Foundations of Astronomy
13th Edition
ISBN: 9781305079151
Author: Michael A. Seeds, Dana Backman
Publisher: Cengage Learning
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Chapter 12, Problem 1DQ
To determine
How the energy is transported within a brown dwarf.
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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.)
We learned in class that, when stars collapse under their own gravity, they conserve angular momentum, which is proportional to
mass times radius times rotational speed. Suppose the entire sun (radius 695,700 km) were to collapse to a neutron star with a
radius of only 10 km. Before the collapse, the rotational speed at the equator = 2.0 km/s, and the rotational period is 25 days.
Using the same steps that you used for the white dwarf calculations, calculate the final rotation period if the entire sun were to
collapse to a 10 km radius neutron star. Give your answer in units of seconds.
Answer:
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One way to calculate the radius of a star is to use its luminosity and temperature and assume that the star radiates approximately like a blackbody. Astronomers have measured the characteristics of central stars of planetary nebulae and have found that a typical central star is 16 times as luminous and 20 times as hot (about 110,000 K) as the Sun. Find the radius in terms of the Sun’s. How does this radius compare with that of a typical white dwarf?
Chapter 12 Solutions
Foundations of Astronomy
Ch. 12 - Prob. 1RQCh. 12 - Prob. 2RQCh. 12 - Prob. 3RQCh. 12 - Prob. 4RQCh. 12 - Prob. 5RQCh. 12 - Describe the law of hydrostatic equilibrium.Ch. 12 - Prob. 7RQCh. 12 - Prob. 8RQCh. 12 - Prob. 9RQCh. 12 - Prob. 10RQ
Ch. 12 - Prob. 11RQCh. 12 - Prob. 12RQCh. 12 - Prob. 13RQCh. 12 - Prob. 14RQCh. 12 - Prob. 15RQCh. 12 - Prob. 16RQCh. 12 - Prob. 17RQCh. 12 - Prob. 18RQCh. 12 - Prob. 19RQCh. 12 - What gives the triple-alpha process its name? Why...Ch. 12 - Prob. 21RQCh. 12 - Prob. 22RQCh. 12 - Prob. 23RQCh. 12 - Prob. 24RQCh. 12 - Prob. 25RQCh. 12 - Prob. 26RQCh. 12 - Prob. 27RQCh. 12 - Prob. 28RQCh. 12 - Prob. 29RQCh. 12 - Prob. 30RQCh. 12 - Prob. 31RQCh. 12 - How Do We Know? How can mathematical models allow...Ch. 12 - Prob. 1DQCh. 12 - Prob. 2DQCh. 12 - Prob. 3DQCh. 12 - Prob. 4DQCh. 12 - Prob. 5DQCh. 12 - Prob. 6DQCh. 12 - Prob. 1PCh. 12 - Prob. 2PCh. 12 - Prob. 3PCh. 12 - Prob. 4PCh. 12 - Prob. 5PCh. 12 - Prob. 6PCh. 12 - Prob. 7PCh. 12 - Prob. 8PCh. 12 - Prob. 9PCh. 12 - Prob. 10PCh. 12 - Prob. 11PCh. 12 - Prob. 12PCh. 12 - Prob. 13PCh. 12 - Prob. 14PCh. 12 - Prob. 15PCh. 12 - Prob. 16PCh. 12 - Prob. 1LTLCh. 12 - Prob. 2LTLCh. 12 - Prob. 3LTLCh. 12 - Prob. 4LTLCh. 12 - Prob. 5LTL
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- According to the text, a star must be hotter than about 25,000 K to produce an H II region. Both the hottest white dwarfs and main-sequence O stars have temperatures hotter than 25,000 K. Which type of star can ionize more hydrogen? Why?arrow_forwardWhere in the Galaxy would you expect to find Type II supernovae, which are the explosions of massive stars that go through their lives very quickly? Where would you expect to find Type I supernovae, which involve the explosions of white dwarfs?arrow_forwardWhat physical properties are different for an M giant with a luminosity of 1000 LSunand an M dwarf with a luminosity of 0.5 LSun? What physical properties are the same?arrow_forward
- How would a white dwarf that formed from a star that had an initial mass of 1 MSunbe different from a white dwarf that formed from a star that had an initial mass of 9 MSun?arrow_forwardApproximately 6000 stars are bright enough to be seen without a telescope. Are any of these white dwarfs? Use the information given in this chapter to explain your reasoning.arrow_forwardHow much would you weigh if you were suddenly transported to the white dwarf Sirius B? You may use your own weight (or if don’t want to own up to what it is, assume you weigh 70 kg or 150 lb). In this case, assume that the companion to Sirius has a mass equal to that of the Sun and a radius equal to that of Earth. Remember Newton’s law of gravity: F=GM1M2/R2 and that your weight is proportional to the force that you feel. What kind of star should you travel to if you want to lose weight (and not gain it)?arrow_forward
- If a 3 and 8 MSunstar formed together in a binary system, which star would: A. Evolve off the main sequence first? B. Form a carbon- and oxygen-rich white dwarf? C. Be the location for a nova explosion?arrow_forwardWhat is the escape velocity from the white dwarf in Exercise 23.35? How much greater is it than the escape velocity from Earth?arrow_forwardA star begins its life with a mass of 5 MSunbut ends its life as a white dwarf with a mass of 0.8 MSun. List the stages in the star’s life during which it most likely lost some of the mass it started with. How did mass loss occur in each stage?arrow_forward
- Describe the evolution of a star with a mass similar to that of the Sun, from the protostar stage to the time it first becomes a red giant. Give the description in words and then sketch the evolution on an HR diagram.arrow_forwardThe ring around SN 1987A (Figure 23.12) started interacting with material propelled by the shockwave from the supernova beginning in 1997 (10 years after the explosion). The radius of the ring is approximately 0.75 light-year from the supernova location. How fast is the supernova material moving, assume a constant rate of motion in km/s? Figure 23.12 Ring around Supernova 1987A. These two images show a ring of gas expelled by a red giant star about 30,000 years before the star exploded and was observed as Supernova 1987A. The supernova, which has been artificially dimmed, is located at the center of the ring. The left-hand image was taken in 1997 and the right-hand image in 2003. Note that the number of bright spots has increased from 1 to more than 15 over this time interval. These spots occur where high-speed gas ejected by the supernova and moving at millions of miles per hour has reached the ring and blasted into it. The collision has heated the gas in the ring and caused it to glow more brightly. The fact that we see individual spots suggests that material ejected by the supernova is first hitting narrow, inward-projecting columns of gas in the clumpy ring. The hot spots are the first signs of a dramatic and violent collision between the new and old material that will continue over the next few years. By studying these bright spots, astronomers can determine the composition of the ring and hence learn about the nuclear processes that build heavy elements inside massive stars. (credit: modification of work by NASA, P. Challis, R. Kirshner (Harvard-Smithsonian Center for Astrophysics) and B. Sugerman (STScI))arrow_forwardWould you expect to find any white dwarfs in the Orion Nebula? (See The Birth of Stars and the Discovery of Planets outside the Solar System to remind yourself of its characteristics.) Why or why not?arrow_forward
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