21st Century Astronomy

Laura Kay, Stacy Palen, Brad Smith

Chapter 19

The Expanding Universe - all with Video Answers

Educators

Chapter Questions

Problem 1

In astronomy, isotropy means that the universe is the same
a. in all locations.
b. in all directions.
c. at all times.
d. at all size scales.

Farhanul Hasan

Farhanul Hasan

Numerade Educator

Problem 2

In astronomy, homogeneity means that the universe is the same a. in all locations.
b. in all directions. c. at all times.
d. at all size scales.

Farhanul Hasan

Numerade Educator

Problem 3

Cosmological redshifts are calculated from observations of spectral lines from
a. individual stars in distant galaxies.
b. clouds of dust and gas in distant galaxies.
c. spectra of entire galaxies.
d. rotations of the disks of distant galaxies.

Farhanul Hasan

Numerade Educator

Problem 4

When they look into the universe, astronomers observe that nearly all galaxies are moving away from the Milky Way. This observation suggests that
a. the Milky Way is at the center of the universe.
b. the Milky Way must be at the center of the expansion.
c. the Big Bang occurred at the location of the Milky Way.
d. an observer in a distant galaxy would make the same observation.

Farhanul Hasan

Numerade Educator

Problem 5

Hubble's law requires the measurement of two properties of a galaxy:_____ and ______ .a. size; mass
b. distance; rotation speed
c. distance; recessional velocity
d. size; recessional velocity

Farhanul Hasan

Numerade Educator

Problem 6

Some galaxies have redshifts $z$ that if equated to $v / c$ correspond to velocities greater than the speed of light. Special relativity is not violated in this case
a. because of relativistic beaming.
b. because of superluminal motion.
c. because redshifts carry no information.
d. because these velocities do not measure motion through
space.

Farhanul Hasan

Numerade Educator

Problem 7

The Big Bang theory predicted (select all that apply)
a. the Hubble law.
b. the cosmic microwave background radiation.
c. the cosmological principle.
d. the abundance of helium.
e. that the sky should be dark at night.
f. the period-luminosity relation of Cepheid variables.

Sarah Mccrumb

Numerade Educator

Problem 8

The simplest way to estimate the age of the universe is from
a. using the slope of the Hubble law.
b. the age of Moon rocks.
c. models of stellar evolution.
d. measurements of the abundances of elements.

Farhanul Hasan

Numerade Educator

Problem 9

The CMB includes information about (select all that apply)
a. the age of the universe.
b. the temperature of the early universe.
c. the density of the early universe.
d. density fluctuations in the early universe.
e. the motion of Earth around the center of the Milky Way.

Farhanul Hasan

Numerade Educator

Problem 10

Repeated measurements showing that the current helium abundance is much less than the value predicted by the Big Bang would imply that
a. some part of the Big Bang theory is incorrect or incomplete
b. the current helium abundance is wrong.
c. scientists don't know how to measure helium abundances.

Farhanul Hasan

Numerade Educator

Problem 11

$\mathbf{T} / \mathbf{F}:$ Observers in a very distant galaxy would observe that galaxies far from them are more redshifted than are galaxies nearby.

Farhanul Hasan

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Problem 12

T/F: The distribution of galaxies is both homogeneous and isotropic.

Farhanul Hasan

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Problem 13

T/F: Peculiar velocities of distant galaxies are often larger than the velocities from the Hubble flow.

Farhanul Hasan

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Problem 14

T/F: The expansion of space means that galaxies are becoming larger over time.

Farhanul Hasan

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Problem 15

$\mathbf{T} / \mathbf{F}:$ cosmological redshift is caused by the movement of galaxies through space.

Farhanul Hasan

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Problem 16

If you found a galaxy with an H\alpha emission line that had a wavelength of $756.3 \mathrm{nm}$, what would be the galaxy's red shift? Note that the rest wavelength of the Ho emission line a. 0.01
b. 0.05 c. 0.10
d. 0.15

Farhanul Hasan

Numerade Educator

Problem 17

The cosmological principle says that
a. the universe is expanding.
b. the universe began in the Big Bang.
c. the rules that govern the universe are the same everywhere
d. all of the above

Farhanul Hasan

Numerade Educator

Problem 18

Peculiar velocities are
a. the velocities of galaxies that are moving toward the Milky Way Galaxy.
b. the velocities of galaxies that result from something other than the expansion of space.
c. the velocities of galaxies toward their neighbors.
d. the random velocities of galaxies from when they formed.

Farhanul Hasan

Numerade Educator

Problem 19

Why is the Milky Way Galaxy not expanding together with the rest of the universe?
a. It is not expanding because it is at the center of the expansion.
b. It is expanding, but the expansion is too small to measure.
c. The Milky Way is a special location in the universe.
d. Local gravity dominates over the expansion of the universe.

Farhanul Hasan

Numerade Educator

Problem 20

As astronomers extend their distance ladder beyond $30 \mathrm{Mpc}$ they change their measuring standard from Cepheid variable stars to Type Ia supernovae. Why is this change necessary?
a. Type Ia supernovae are more luminous than Cepheid variables.
b. Type Ia supernovae are less luminous than Cepheid variables.
c. Type Ia supernovae vary more slowly than do Cepheid variables.
d. Type Ia supernovae vary more quickly than do Cepheid variables.

Farhanul Hasan

Numerade Educator

Problem 21

The scale factor keeps track of
a. the movement of galaxies through space.
b. the current distances between many galaxies.
c. the changing distance between any two galaxies.
d. the location of the center of the universe.

Farhanul Hasan

Numerade Educator

Problem 22

The Big Bang is
a. the giant supernova explosion that triggered the formation of the Solar System.
b. the explosion of a supermassive black hole.
c. the eventual demise of the Sun.
d. the beginning of space and time.

Farhanul Hasan

Numerade Educator

Problem 23

The CMB is essentially uniform in all directions in the sky This is an example of
a. anisotropy.
b. isotropy.
c. thermal fluctuations.
d. none of the above

Farhanul Hasan

Numerade Educator

Problem 24

The CMB comes from
a. the moment when the universe became transparent.
b. the outer Solar System.
c. the edge of the universe.
d. the instant of the Big Bang.

Farhanul Hasan

Numerade Educator

Problem 25

According to the definitions in Chapter 1 , the Big Bang is
a. an idea.
b. a hypothesis.
c. a law.
d. a theory.

Farhanul Hasan

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Problem 26

What was the subject of the Great Debate, and why was it important to astronomers' understanding of the scale of the universe?

Farhanul Hasan

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Problem 27

How did observations of Cepheid variable stars finally settle the Great Debate?

Farhanul Hasan

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Problem 28

Why is it better to observe more than one type of standard candle in a distant galaxy?

Farhanul Hasan

Numerade Educator

Problem 29

Imagine that you are standing in the middle of a dense fog.
a. Would you describe your environment as isotropic? Why or why not?
b. Would you describe it as homogeneous? Why or why not?

Sarah Mccrumb

Numerade Educator

Problem 30

Early in the 20 th century, astronomers discovered that most galaxies are moving away from the Milky Way (that is, they are redshifted.)
a. What was the significance of this discovery?
b. Edwin Hubble later made an even more important discovery: that the speed at which galaxies are receding is proportional to their distance. Why was this among the more important scientific discoveries of the 20 th century?

Farhanul Hasan

Numerade Educator

Problem 31

Why is it not possible to use the measured radial velocities of nearby galaxies, such as the Andromeda Galaxy, to evaluate the Hubble constant $\left(H_{0}\right) ?$

Farhanul Hasan

Numerade Educator

Problem 32

Explain what astronomers mean by distance ladder.

Farhanul Hasan

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Problem 33

Why is it important to know the type of progenitor of a Type Ia supernova in a distant galaxy?

Farhanul Hasan

Numerade Educator

Problem 34

As the universe expands from the Big Bang, galaxies are not actually flying apart from one another. What is really happening?

Farhanul Hasan

Numerade Educator

Problem 35

Knowing that you are studying astronomy, a curious friend asks where the center of the universe is located. You answer “Right here and everywhere." Explain in detail why you give this answer.

Farhanul Hasan

Numerade Educator

Problem 36

The general relationship between recessional velocity $\left(v_{r}\right)$ and redshift $(z)$ is $v_{r}=c z .$ This simple relationship fails, however, for very distant galaxies with large redshifts. Explain why.

Farhanul Hasan

Numerade Educator

Problem 37

Why is it significant that the CMB displays a Planck spectrum?

Farhanul Hasan

Numerade Educator

Problem 38

What is the significance of the tiny brightness variations that are observed in the CMB?

Farhanul Hasan

Numerade Educator

Problem 39

What important characteristics of the early universe are revealed by today's observed abundances of various isotopes, such as $^{2} \mathrm{H}$ and $^{3} \mathrm{He} ?$

Farhanul Hasan

Numerade Educator

Problem 40

a. Why is it important that the different "rungs" of the distance ladder overlap in the distances that they measure?
b. Why does the figure end at the right edge-because there are no more ways to measure distance or because there is no more universe to measure? How do you know?

Farhanul Hasan

Numerade Educator

Problem 41

Sketch what the graph in Figure $19.8 \mathrm{b}$ would look like for each of the following cases:
a. a universe in which galaxies moved randomly through
space
b. a contracting universe
c. a universe that started out expanding but is now contracting

Farhanul Hasan

Numerade Educator

Problem 42

Study Figure $19.19 .$ Error bars have not been plotted in this figure. Why not? Was this a very precise measurement or a very imprecise measurement? How does the precision of the measurement affect your confidence in the conclusions drawn from it?

Sarah Mccrumb

Numerade Educator

Problem 43

This figure includes both predictions and observations.
a. What do the vertical yellow bar and the slanted lines and curves represent: theory or observation?
b. What do the pastel horizontal lines and the vertical black line represent: predictions or observations?
c. Do the predictions and observations match? Choose one example, and explain how you know.

Farhanul Hasan

Numerade Educator

Problem 44

The Hubble time $\left(1 / H_{0}\right)$ represents the age of a universe that has been expanding at a constant rate since the Big Bang. Assuming an $H_{0}$ value of $70 \mathrm{km} / \mathrm{s} / \mathrm{Mpc}$ and a constant rate of expansion, calculate the age of the universe in years. How is the age different if $H_{0}=75 \mathrm{km} / \mathrm{s} / \mathrm{Mpc} ?\left(\text { Note: } 1 \text { year }=3.16 \times 10^{7}\right.$ seconds and $1 \mathrm{Mpc}=3.09 \times 10^{19} \mathrm{km} .$

Farhanul Hasan

Numerade Educator

Problem 45

Throughout the latter half of the 20 th century, estimates of $H_{0}$ ranged from 55 to $110 \mathrm{km} / \mathrm{s} /$ Mpc. Calculate the age of the universe in years for each of these estimated values of $H_{0}$.

Farhanul Hasan

Numerade Educator

Problem 46

A distant galaxy has a redshift $z=5.82$ and a recessional velocity $v_{r}=287,000 \mathrm{km} / \mathrm{s}$ (about 96 percent of the speed of light).
a. If $H_{\mathrm{o}}=70 \mathrm{km} / \mathrm{s} / \mathrm{Mpc}$ and if Hubble's law remains valid out to such a large distance, then how far away is this galaxy?
b. Assuming a Hubble time of 13.7 billion years, how old was the universe at the look-back time of this galaxy?
c. What was the scale factor of the universe at that time?

Farhanul Hasan

Numerade Educator

Problem 47

The spectrum of a distant galaxy shows the Ho line of hydrogen $\left(\lambda_{\text {rest }}=656.28 \mathrm{nm}\right)$ at a wavelength of $750 \mathrm{nm}$ Assume that $H_{\mathrm{o}}=70 \mathrm{km} / \mathrm{s} / \mathrm{Mpc}$
a. What is the redshift (z) of this galaxy?
b. What is its recessional velocity $\left(v_{r}\right)$ in kilometers per second?
c. What is the distance of the galaxy in megaparsecs?

Farhanul Hasan

Numerade Educator

Problem 48

A distant galaxy has a redshift $z=7.6$
a. What would be the observed wavelength of the Ha line $\left(\lambda_{\text {rest }}=656.28 \mathrm{nm}\right) ?$
b. In what region of the spectrum would this line be located?

Farhanul Hasan

Numerade Educator

Problem 49

Suppose you observe two galaxies: one at a distance of $10.7 \mathrm{Mpc}$ with a recessional velocity of $580 \mathrm{km} / \mathrm{s}$, and another at a distance of 337 Mpc with a radial velocity of 25,400 $\mathrm{km} / \mathrm{s}$.
a. Calculate the Hubble constant ( $H_{0}$ ) for each of these two observations.
b. Which of the two calculations would you consider to be more trustworthy? Why?
c. Estimate the peculiar velocity of the closer galaxy.
d. If the more distant galaxy had this same peculiar velocity, how would your calculated value of the Hubble constant change?

Farhanul Hasan

Numerade Educator

Problem 50

The temperature of the CMB is $2.73 \mathrm{K}$. What is the peak wavelength of its Planck blackbody spectrum expressed both in microns and in millimeters?

Farhanul Hasan

Numerade Educator

Problem 50

The temperature of the CMB is $2.73 \mathrm{K}$. What is the peak wavelength of its Planck blackbody spectrum expressed both in microns and in millimeters?

Farhanul Hasan

Numerade Educator

Problem 52

The average density of normal matter in the universe is $4 \times 10^{-28} \mathrm{kg} / \mathrm{m}^{3} .$ The mass of a hydrogen atom is $1.66 \times 10^{-27} \mathrm{kg}$ On average, how many hydrogen atoms are there in each cubic meter in the universe?

Farhanul Hasan

Numerade Educator

Problem 53

To get a feeling for the emptiness of the universe, compare its density $\left(4 \times 10^{-28} \mathrm{kg} / \mathrm{m}^{3}\right)$ with that of Earth's atmosphere at sea level $\left(1.2 \mathrm{kg} / \mathrm{m}^{3}\right) .$ How much denser is Earth's atmosphere? Write this ratio using standard notation.

Farhanul Hasan

Numerade Educator

Problem 54

Assume that the most distant galaxies have a redshift $z=10$ The average density of normal matter in the universe today is $4 \times 10^{-28} \mathrm{kg} / \mathrm{m}^{3} .$ What was its density when light was leaving those distant galaxies? (Hint: Keep in mind that volume is proportional to the cube of the scale factor.)

Farhanul Hasan

Numerade Educator

Problem 55

Suppose a Type Ia supernova is found in a distant galaxy. The measured supernova brightness is $10^{-17} \mathrm{W} / \mathrm{m}^{2}$. What is the distance of the galaxy?

Farhanul Hasan

Numerade Educator

Problem 56

Go to the Goddard Multimedia website and view the animation of a Cepheid variable star in a spiral galaxy (http://svs .gsfc.nasa.gov/goto?10145). Explain how astronomers use data like these to estimate the distance to the galaxy. What is actually observed, what is assumed, and what is calculated? (Review the discussion in Chapter 16 as needed.)

Farhanul Hasan

Numerade Educator

Problem 57

For more details on the history of the discovery of the expanding universe, go to the American Institute of Physics' "Cosmic Journey: A History of Scientific cosmology" website (http://aip.org/history/cosmology). Read through the sections titled "Island Universes," "The Expanding Universe," and “Big Bang or Steady State?" Why was Albert Einstein "irritated" by the idea of an expanding universe? What was the contribution of Belgian astrophysicist (and Catholic priest) Georges Lemaitre? What is the steady-state theory, and what was the main piece of evidence against it?

Alex Garger

Numerade Educator

Problem 58

Go to the University of Washington Astronomy Department's "Hubble's Law: An Introductory Astronomy Lab" Web page (ww w.astro.washington.edu/courses/labs/ clearinghouse/labs/HubbleLaw/hubbletitle), and do the lab exercise, which uses real data from galaxies to calculate Hubble's law. Your instructor will indicate whether you should use the regular or the shorter version.

Tara Appleyard

Numerade Educator

Problem 59

Go to the "Astronomy" page of the Phys.Org website (http://phys.org/space-news/astronomy), click on "Search," and enter "Type Ia supernova" in the Search box. Find a recent story about one of these supernovae. What is its distance and brightness? What type of star produced the explosion?

Zachary Warner

Numerade Educator

Problem 60

Observations of the CMB from the Planck space telescope are expected to be released in $2013 .$ Go to ESA's Planck website (http://esa.int/SPECIALS/Planck) and view the all-sky CMB map. Compare this with the $W M A P$ data in Figure $19.18 \mathrm{c} ;$ what is different? What has been learned from this mission?

Sarah Mccrumb

Numerade Educator