Problem%20Set%204%20Solutions - Problem Set 4 Solutions...

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- 1 - Problem Set 4 Solutions Astronomy 202 Assigned: 20 March 2006 Due: 03 April 2006 Chapter 20 Review and Discussion: 1, 3, 11, 16, 20 1. Why don’t stars live forever? Which types of stars live the longest? Stars burn hydrogen into helium. When the hydrogen in the nuclear burning region is exhausted the star either shuts down completely (dies) or moves to another fuel. Eventually however, no further fuel will be available and the star dies. Since lower mass stars burner at a much lower rate then higher mass stars and have more fuel relative to their burning rate they live the longest. Theoretically, a 0.5 solar mass star has a lifetime longer than the age of the universe while solar mass star lives only tens of millions of years. 3. How long can a star like the Sun keep burning hydrogen in its core? As a main sequence star, stars like the Sun fuse hydrogen into helium for about 10 billion years. As the hydrogen is depleted in the core, hydrogen fusion continues in a shell around the core for about another billion years. 11. How do the late evolutionary stages of high-mass stars differ from those of low-mass stars? Low mass stars eventually form a carbon core (the product of He burning) that collapses but is unable to attain a high enough temperature to allow the fusion of carbon. The outer part of the star continues to expand and as the final shells of hydrogen and helium fusion die out, this outer part of the star is ejected into space. This cloud of gas is known as a planetary nebula. The core of the star remains, continues to cool, and is known as a white dwarf. High mass stars also form a carbon core that collapses and fuses into still heavier elements. This happens again and again, very quickly. With the formation of the last core, the star may suddenly explode due to the implosion of the core. 16. Why are white dwarfs hard to observe? White dwarfs are difficult to observe because they are so faint. As they age, they get cooler and fainter and so become even harder to observe. Consider a 2000 km radius white dwarf at 10000K. Relative to the Sun L/L S = R 2 T 4 / R S 2 T S 4 = (2000/700000) 2 * (10000/5780) 4 = 0.00007. This is 10.3 magnitudes fainter (absolute) than the Sun! So if you had one at a distance of 10 pc it would have an apparent magnitude of about 15. 20. Why is it odd that the binary system Algol consists of a low-mass red giant orbiting a high-mass main-sequence star? How did Algol come to be in this configuration? What is odd is that the lower mass star is the more evolved. Since higher mass stars evolve faster one would expect the more massive to be more evolved. If two stars in a binary are sufficiently close to each other, during stellar evolution, mass-transfer may occur. Since the more massive star would be the first to
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- 2 - evolve, it would transfer mass over to the lower mass star. The mass-transfer can be so extensive that the lower mass star becomes the more massive of the two. This is what happened to the Algol system.
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Problem%20Set%204%20Solutions - Problem Set 4 Solutions...

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