hw1 - of “empty” space 3 How much energy did it take...

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Phys 341: Homework #1 Due Sept. 13 I will give partial credit for partial solutions, but only if you show your work and explain your reasoning. Be careful with units. 1. (a) Consider a globular cluster containing about 10 6 stars in a sphere of radius 10 pc. Use dimensional analysis to estimate the speed with which the stars move inside the cluster. (b) Now repeat the analysis for a galaxy containing 10 11 stars in a radius of 10 kpc. (c) Finally, estimate the speed of galaxies moving in a cluster of galaxies with mass M 10 14 M ± and radius 1 Mpc. 2. The universe is believed to be about 14 billion years old. Use dimensional analysis to estimate the average density of the universe. About how many hydrogen atoms are there in 1 m 3
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Unformatted text preview: of “empty” space? 3. How much energy did it take for the Death Star to blow up Alderaan? 1 Let’s make an estimate. (a) Use dimensional analysis to estimate the gravitational binding energy of a planet of mass M and radius R . Estimate the gravitational binding energy of Alderaan, assuming it was similar to Earth. (b) How much matter would the Death Star have to convert to energy (by E = mc 2 ) in order to blow up Alderaan? (c) Estimate the size of the room in which the matter was stored. You will need to assume something about the density of the matter; explain your assumptions. Now do you understand why the Death Star was so big? 1 If you don’t get the reference, ask around! 1...
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