Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 19, Problem 49Q
To determine
The Earth’s surface temperature when the Sun becomes a red giant.
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When the Sun becomes a red giant, it's luminosity will be 2000 times its current value. The solar flux at Earth will also increase by a factor of 2000. Neglecting the greenhouse effect, the surface temperature of the earth is determined by thermal equilibrium: the flux of radiation absorbed equals the flux of radiation emitted. This means the Earth's surface flux must also increase by a factor of 2000. If the current average surface temperature is 58 degrees F, what will the average surface temperature be when the Sun is a red giant.
Express your answer in units of degrees Fahrenheit.
[Hint: Recall that the Stefan-Boltzmann law says that the flux F emitted by a blackbody is related to its surface temperature T (measured in Kelvins) is F=σT4 . Use this law in the form of a ratio, expressing T in Kelvins. Then convert back to Fahrenheit.]
Assume that when a certain main sequence star becomes a giant gas, its luminosity increases from L to 1000 L and its radius also increases from R to 1000 R. If the initial surface temperature is T, what approximately is the final surface temperature?
A. 0.032 T
B. 0.18 T
C. 0.0010 T
D. 0.010 T
For a main sequence star with luminosity L, how many kilograms of hydrogen is being converted into helium per second? Use the formula that you derive to estimate the mass of hydrogen atoms that are converted into helium in the interior of the sun (LSun = 3.9 x 1026 W).
(Note: the mass of a hydrogen atom is 1 mproton and the mass of a helium atom is 3.97 mproton. You need four hydrogen nuclei to form one helium nucleus.)
Chapter 19 Solutions
Universe: Stars And Galaxies
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- In about 5 billion years, the sun will evolve to a red giant. Assume that its surface temperature will decrease to about half its present value of 6000 K, while its present radius of 7.0108 m will increase to 1.51011 m (which is the current Earth-sun distance). Calculate the ratio of the total power emitted by the sun in its red giant stage to its present power.arrow_forwardAppendix J lists the stars that appear brightest in our sky. Are most of these hotter or cooler than the Sun? Can you suggest a reason for the difference between this answer and the answer to the previous question? (Hint: Look at the luminosities.) Is there any tendency for a correlation between temperature and luminosity? Are there exceptions to the correlation?arrow_forwardIf the Sun were replaced by a white dwarf with a surface temperature of 10,000 K and a radius equal to Earth’s, how would its luminosity compare to that of the Sun?arrow_forward
- Before the star that became SN 1987A exploded, it evolved from a red supergiant to a blue supergiant while remaining at the same luminosity. As a red supergiant, its surface temperature would have been approximately 4000 K, while as a blue supergiant, its surface temperature was 16,000 K. How much did the radius change as it evolved from a red to a blue supergiant?arrow_forwardA star such as our Sun will eventually evolve to a “red giant” star and then to a “whitedwarf” star. A typical white dwarf is approximately the size of Earth, and its surfacetemperature is about 2.5×103 K. A typical red giant has a surface temperature of 3.0×104K and a radius ~100,000 times larger than that of a white dwarf.a) What is the average radiated power per unit area by each of these types of stars?b) What is the ratio of total power radiated from the white dwarf over the power of thered giant? assume that both stars have emission e = 1arrow_forwardThe Orion Nebula is a gas-rich region in which stars are being born. The nebula is at a distance of about 1344 lyr from Earth.Suppose you observe a star in the Orion Nebula to have an apparent magnitude of 6.75. Calculate the absolute magnitudeof the star. Also calculate the luminosity of the star in units of the solar luminosity (knowing that the absolute magnitude ofthe Sun is 4.8).arrow_forward
- Use t = 1 M2.5 to compute the life expectancy of a 0.6-solar-mass star. (A solar lifetime is approximately 10 billion years.) yrWhy might this be an underestimate if the star is fully mixed by convection? a) If the star is fully mixed its mass will be much larger than 0.6 solar masses. b) If the star is fully mixed its mass will be much smaller than 0.6 solar masses. c) If the star is fully mixed it will be able to use a larger portion of its hydrogen in fusion than the Sun. d) If the star is fully mixed it will be able to use a smaller portion of its hydrogen in fusion than the Sun.arrow_forward(a) The surface temperature of a star is 25,000 K and it has a luminosity about 1% that of our Sun. What kind of star is it? (B) The surface temperature of a star is 3,000 K and it has a luminosity about 104 time that of our Sun. What kind of star is it?arrow_forwardAssuming that at the end of the He burning phase of the stellar core (r < R_core) has no H or He or other metals and is composed completely of Carbon, X=Y=0, X_c = 1 ; The envelope above the core has a normal stellar composition ( r > R_core). Calculate the length of time in years that a 1M_sol and 10M_sol star will live on the horizontal branch or the time between the start and end of the He burning phase. Assume that the normal relationship between mass and luminosity holds for horizontal branch stars. Please be as detailed as possiblearrow_forward
- We will take a moment to compare how brightly a white dwarf star shines compared to a red giant star. For the sake of this problem, let's assume a white dwarf has a temperature around 10,000 K and a red giant has a temperature around 5,000 K. As for their stellar radiatin, the white dwarf has a radius about 1/100th that of the Sun, and a red giant has a radius around 100 times larger than the Sun. With this in mind, how does the luminosity of a red giant star compare to that of a white dwarf (Hint: do not try to enter all of these numbers into the luminosity equation {it won't go well}; instead, remember that you are only interested in the ratio between the two, so all common units and components can be divided out)? Please enter your answer in terms of the luminosity of the red giant divided by the luminosity of the white dwarf and round to two significant figures. Also, please avoid using commas in your answer.arrow_forwardWhy do nebulae near hot stars look red? Why do dust clouds near stars usually look blue?arrow_forwardIf a 100 solar mass star were to have a luminosity of 107 times the Sun’s luminosity, how would such a star’s density compare when it is on the main sequence as an O-type star, and when it is a cool supergiant (M-type)? Use values of temperature from Figure 18.14 or Figure 18.15 and the relationship between luminosity, radius, and temperature as given in Exercise 18.47. Figure 18.15 Schematic HR Diagram for Many Stars. Ninety percent of all stars on such a diagram fall along a narrow band called the main sequence. A minority of stars are found in the upper right; they are both cool (and hence red) and bright, and must be giants. Some stars fall in the lower left of the diagram; they are both hot and dim, and must be white dwarfs. Figure 18.14 HR Diagram for a Selected Sample of Stars. In such diagrams, luminosity is plotted along the vertical axis. Along the horizontal axis, we can plot either temperature or spectral type (also sometimes called spectral class). Several of the brightest stars are identified by name. Most stars fall on the main sequence.arrow_forward
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