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Download ASTR100 Homework #5 Solutions Chapter 11 #29, 31 Due
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ASTR100 Homework #5 Solutions Due Thursday Nov 19, 2007 Chapter 11 Chapter 12 Chapter 13 Extra Credit Chapter 12 #29, 31 #22, 26 #25 #46 Chapter 11 #29 Choose the best answer to each of the following, and explain your reasoning with one or more complete sentences. Which of these stars has the coolest surface temperature? (a) A star (b) F star (c) K star The order of Hottest to Coldest is O B A F G K M. You can memorize it using “Oh Be A Fine Girl/Guy Kiss Me” Therefore c) K stars are coldest _________________________________________________________________________________ #31 Which of these Stars has the longest lifetime? (a) main-sequence A star (b) main-sequence G star (c) main-sequence M star The colder the star, the longer it takes to burn through its energy source. Hottest stars are O, coldest stars are M (again… O B A F G K M) c) M stars are the coldest, so those will live the longest __________________________________________________________________________________ Chapter 12 #22 Decide whether the statement makes sense or does not. Explain clearly. If you could look inside the Sun today, you’d find that its core contains a much higher proportion of helium and a lower proportion of hydrogen than it did when the Sun was born. This statement makes sense because over the last 4.5 billion years the Sun has been busy converting its Hydrogen into Helium via the Proton-Proton Chain. During this process the Sun will lose mass and radiate it away as energy. When the sun was born the percentages were about 94% hydrogen and 4% Helium, but now we can expect the percent of Hydrogen still available for fusion is closer to 60%. Don’t worry, because there’s still plenty left! ____________________________________________________________________________________ #26 The Gold in my new ring came from a supernova explosion. This statement makes sense. In the final stages of a high mass star’s life, the star has exhausted all of its energy sources, resulting in an inert iron core, which is supported by the degeneracy principle. This prohibits the electrons from getting too close together, but once gravity pushes the electrons past this quantum limit, they combine with protons, to form neutrons. Within seconds the core, with a mass comparable to our sun, is collapsed into a ball of neutrons the size of only a few kilometers. The collapse stops at this point because now the neutrons are supported by their own form of degeneracy pressure. This gravitational collapse of the core releases tons of energy in the form of a SUPERNOVA, which blows away the outer layers of the star. All elements heavier than iron which includes gold, were created in these massive supernova explosions. _____________________________________________________________________________________ Chapter 13 #25 Choose the best answer to each of the following, and explain your reasoning with one or more complete sentences. Which of these objects has the smallest radius? (a) 1.2 Msun White Dwarf (b) 0.6 Msun White Dwarf (c) Jupiter The smallest object is (a) the 1.2 Msun White Dwarf. This is because a White Dwarfs is comparable to the size of the Earth, which rules out Jupiter. Also the more massive a white dwarf is, the smaller it is! This is because the more mass a white dwarf has, the more its electrons must squeeze together to maintain enough outward pressure to support the extra mass. There is a limit on the amount of mass a white dwarf can have, however. This limit is 1.4 times the mass of our Sun. _____________________________________________________________________________________ Extra Credit Chapter 12 #46 The distance from Earth of the read supergiant Betelgeuse is approximately 427 light-years. If it were to explode as a supernova, it would be one of the brightest stars in the sky. Right now, the brightest star other than the Sun is Sirius, with a luminosity of 26 Lsun and a distance of 8.6 light-years. How much brighter than Sirius would the Betelgeuse supernova be in our sky if it reached a maximum luminosity of 1010 Lsun? Distance Luminosity Betelgeuse 427 light-years 𝟏𝟎𝟏𝟎 Lsun Sirius 8.6 light-years 26 Lsun For this problem we need to find the ratio of Apparent Brightness for the two objects… where B = L / 4πR^2 or Apparent Brightness = Luminosity 4 (π) (𝑅𝑎𝑑𝑖𝑢𝑠)2 Therefore, the Betelgeuse supernova would be 156015.52 times brighter than Sirius in our sky. There are no units to worry about since the problem was set up as a ratio.