does It Make Sense?

14. Our solar system is bigger than some galaxies. This statement does not

15. The universe is billions of light-years in age. This statement does not make

sense because it uses the term light-years as a time, rather than as a distance.

16. It will take me light-years to complete this homework assignment! This

17. Someday, we may build spaceships capable of traveling a light-year in only

18. Astronomers recently discovered a moon that does not orbit a planet. This

19. NASA will soon launch a spaceship that will photograph our Milky Way

Galaxy from beyond its halo. This statement does not make sense because

20. The observable universe is the same size today as it was a few billion years

21. Photographs of distant galaxies show them as they were when they were

much younger than they are today. This statement makes sense because

22. At a nearby park, I built a scale model of our solar system in which I used

a basketball to represent the Earth. This statement does not make sense.

23. Because nearly all galaxies are moving away from us, we must be located at

the center of the universe. This statement does not make sense, as we can

Quick Quiz

Process of Science

34. Major changes in scientific views are possible because science relies on

physical evidence. Science must be backed by evidence from observations

35. Using the Voyage model scale (1 to 10 billion), Earth is barely 1 mm across,

36. Answers will vary. This question is designed to get students thinking about

Instructor Guide for The Essential Cosmic Perspective, Eighth Edition 31

Group Work Exercise (no solution provided)

Short Answer/Essay Questions

38. This is a short essay question. Key points should include discussion of the

39. There is no danger of a collision between our star system and another in the

near future. Such collisions are highly improbable in any event remember

40. a. The diagrams should be much like Figure 1.15, except that the distances

between raisins in the expanded figure will be 4 centimeters instead of

3 centimeters.

b. Distances and Speeds of Other Raisins as Seen from the Local Raisin

Raisin

Number

Distance Before

Baking

Distance After Baking

(1 hour later) Speed

1 1 cm 4 cm 3 cm/hr

c. As viewed from any location inside the cake, more distant raisins appear

Quantitative Problems

42. a. A light-second is the distance that light travels in 1 second. We know

that light travels at a speed of 300,000 km/s, so a light-second is a

distance of 300,000 kilometers.

b. A light-minute is the speed of light multiplied by 1 minute:

43. Recall that

distance traveled

speed time of travel

a. According to Appendix E, the Earth Moon distance is 3.844 105 km.

Using this distance and the equation above for travel time, we get

b. Appendix E also tells us that the distance between Earth and the Sun is

8

1.496 10 km.

44. We are asked to find how many times larger in diameter the Milky Way

Galaxy is than the rings of Saturn

270,000 kilometers across and that the Milky Way is 100,000 light-years in

Instructor Guide for The Essential Cosmic Perspective, Eighth Edition 33

the diam

45. a. The circumference of Earth is 2 6380 km = 40,087 km. At a speed of

100 km/hr, it would take:

b. We find the time by dividing the distance to Earth from the Sun by the

c. Similarly, it would take 6700 years to drive from the Sun to Pluto at 100

Planet Driving Time

Mercury 66 years

d. We are given the distance to Alpha Centauri in light-years; converting to

kilometers, we get:

46. a. To reach Alpha Centauri in 100 years, you would have to travel at

47. A faster expansion rate means the universe reached its current size in less

time, so the fact that Allen measured a faster expansion rate means he will