problem_set_7_sol

# problem_set_7_sol - Astronomy 160 Frontiers and...

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Astronomy 160: Frontiers and Controversies in Astrophysics Homework Set # 7 Solutions 1) Suppose the density of the universe is exactly equal to the critical density (with H = 70 km/s/Mpc), and all the matter is contained within identical galaxies, one per cubic megaparsec. a) Determine the mass of each galaxy. ρ = ρ c = 3 H 2 8 πG = H 2 8 G = (70) 2 8 × 7 × 10 - 11 [ km · s - 1 · Mpc - 1 ] [ m 3 · kg - 1 · s - 2 ] = 50 × 10 2 × 10 6 50 × 10 - 11 [ kg ] [ m · Mpc 2 ] = 10 19 3 × 10 - 23 [ kg ] [ Mpc 3 ] ρ = 1 3 10 42 = 3 × 10 41 kg/Mpc 3 Since there is only one galaxy per cubic Mpc, the mass of each galaxy is 3 × 10 41 kg. b) Most stars are a little bit less massive than the Sun, but a lot less bright. Suppose an average solar mass of material in these galaxies generates only 1/10 the brightness of the Sun, calculate the apparent magnitude of the nearest such galaxy (at a distance of 1 Mpc). The total number of solar mass “chunks” is:

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problem_set_7_sol - Astronomy 160 Frontiers and...

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