Question 11.1

Stellar parallax measurements are used in astronomy to determine which of the following properties of stars?

• a. sizes
• b. rotation rates
• c. distances
• d. colors
• e. temperatures

Question 11.2

The brightness a star would have if it were at 10 pc from Earth is called its

• a. absolute magnitude
• b. apparent magnitude
• c. center of mass
• d. luminosity
• e. spectral type

Question 11.3

Measurements of a binary star system are required to determine what property of stars?

• a. luminosity
• b. apparent magnitude
• c. distance
• d. mass
• e. temperature

Question 11.4

A star with which of the following apparent magnitudes appears brightest from Earth?

• a. 6.8
• b. 3.2
• c. 0.41
• d. −0.44
• e. −1.5

Question 11.5

A star of what spectral class has the strongest (darkest) H_α line? (Hint: See Figure 11-5.)

• a. B2
• b. A0
• c. A5
• d. G5
• e. M0

Question 11.6

Describe how the parallax method of finding a star’s distance is similar to the binocular (two-eye) vision of animals.

Question 11.7

What is stellar parallax?

Question 11.8

How do astronomers use stellar parallax to measure the distances to stars?

Question 11.9

Why do stellar parallax measurements work only with relatively nearby stars?

Question 11.10

What is the difference between apparent magnitude and absolute magnitude?

Question 11.11

Briefly describe how you would determine the absolute magnitude of a nearby star.

Question 11.12

What does a star’s luminosity measure?

Question 11.13

How is the magnitude scale “backward” from what common sense dictates?

Question 11.14

Does the star Betelgeuse, whose apparent magnitude is m = + 0.5, look brighter or dimmer to us than the star Pollux, whose apparent magnitude is m = +1.1?

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Question 11.15

*Consider two identical stars, with one star 5 times farther away than the other. How much brighter will the closer star appear than the more distant one?

Question 11.16

How and why is the spectrum of a star related to its surface temperature?

Question 11.17

What is the primary chemical component of most stars?

Question 11.18

A star of which spectral type has the strongest Na I absorption lines? At approximately what wavelength is this line normally found? (Hint: See Figure 11-5.)

Question 11.19

Why does a G2 star have many more absorption lines than a B0 star?

Question 11.20

Draw an H-R diagram and sketch the regions occupied by main-sequence stars, giants, supergiants, and white dwarfs. Briefly discuss the different ways you could have labeled the axes of your graph.

Question 11.21

To test your understanding of the H-R diagram, do Interactive Exercise 11.1 on the assigned Web site. You can print out your answers, if required.

Question 11.22

How can observations of a visual binary lead to information about the masses of its stars?

Question 11.23

What is a radial-velocity curve? What kinds of stellar systems exhibit such curves?

Question 11.24

What is the difference between a single-line and a double-line spectroscopic binary?

Question 11.25

What is meant by the light curve of an eclipsing binary? What sorts of information can be determined from such a light curve?

Question 11.26

What is the mass-luminosity relation? To what kind of stars does it apply?

Question 11.27

Refer to Figure 11-7:

• a. Which are the hottest and coolest named stars on the diagram?
• b. Which are the brightest and dimmest named stars on the diagram?
• c. Which are the hottest and coolest named mainsequence stars on the diagram?
• d. Which named stars are white dwarfs? giants? supergiants?

Question 11.28

What is the inverse-square law? Use it to explain why a headlight on a car can appear brighter than a star, even though the headlight emits far less light energy per second.

Question 11.29

*Van Maanen’s star, named after the Dutch astronomer who discovered it, has a parallax angle of 0.232 arcsec. How far away is the star?

Question 11.30

Explain how sailors on a ship traveling parallel to a coastline at a known speed can use parallax angle measurements to determine the distance to the shore.

Question 11.31

*Suppose that a dim star was located 2 million AU from the Sun. Find (a) the distance to the star in parsecs and (b) the parallax angle of the star.

Question 11.32

*How many times brighter is a star of apparent magnitude m = −1 than a star of apparent magnitude m = +7?

Question 11.33

Sketch the radial-velocity curve of a binary whose stars are moving in nearly circular orbits that are a. perpendicular and b. parallel to our line of sight.

Question 11.34

Sketch the light curve of an eclipsing binary whose stars are moving along highly elongated orbits with the major axis of the orbits a. pointed toward Earth and b. perpendicular to our line of sight.

Question 11.35

a. What is the approximate mass of a main-sequence star that is 10,000 times as luminous as the Sun? b. What is the approximate luminosity of a main-sequence star whose mass is one-tenth that of the Sun?

Question 11.36

What is the approximate surface temperature of a main-sequence star luminosity 100 times as bright as the Sun?

Question 11.37

Discuss the advantages and disadvantages of measuring stellar parallax from a space telescope at the distance of Jupiter from the Sun compared to the same measurements made from Earth’s surface.

Question 11.38

How does a star’s rotation affect the appearance of its spectral lines? Hint: Assume we are looking at the star from above its equator. Then, at every instant, half of the spinning star is approaching Earth, while the other half is receding. Consider the resulting Doppler shift in the spectral lines.

Question 11.39

All of the stars in our Milky Way Galaxy actually were the same distance from Earth, say, 10 pc? Describe what the night sky might look like. How about the daytime sky? Hint: If you are doing this quantitatively, assume for simplicity that all of the stars have the same absolute magnitudes as the Sun and that there are roughly 200 billion stars in the Galaxy.

Question 11.40

All stellar parallax angles, p, were observed to be increasing? What would that imply about the motions of stars? Is there another observational technique that could be used to confirm this motion?

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Question 11.41

A star’s parallax were observed to oscillate—regularly increase in angle and then decrease in angle—over a period of 100 years? What would that imply about the star?

Question 11.42

The Sun were part of a binary star system of two main-sequence stars and Earth orbited around one of the stars, with the gravitational force from the other star making the Earth′s orbit much more elliptical than it is today? You might want to discuss such things as climate, tides, impacts from meteoroids and asteroids, and habitability.

Question 11.43

The Sun were an M-type star, rather than a G-type star? Assuming that Earth orbiting the M-type star had the same composition and orbit distance as it does today, what would be different here?

Question 11.44

The Sun were a B-type star, rather than a G-type star? Assuming that Earth orbiting the B-type star had the same composition and orbit distance as it does today, what would be different here? We will pick up this question again in Chapter 13 for further insights.

Question 11.45

Search the Web for the periods of 10 binary star systems. Plot these on a graph of time (on the horizontal axis) versus number of systems. If possible, combine this information with similar data from your classmates. Do you see any patterns in the periods of these star systems?

Question 11.46

To explore the range of periods of binary star systems, locate on the Web binary star systems with periods of (a) less than 1 week, (b) between 1 day and 1 week, (c) between 1 and 2 years, (d) between 40 and 50 years, and (e) more than 400 years.

Question 11.47

Of all the spectral classes of stars (O, B, A, F, G, K, M), which is least common?

Question 11.48

Comparing them side by side, which of the following most accurately describes the Sun’s luminosity relative to other stars?

• a. it is among the most luminous of stars
• b. it is of average luminosity
• c. it is less luminous than the average luminosity of stars
• d. it is among the least luminous of all stars
• e. all stars are equally luminous

Question 11.49

What colors are the hottest and coolest stars?

Question 11.50

If a star is a red giant, how does its surface temperature compare to that of the Sun?

Question 11.51

Use Starry Night™ to examine the 10 brightest stars in Earth’s night sky. Select Favourites > Explorations > Atlas. Use the View > Constellations menu command to display constellation Boundaries, Labels, and Astronomical stick figures. Use the File (Windows) or Starry Night (Mac) menu command to open the Preferences dialog window. Ensure that the Cursor Tracking (HUD) preferences include Apparent Magnitude, Distance from Observer, Luminosity and Temperature in the Show list. Before closing the Preferences dialog window, it might be helpful to increase the saturation for Star colour under the Brightness/Contrast preferences. Click on the Lists side pane tab, expand the Observing Lists, and click the 10 Brightest Stars option. Then expand the List Viewer layer and select All Targets from the Show dropdown menu to see a list of the 10 brightest stars in Earth’s night sky. Double-click on each of the stars in this list in turn to center the star in the view. Use the HUD to compile a table of these stars that includes each star’s apparent magnitude, distance, luminosity, and temperature. You may also wish to sketch the star’s position within its constellation. Alternatively, you may find it helpful to print out relevant star charts around these stars, using Starry Night™. (a) Which is the brightest star in Earth’s night sky? What features of this star make it so bright in our sky? (b) Which of these brightest stars has the highest temperature? What would you expect to be the color of this star compared to others in the list?

(c) Which of these stars is intrinsically the most luminous? (d) Use Starry Night™ to determine which of these stars is visible from your location. Click the Home button, then the Stop button, and finally the Sunset button to show the view from your home location today at sunset. Again, it may be helpful to display the constellation Boundaries, Labels, and Astronomical stick figures in the view. Open the Lists side pane and double-click each entry in the list of the 10 Brightest Stars. If the star is visible in your sky, the program will center it in the view or alternately suggest a Best Time for observing this star. For those stars in the list that are visible from your home location, go outside if possible and observe them in the real sky. See if you can tell which of these stars has the highest temperature on the basis of your conclusion regarding the star’s color and check your estimate against the table you compiled in part (a) (Hint: The colors of stars are not very distinct and a dark sky background is needed in order to distinguish differences in stellar colors.)

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Question 11.52

Locate the stars Betelgeuse and Rigel in Orion. Observe them both with the unaided eye and through a small telescope. Are they the same color? To determine their color(s), it helps to compare them to their neighbors.

Question 11.53

Use the Starry Night™ program to investigate the Hertzsprung-Russell (H-R) diagram. Select Favourites > Explorations > Denver. Open the Status pane, expand the H-R Options layer, and choose the following options: Use absolute magnitudes and Labels.

In the expanded Labels panel, click On the Gridlines, Regions, Main Sequence, and Spectral class options. Now, expand the Hertzsprung-Russell layer to show the H-R diagram that plots all of the stars that are currently in the main view. This graphical representation shows the absolute magnitudes of stars as a function of their spectral class. The surface temperatures of stars are represented by a sequence of spectral classes that are assigned the letters O, B, A, F, G, K and M, with temperatures plotted in an inverse direction, the hottest O-type stars appearing to the left of the diagram. Absolute magnitude is related to the star’s luminosity; the smaller the absolute value of absolute magnitude, the larger the luminosity. (a) Use the hand tool to scroll around the sky. Watch the H-R diagram change as different stars enter and leave the main window. Right-click (Ctrl-click on a Mac) on a blank part of the sky and select Hide Horizon from the contextual menu so that you can survey the entire sky. Does the distribution of stars in the H-R diagram change drastically from one part of the sky to another, or are all types of stars approximately equally represented in all directions from the Earth? (b) If you place the cursor over a star, a red dot appears in the H-R diagram at the position for this star. Use this facility to estimate and make a note of the spectral-luminosity classification and the absolute magnitude, M_V, of the following stars that are labeled in the main window: Altair, Deneb, Enif, 74 Ophiuchi, and 51 Pegasi. (Remember that each spectral class is divided into ten subclasses from 0 to 9.) (c) Based on its spectral-luminosity classification, which of these five stars is most similar to the Sun? What is the name of the region of the H-R diagram occupied by this star? If these two physical properties are similar for the Sun and this star, which other two parameters will necessarily be similar? Explain.