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Problem_7 - ASTRONOMY 292 Dr Ryden Winter 2006 Problem Set...

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ASTRONOMY 292 Dr. Ryden – Winter 2006 Problem Set 7 due Wednesday, March 8 at class time Note: In solving these problems, you’ll probably find my lecture notes more useful than the textbook. 1) Suppose you are in an infinitely large, infinitely old universe in which the average number density of stars is n ? = 10 9 Mpc - 3 and the average stellar radius is equal to the Sun’s radius: r ? = 1 r fl . How far, on average, can you see in any direction before your line of sight hits a star? (Assume that standard Euclidean geometry holds true.) If the stars are clumped into galaxies with number density n gal = 1 Mpc - 3 and average radius r gal = 2 kpc, how far, on average, can you see in any direction before your line of sight hits a galaxy? 2) Imagine a universe full of regulation baseballs, each of mass m bb = 0 . 145 kg and radius r bb = 0 . 0369 m. If the baseballs are uniformly dis- tributed throughout the universe, what number density of baseballs is re- quired to make the density equal to the current critical density, ρ c, 0 = (3 H 2 0 ) / (8 πG )? Given this density of baseballs, how far, on average, would
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