HW10 - MasteringAstronomy 11:32 AM\liumgv...

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Unformatted text preview: MasteringAstronomy 4/5/10 11:32 AM \liumgv llu.» \nxignirrt'nt Print Verslo HW10 (questions from chapt 17 and 20 email me questions) Due: 11:59pm on Thursday, April 22, 2010 Note: You will receive no credit for late submissions. To learn more, read your instructors Gradan Policy Ranking Task: H-R Diagram, Luminosity, and Temperature Description: A multi-part activity requiring reasoning about the surface temperature and luminosity of stars as indicated on the H-R diagram. Part A Consider the four stars shown following. Rank the stars based on their surface temperature from highest to lowest. Hint A.l How is the color of light related to its wavelength? Which of the following lists the visible colors in correct order from shortest wavelength to longest wavelength? ANSWER: ' - actually peaks in the green. You should then be able to complete the ranking task in Part A. Hint A.2 How does the wavelength of light depend on an object’s temperature? According to the laws of thermal radiation, hotter objects have spectra that peak at ANSWER: E ashorterwavelength ’lon er \vavelen th The object’s color generally looks like the color of light at the peak wavolength. Now, remember that shorter wavelength means bluer light, and you should be able to complete the ranking task in Part A. Hint At3 ‘ The—Colorwof the Sun The Sun appears yellow or white to the eye, but its spectrum actually peaks in the middle of the Visible region, which corresponds to yellow or green in color. Note that this means the Sun‘s spectrum peaks at a wavelength shorter than that of a blue star. but longer than that of an orange or red star. Notice that temperature is related to color, and follows the order of the colors in the rainbow: Blue (or violet) stars are the hottest, while red stars are the coolest. In the parts that follow. the H-R diagrams show the correlation between color and temperature on the horizontal axis. Five stars are shown on the following H~R diagrams. Rank the stars based on their surf ace temperature from highest to lowest. If two (or more) stars have the same surface temperature, drag one star on top of the other(s). Hint 3.1 How does the H-R diagram show surface temperature? On the H—R diagram, surface temperature increases . pward, so stars low on the luminosity axis have lower surface temperature than stars higher up aright to left, so stars farther to the left along the spectral type axis have higher surface temperature than stars to the right agonally from the lower left to the upper right ANSWER: e, X“ a”; M having the lowest surface temperature. Now. look to see how the surface temperatures of the five stars compare and you will then be able to complete Part B of this ranking task. ANSWER: All five stars appear at the same place along the horizontal axis showing spectral type. Because spectral type is related to surface temperature, all five stars must have the same surface temperature. Now proceed to Part C to determine how these stars vary in luminosity. Part C Five stars are shown on the following H-R diagrams; notice that these are the same five stars shown in Part B, Rank the stars based on their http://session.masteringastronomy.com/myct Page 1 of 17 MasteringAstronomy luminosity from highest to lowest. If two (or more) stars have the same luminosity, drag one star on top of the other(s). luminosity axis represents a change by a factor of 10 from the prior tickmark, so the range of luminosities is quite large. Continue to Parts D Luminosity is shown along the Vertical axis, with stars higher up more luminous than those lower down. Note that each tickmark along the U Part D Five stars are shown on the following H—R diagrams. Rank the stars based on their surface temperature from highest to lowest. If two (or more) stars have the same surface temperature, drag one star on top of the other(s). Hint D.l How does the H-R diagram show surface temperature? On the 1-D? diagram. surface temperature increases ANSWER: E » upward, so stars low on the luminosny axts have lower surface temperature than stars higher up I @right to left, so stars farther to the left along the spectral type axis have higher surface temperature than stars to the right « diagonally from the lOWer left to the upper right Spectral type is related to surface temperature, with stars of spectral type 0 haying the highest surface temperature and stars of spectral type 3% M having the lowest surface temperature. Now, look to see how the surface temperatures of the five stars compare and you will then be able to complete Part B of this ranking task. ANSWER: i i t r’ l ' Spectral type is related to surface temperature, with stars of spectral type 0 having the highest surface temperature and stars of spectral type M having the lowest surface temperature. In other words, spectral type increases to the left on the H—R diagram. Now proceed to Part E to determine how these stars compare in luminosity. Part E Five stars are shown on the following H-R diagrams. Rank the stars based on their luminosity from highest to lowest; notice that these are the same five stars shown in Part D. If two (or more) stars have the same luminosity, drag one star on top of the other(s). ANSWER All five stars have the same luminosity because they are all at the same height along the vertical (luminosity) axis. Continue to Parts F and G T for more practice in reading surface temperature and luminosity on the HR diagram. Five stars are shown on the following H—R diagrams. Rani: the stars based on their surface temperature from highest to lowest. If two (or more) stars have the same surface temperature, drag one star on top of the other(s). Hint F.l How does the H-R diagram show surface temperature? On the H—R diagram, surface temperature increases ANSWER: upward, so stars low on the luminosity axis have lower surface temperature than stars higher up 3 § @right to left, so stars farther to the left along the spectral type axis have higher surface temperature than stars to the right I ‘diagonally from the IOWer left to the upper right httpzl/sessIon.masterlngastronomy.com/myct 4/5/10 11:33 AM Page 2 of 17 MasteringAstronomy 4/5/10 11:33 AM l View Spectral type is related to surface temperature, with stars of spectral type 0 having the highest surface temperature and stars of spectral typeM having the lowest surface temperatur In other words, spectral type increases to the left on the H-R diagram. Part C Five stars are shown on the following H-R diagrams; notice that these are the same five stars shown in Part F. Rank the stars based on their luminosity from highest to lowest. If two (or more) stars have the same luminosity, drag one star on top of the other(s). ANSWER: s always, the HR diagram shows surface temperature along the horizontal axis and luminosity along the vertical axis. Ranking Task: Luminosity, Distance, and the Apparent Brightness of Stars ~ ‘l Description: A multi-part ranking task exploring the relationship among luminosity, apparent brightness, and distance. Part A —l Listed following are several fictitious stars with their luminosities given in terms of the Sun’s luminosity ( L5,“) and their distances from Earth git’en in light—years (1y). Rank the stars based on how bright each would appear in the sky as seen from Earth, from brightest to dimmest. If two (or more) stars have the same brightness in the sky, show this equality by dragging one star on top of the other(s). Hint A.1 What is luminosity? ANSWER: the total amount of light that it radiates into space . 5 7 how bright it is in the night sky The luminosity of a star tells us how lar e the star is in size (radius) l é; The star's brightness in our sky depends on both its luminosity and its distance from us, in accord with the inverse square law for light. You > can use this fact to determine all the correct rankings for Part A. If you need to review the inverse square law for light, consult your textbook F‘g or open the third hint. as Hint A.2 How does a star‘s brightness in our sky depend on its luminosity? Suppose Star X is twice as luminous as Star Y, and both stars are located the same distance from Earth. Then in our night sky, Star X will appear ANSWER: Ihalf as bright as Star Y @twice as bright as Star Y i one-fourth as bright as Star Y r 'four times as bright as Star Y all' b‘ ht Sta Y For a star at a given distance, brightness in our sky is directly proportional to luminosity. Now use this fact along with the inverse square law 8 for light to complete the ranking task. If you need to review the inverse square law for light, consult your textbook or open the third hint. Hint A.3 How does a star's brightness in our sky depend on its distance? Suppose Star X and Star Y have the same luminosity, and Star X is located twice as far from Earth. Then in our night sky, Star X will appear half as bright as StarY ', itwice as bright as Star Y @one-fourth as bright as Star Y ’ Ifour times as bright as Star Y equally as bright as Star Y ANSWER: : a”; g; Brightness in the sky depends on distance in accord with the inverse square law for light: Increasing distance by some factor causes the ~ apparent brightness to decrease (the “inverse” part of the inverse square law) by the square of that factor. For example, doubling distance . decreases the brightness by a factor of 22 = 4, tripling the distance decreases the brightness by a factor of 32 = 9, and so on. This fact is the 1 key to completing the ranking task. Hint A.4 If you are still stuck, open this hint for a strategy to find the answer. The key to completing this ranking task is to compare pairs of stars with the help of the inverse square law for light. 0 Start by comparing Nismo to Shelby: Notice that both have the same luminosity, but Nismo is closer to us. Which one is brighter in our sky? The answer to this question will tell you the ranking order for these two stars. - Next, compare Shelby and Enzo. You will need to use the inverse square law for light to determine which one is brighter, and once you do so you’ll know how to rank these two stars. 0 Then compare Lotus to Enzo, At this point, you should have all the stars ranked except for Ferdinand. - Finally, compare Ferdinand to Shelby, and then you will be done. ANSWER: http://session.masteringastronomy.com/myct Page 3 of 17 MasteringAstronomy ' To be sure you understand the concept, notice the following facts: (1) Nismc is clearly brighter in the sky than Shelby, because it has the same uminosity but is nearer to us. (2) Enzo is twice as luminous and twice as far as Shelby; the inverse square law for light tells us that doubling distance makes an object four times as dim, so Enzo must be dimmer than Shelby. (3) Similarly, because Lotus has twice the luminosity and wice the distance of Enzo, it must be dimmer than Enzo. (4) Ferdinand has four times the luminosity and twice the distance of Shelby, so the nverse square law for light tells us that they are equally bright in our sky. Putting all four facts together leads to the correct answer. Pan B Listed following is the same set of fictitious stars given in Part A. Rank the stars based on how bright each would appear in the sky as seen from Jupiter, from brightest to dimmest. Hint B.l Are the stars closer to Earth or to Jupiter? Compared to their distance from Earth, the stars are _____ Jupiter. closer to E «_»farther from g @about the same distance from ANSWER. Recall that in a 1~to~10—billion scale model, Earth and Jupiter each lie within a few minutes' walk of the grapefruit—size Sun, while even the nearest stars are thousands of kilometers away. As a result, there is no noticeable difference between the way stars will appear in Earth’s sky and the way the same stars will appear in Jupiter‘s sky. ANSWER: I Stars are so far away that any difference in distance to the stars from Earth and Jupiter is negligible. As a result, the answer to this part is the ame as the answer to Part A. Part C The following figure shows how four identical stars appear in the night sky seen from Earth. The shading is used to indicate how bright (white) or dim (dark gray) the star would appear in the sky from Earth. Rank the stars based on their distance from Earth, from farthest to closest. ANSWER: 5 i r r r l i i For stars of the same luminosity. apparent brightness decreases with distance (following the inverse square law for light). Therefore, the star . that appears dimmest must be the most distant and the star that appears brightest must be the nearest. Remember that this is true ONLY if you ;: know that all stars have the same intrinsic luminosity. Because there is no way to know luminosity just by looking at a star in the sky, you ; cannot in general use brightness to say anything about distance. s, , Sorting Task: Patterns among Stars t :Description: A sorting task in which students identify distinguishing characteristics of white dwarfs, main-sequence stars, and giants and supergianls. Part A Listed following is a set of statements describing individual stars or characteristics of stars. Match these to the appropriate object category. Hint A.l What are giant and super-giant stars? Giants and supergiants exceed most other stars in ANSWER: surface temperature only 7 ’luminosity only ‘ ‘radius only @both radius and luminosity ' both surface temperature and luminosity r l i l r r t @ iants and supergiants are found in the upper right portion of the H~R diagram, indicating high luminosity but relatively low surface temperature, which means they must be very large in radius. Hint A.2 What are main-sequence stars? httpzl/session.masteringastronomy.com/myct 4/5/10 11:33 AM Page 4 of 17 MasteringAstronomy ANSWER: l I l i a rare type of extremely massive star l Main~sequence stars are . stars that are in the longest~lasting phase of their lives, in which they fuse hydrogen into i ‘ helium in their cores i ’ stars that have e ’hathted their supplies of energy for fusion i i i gMain-sequence stars therefore represent the vast majority of all stars. Hint A.3 What are white dwarfs? ANSWER: ® dim I . Y i Ivcry luminous : White dtt arfs are small and _. V ,Shon lived ‘ool White dwarfs are dim but hot stellar corpses — essentially the exposed cores of stars that have shed their outer layers — which is why they are found in the lower left of the H—R diagram. i i i i i i i " Be sure that you understand why each of these characteristics goes with either giants/supergiants, main~sequence stars, or white dwarfs. If you tat Visual Activity: Using an H-R Diagram to Explore the Properties of Main-Sequence Stars Description: A multi-part visual activity that uses an interactive H-R diagram to explore the properties of main-sequence stars. Explore the interactive figure before beginning to answer the questions. Click the “show stars” button to see the main sequence and then move the “radius” slider (at bottom) to see the location along the main sequence of a main~sequence star with that particular radius. You can do the same for temperature, luminosity, mass, or lifetime: Clicking one of these properties in the list along the right changes the slider to that property. Note that this interactive figure allows you to vary properties of main-sequence Stars only, not of any other type of star (such as giants or white dwarfs). Part A Compared to a main«sequence star with a short lifetime, a main-sequence star with a long lifetime is Hint A.1 What is the surface temperature of a high-luminosity main-sequence star? A typical surface temperature for a high-luminosity mainvsequence star is less than about 10,000 K I fibetween about 10,000 K and 50,000 K i ‘ greater than about 50,000 K ANSWER: As you can see when you click "show stars," high—luminosity main-sequence stars are in the upper left of the diagram, and the left stde corresponds to surface temperatures ranging from above 10,000 to about 50,000 K. Now, use the interactive figure to determine whether these high-luminosit ' mam»sequence stars have long or sh l f mes. [Hint A.2 What is the mass of a hot main-sequence star? A typical mass for a mainvsequcnce star with high surface temperature is httpzl/session.masteringastronomy.com/myct 4/5/10 11:33 AM Page 5 of 17 MasteringAstronomy 4/5/10 11:33 AM ANSWER: i ’less than about 5 solar masses @between about 5 and 100 solar masses ‘ i greater than about 100 solar masses 5" Notice that surface temperature increases to the left on the diagram, so high-surface-temperature stars are those on the left side. If you use a . more luminous. hotter, larger, and more massive more luminous, hotter, smaller, and less massive less luminous, cooler, larger, and more massive @less luminous, cooler, smaller, and less massive g; Note that there are physical reasons why long-lived stars have these properties: They are less luminous because they burn their fuel at a much lower rate than short-lived stars; they burn it at this lower rate because they are less massive (which means less compression and hence a lower , 1 fusion rate in their cores); and their lower masses lead to their smaller sizes and lowar surface temperatures. Part B Compared to a high—luminosity main—sequence star, stars in the upper right of the H-R diagram are [Hint B.l Which star is hotter? Be sure you have clicked on the "show stars" button and then locate Spica (near the top of the main sequence) and Betelgeuse (near the upper right) in the H-R diagram. True or False? Spica has a higher surface temperature than Betelgeuse. / Be sure to notice that temperature increases to the left on the H—R diagram. % Hint B.2 Which star is larger? Be sure you have clicked on the "show stars" button and then locate Spica (near the top of the main sequence) and Betelgeuse (near the upper right) in the H—R diagram. True or False? Bctelgeuse is larger in radius than Spica. Be sure to notice the diagonal lines showing that radius increases from the lower left to the upper right on the H-R diagram. ANSWER: hotter and larger in radius : @cooler and larger in radius ' ‘ ‘ cooler and smaller in radius . hotter and smaller in radius i 9 Be sure to notice that luminosity increases upward on the diagram, surface temperature increases to the left, and radius increases diagonally from the lower left to the upper right. Therefore, stars in the upper right must be high in luminosity and radius, but low in surface temperature. ’ These stars are called giants or supergiants because of their large radii. Part C Compared to a low—luminosity main—sequence star, stars in the lower left of the H—R diagram are Hint C.l Which star is hotter? Be sure you have clicked on the "show stars" button and then locate Sirius B (near the lower left) and Ross 128 (near the lower right) in the H-R diagram. True or False? Sirius B has a higher surface temperature than Ross 128. @Be sure you notice that temperature increases to the left on the H—R diagram. Hint C.2 Which star is larger? Be sure you have clicked on the "show stars“ button and then locate Sirius B (near the lower left) and Ross 128 (near the lower right) in the H—R diagram. True or False? Sims B is larger in radius than Ross 128. gBe sure you notice the diagonal lines showing that the smallest radii are found on the lower left on the HR diagram. ANSWER: , hotter and larger in radius i ‘ cooler and larger in radius ' cooler and smaller in radius 1 Q hotter and smaller in radius é Notice that the stars in the lower left of the diagram are called white dwarfs: while because they are hot enough to appear "white hot” to our ‘T eyes, and dwarfs because of their small sizes. A typical white dwarf is no larger in size (radius) than our Earth, but has as much mass as the httpzl/session.masterlngastronomy.com/myct Page 6 of 17 MasteringAstronomy ti Sun. Chapter 17 Multiple Choice Quiz 1 j Description: (a) Which of the following is not an intrinsic property of a star? (b) As the distance of an obs...
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