ch. 12 cosmic distances

You learned about the general concept of parallax in Chapter 2, and the video offers a review of the basic ideas. To check your understanding of the concept, which of the following is a valid way of demonstrating parallax for yourself?

Hold up your hand in front of your face, and alternately close your left and right eyes.

Which of the following makes it possible for us to observe stellar parallax (from Earth)?

Earth's orbit around the Sun

Compared to a nearer star, a more distant star will have a __________.

smaller parallax angle

Suppose there was a star with a parallax angle of 1 arcsecond. How far away would it be?

3.26 light-years

Use the parallax formula to complete the following statements correctly.

A star with a parallax angle of 0.1 arcsecond is 32.6 light-years away from us.

A star with a parallax angle of 0.01 arcsecond is 326 light-years away from us.

A star with a parallax angle of 0.001 arcsecond is 3260 light-years away from us.

A star with a parallax angle of 0.0001 arcsecond is 32,600 light-years away from us.

The GAIA spacecraft is capable of measuring parallax angles as small as about 0.00002 arcsecond (20 microarcseconds). Based on this fact, GAIA should in principle be able to measure the distances of stars located __________.

throughout the Milky Way Galaxy, but not in the Andromeda galaxy or other more distant galaxies

To get started, click on the blue Cepheids link on the main screen of the Interactive Figure. The Interactive Figure (in red) shows a graph of the Cepheid period-luminosity relation. This graph indicates that __________.

Cepheids with longer periods have higher luminosities

A Cepheid with a period of 30 days has an average luminosity that is about __________ times the luminosity of the Sun.

10,000

Next, click the label on the bottom of the Interactive Figure that reads Cepheids as Standard Candles to bring up the next screen. Read the instructions that appear in the upper left hand corner and study the animation.

The Cepheid varies in radius, and its luminosity is greater when its radius is larger.

From here, click the Next button in the Interactive Figure to bring up the screen that shows a Cepheid light curve in the upper left.

What is the approximate luminosity of the Cepheid whose light curve is shown in the graph?

8000Lsun

Notice that the window with the light curve also has a box that tells you the average apparent brightness of the Cepheid, which shows a value of 1.3×1041.3×104. (The units are shown in the box, but you only need to focus on the numerical value.) Based on this apparent brightness and the luminosity you found in Part D, what is the approximate distance to this Cepheid?

2 million light-years

Which of the following three-step processes correctly describes how we use Cepheids as a tool to make cosmic distance measurements?

In all cases, assume that the Cepheid's apparent brightness has been carefully measured through observations.

Step 1: Measure the period of the Cepheid's brightness variations.

Step 2: Use the period-luminosity relation to determine the Cepheid's luminosity.

Step 3: Calculate the Cepheid's distance from its luminosity and apparent brightness.

Radar, the first link in the cosmic distance chain, is used to establish the baseline distance necessary for the second link, parallax. What baseline distance must we know before we can measure parallax?

the Earth-Sun distance

Which cosmic distance measurement techniques are considered standard candle techniques?

-Cepheids

-white dwarf supernovae (distant standards)

-main-sequence fitting

Suppose that Cepheids did not exist and there were no other standard candle technique that worked at the same distances. Which statement would be true?

We would not be able to measure the distances of distant galaxies.

Why do we use Hubble's law to estimate the distances of most distant galaxies, rather than using white dwarf supernovae in all cases?

We have not observed white dwarf supernovae in most galaxies.

Imagine that radar had never been invented and that we instead had to rely on a less reliable method of measuring distances in our solar system. If that method led us to underestimate the Earth-Sun distance by 10%, how would it affect other measurements in the distance chain?

They would all be off by the same 10%.

Which technique is the most useful for measuring the distance to a galaxy located 10 million light-years away?

Cepheids

Before we can use parallax to measure the distance to a nearby star, we first need to know __________.

the Earth-Sun distance

Which of the following is a valid way of demonstrating parallax for yourself?

Hold up your hand in front of your face, and alternately close your left and right eyes.

What is the cause of stellar parallax?

Earth's orbit around the sun

The more distant a star, the __________.

smaller its parallax angle

Approximately what is the parallax angle of a star that is 20 light-years away?

0.16 arcsecond

Suppose that a star had a parallax angle of exactly 1 arcsecond. Approximately how far away would it be, in light-years?

3.3 light-years

Which of the following statements best describes what astronomers mean when they say that the universe is expanding?

The average distance between galaxies is increasing with time.

Note that an observer located at the Local Raisin would see Raisins 1, 2, and 3 all move away from her during the video. What would an observer located at Raisin 2 see?

Raisin 1 and Raisin 3 both move away from her.

The table in the video shows you the speeds of Raisins 1, 2, and 3 as measured from the Local Raisin. Suppose instead that you measured speeds as seen from Raisin 2. An observer at Raisin 2 would measure __________.

Local Raisin speed = 4.0 cm/hr; Raisin 1 speed = 2.0 cm/hr; Raisin 3 speed = 2.0 cm/hr

The following statements describe ways in which the analogy might apply to the real universe. Which statements are correct?

- The average distance increases with time both between raisins in the cake and between galaxies in the universe.

-An observer at any raisin sees more distant raisins moving away faster, just as an observer in any galaxy sees more distant galaxies moving away faster.

-The raisins stay roughly the same size as the cake expands, just as galaxies stay roughly the same size as the universe expands.

Based on what you've learned from the raisin cake analogy, which two properties of distant galaxies do astronomers have to measure to show that we live in an expanding universe?

their distances and speeds

Today, the evidence that we live in an expanding universe is extremely strong because astronomers have measured the motions of millions of galaxies. Nevertheless, in science, we must always remain open to the possibility that some future observation could call even our most strongly supported theories into question. Which of the following hypothetical observations would not be consistent with what we expect in an expanding universe?

You discover an extremely distant galaxy that is moving toward us.

The following figures give the approximate distances of five galaxies from Earth. Rank the galaxies based on the speed with which each should be moving away from Earth due to the expansion of the universe, from fastest to slowest.

5 billion light-years, 2 billion light-years, 800 million light-years, 230 million light-years, 70 million light-years

The following figures give the approximate speeds at which five galaxies are moving away from Earth due to the expansion of the universe. Rank the galaxies based on their distance from Earth, from farthest to closest.

130,00 km/s

45,00 km/s

18,730 km/s

5,265 km/s

1,577 km/s

The following figures give the approximate speeds at which five galaxies are moving away from Earth due to the expansion of the universe. Rank the galaxies based on the amount of redshift that would be observed in each galaxy's spectrum, from largest to smallest.

130,00 km/s

45,00 km/s

18,730 km/s

5,265 km/s

1,577 km/s

Hubble's law is a relationship between galaxy speeds and galaxy distances. This relationship can be shown as a line on a graph of speed versus distance. Each of the following four graphs shows a possible relationship expressing Hubble's law. Rank the graphs based on their predictions of the speed, from fastest to slowest, for a galaxy located 400 million light-years away from Earth.

Put them from left to right with the line going down. (Start with the steepest and then end with the least step)

The following four graphs are the same as those from Part D, with each showing a possible relationship for Hubble's law. Rank the graphs based on the prediction they each would make for the current age of the universe, from oldest to youngest.

Put them in the opposite direction as the last question. (least steep is the oldest and the steepest is the youngest)

The following diagrams represent a balloon analogy for the expansion of the universe. Each diagram shows two balloons: The small pink balloon represents the universe at an early time and the large red balloon represents the universe at some later time. The black dot on each balloon represents a galaxy. Rank the diagrams based on how much the galaxy has expanded in size (due to the overall universal expansion) from the early time to the later time in each case, from most expansion to least expansion. If you think that two (or more) of the diagrams show galaxies that have expanded by the same proportion, indicate this equality by dragging one diagram on top of the other(s).

all balloons in center (on top of each other) because galaxies aren't expanding

The following diagrams are similar to those in Part A, except this time each one shows two galaxies: "your galaxy" and a second galaxy. Rank the diagrams based on how far the second galaxy has moved away from your galaxy due to expansion of the universe between the early time and the later time, starting at the left with the one that has moved the largest distance and moving to the one that has moved the smallest distance at the right.

Largest distance are the dots farthest apart to dots closest together (smallest)

The following diagrams are similar to those from Part B, with each diagram showing the position of "your galaxy" and another galaxy at an early and later time in the history of the universe. Rank the diagrams based on the speed at which the other galaxy is moving away from your galaxy as the universe expands, from fastest to slowest.

Same as part B: fastest are the dots farthest apart to dots closest together (slowest)

The following diagrams are similar to those from parts B and C, with each diagram showing the position of "your galaxy" and another galaxy at an early and later time in the history of the universe. (But note that this set of diagrams differs from the prior sets.) Rank the diagrams based on the speed at which the other galaxy is moving away from your galaxy as the universe expands, from fastest to slowest. If two (or more) of the diagrams show galaxies moving at the same speed, show this equality by dragging one diagram on top of the other(s). (Hint: Notice that two of the diagrams show the galaxies separated by one distance and two of the diagrams show them separated by a different distance; that is, there are only two different distances shown among the four diagrams.)

The two with points farthest apart are fastest (on top of each other); and the two with points closest together are slowest (on top of each other)

Consider the following hypothetical observations, some of which are real and some of which are fictional. For each observation, your job is to answer this question: If the observation were real, would it provide evidence for or against the idea that the universe is expanding? Sort each observation into the appropriate bin as follows:Place an observation in the "Supports the expanding universe" bin if it would provide evidence that the universe is expanding.Place an observation in the "Contradicts the expanding universe" bin if it would provide evidence that would force us to reconsider the idea of an expanding universe.Place an observation in the "Neither supports nor contradicts" bin if it does not allow us to distinguish between a universe that is expanding and a universe that is not expanding.

Supports the expanding universe

-All galaxies in the Coma cluster of galaxies have redshifted spectra.

-Galaxies 200 million light-years away move away from us twice as fast as galaxies 100 million light-years away.

-The measured rate of expansion is the same in all directions.

Contradicts the expanding universe

-Irregular galaxies outside the Local Group are moving toward us.

-Galaxy speeds are faster in summer than in winter.

-Spiral galaxies move away from us 10% faster than elliptical galaxies at the same distances.

Neither supports nor contradicts

-The Andromeda Galaxy, a member of our Local Group, is moving toward us.

Consider the hypothetical observation "Irregular galaxies outside the Local Group are moving toward us." From Part A, this observation would contradict the idea of an expanding universe. Why?

Because Hubble's law predicts that all galaxies outside our Local Group should be moving away from us.

Consider the observation "The Andromeda Galaxy, a member of our Local Group, is moving toward us." Why doesn't this observation contradict the idea that the universe is expanding?

Because the galaxies of the Local Group are gravitationally bound together.

We can in principle measure the expansion rate by studying galaxies in many different directions in space and at different times of year. If we compare such observations, we would find that the expansion rate is __________.

the same no matter when or in which direction we measure it

When we observe a distant galaxy whose photons have traveled for 10 billion years before reaching Earth, we are seeing that galaxy as it was when the universe was about

4 billion years old

Which of these statements is a key assumption in our most successful models for galaxy formation?

Some regions of the universe were slightly denser than others

The distance to the cosmological horizon depends on

the age of the universe

Why do virtually all the galaxies in the universe appear to be moving away from our own?

because observers in all galaxies see a similar phenomenon due to the universe's expansion

When the ultraviolet light from hot stars in very distant galaxies finally reaches us, it arrives at Earth in the form of

visible or infrared light

Which of these galaxies is likely to be oldest?

a galaxy in the Local Group

If Earth's orbital radius doubled in size,

the parallax shifts of nearby stars would double in size

According to Leavitt's law, we can determine the luminosity of a Cepheid in a distant galaxy by measuring its

period of brightening and dimming

Compute the distance to M100 with data from the Cepheid 1.

6.1×10 to the 7th

Compute the distance to M100 with data from the Cepheid 2.

5.3×10 to the 7th

Compute the distance to M100 with data from the Cepheid 3.

5.1×10 to the 7th

Do the results for distance to M100 agree?

Computations give different values, but they agree. No object is a perfect candle, so there are always some imperfections. To decrease the uncertainty, we must observe other Cepheids in M100.

Based on your results, what is the average expected distance to M100?

5.5×10 to the 7th

Estimate the uncertainty in the distance you have found.

5×10 to the 6th

Which kind of object is the best standard candle for measuring distances to extremely distant galaxies?

a white dwarf supernova

If you observe two Cepheid variable stars to have the same period and one is brighter than the other

the brighter one is closer

If you observed the redshifts of galaxies at a given distance to be twice as large as they are now, the value you would determine for Hubble's constant would be

twice its current value

Which of these galaxies is most likely to be oldest

(a) a galaxy in the Local Group

(b) a galaxy observed at a distance of 5 billion light-years

(c) a galaxy observed at a distance of 10 billion light-years

(a) a galaxy in the Local Group

Which set of star-position measurements is most likely to show the largest parallax shift for nearby stars?

(a) measurements made 1 month apart

(b) measurements made 6 months apart

(c) measurements made 1 year apart

(b) measurements made 6 months apart

If Earth's orbital radius doubled in size,

(a) the parallax shifts of nearby stars would double in size.

(b) the parallax shifts of nearby stars would be only half their current size.

(c) the parallax shifts of nearby stars would stay the same.

(a) the parallax shifts of nearby stars would double in size.

If all the stars on the main sequence of a star cluster are typically only one-hundredth as bright as their main-sequence counterparts in the Hyades Cluster, then that cluster's distance is

(a) 100 times the Hyades' distance.

(b) 30 times the Hyades' distance.

(c) 10 times the Hyades' distance.

(c) 10 times the Hyades' distance.

Which kind of object is the best standard candle for measuring distances to extremely distant galaxies?

(a) a white dwarf

(b) a Cepheid variable star

(c) a white dwarf supernova

(c) a white dwarf supernova

If you observe two Cepheid variable stars to have the same period and one is brighter than the other,

(a) the brighter one is closer.

(b) the brighter one is farther away.

(c) there is not enough information to determine which star is closer.

(a) the brighter one is closer.

If you observe two Cepheid variable stars to have different periods and the brighter one has a longer period,

(a) the brighter one is closer.

(b) the brighter one is farther away.

(c) there is not enough information to determine which star is closer.

(c) there is not enough information to determine which star is closer.

When the ultraviolet light from hot stars in very distant galaxies finally reaches us, it arrives at Earth in the form of

(a) X rays.

(b) slightly more energetic ultraviolet light

(c) visible light.

(c) visible light.

Why do virtually all the galaxies in the universe appear to be moving away from our own?

(a) because we are located near where the Big Bang happened

(b) because we are located near the center of the universe

(c) because observers in all galaxies see a similar phenomenon due to the universe's expansion

(c) because observers in all galaxies see a similar phenomenon due to the universe's expansion

If you observed the redshifts of galaxies at a given distance to be twice as large as they are now, the value you would determine for Hubble's constant would be

(a) twice its current value

(b) equal to its current value.

(c) half its current value.

(c) half its current value.

What would your estimate be for the age of the universe if you measured Hubble's constant to be 11 kilometers per second per million light-years?

(a) 7 billion years

(b) 14 billion years

(c) 28 billion years

(c) 28 billion years

When we observe a distant galaxy whose photons have traveled for 10 billion years before reaching Earth, we are seeing that galaxy as it was when the universe was about

(a) 10 billion years old.

(b) 7 billion years old.

(c) 4 billion years old.

(c) 4 billion years old.

What is the current temperature of the universe?

(a) absolute zero

(b) a few degrees K

(c) a few thousand degrees K

(b) a few degrees K

What is the charge of an antielectron?

(a) positive

(b) negative

(c) neutral

(a) positive

What happens when a proton collides with an antiproton?

(a) They repel each other.

(b) They fuse together.

(c) They convert into two photons.

(c) They convert into two photons.

Which of the following does not provide strong evidence for the Big Bang theory?

(a) observations of the cosmic microwave background

(b) observations of the amount of hydrogen in the universe

(c) observations of the ratio of helium to hydrogen in the universe

(b) observations of the amount of hydrogen in the universe

What kinds of new particles are produced in particle accelerators?

(a) only matter

(b) only antimatter

(c) both matter and antimatter

(c) both matter and antimatter

What kinds of particles were present in the universe during the particle era?

(a) mostly matter

(b) mostly antimatter

(c) approximately equal amounts of matter and antimatter

(c) approximately equal amounts of matter and antimatter

What kinds of particles were present in the universe during the era of nucleosynthesis?

(a) mostly matter

(b) mostly antimatter

(c) approximately equal amounts of matter and antimatter

(a) mostly matter

What kinds of atomic nuclei were present in the universe during the era of nuclei?

(a) all kinds of nuclei

(b) mostly hydrogen and helium nuclei

(c) only hydrogen nuclei

(b) mostly hydrogen and helium nuclei

If you had been present in the universe at the beginning of the era of atoms, what color light would you have seen?

(a) white light

(b) red light

(c) no visible light, because only microwave light was present

(b) red light

Which of the following does inflation help to explain?

(a) the uniformity of the cosmic microwave background

(b) the amount of helium in the universe

(c) the temperature of the cosmic microwave background

(a) the uniformity of the cosmic microwave background

Adding the idea of inflation to the Big Bang theory accounts for

(a) the origin of hydrogen.

(b) the origin of galaxies

(c) the origin of atomic nuclei.

(b) the origin of galaxies

Which of these pieces of evidence supports the idea that inflation really happened?

(a) observations showing that the universe is expanding

(b) measurements of the abundance of helium in the universe

(c) observations of the cosmic microwave background that indicate a flat geometry for the universe

(c) observations of the cosmic microwave background that indicate a flat geometry for the universe