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SOLUTIONS TO EXERCISE 19
(a) Non-relativistically, z = v/c = (47500 km/s) / (300000 km/s) = 0.158 Relativistically, z = sqrt( (1 + v/c) / (1 - v/c) ) -1 So z = sqrt( 1.158 / 0.842 ) - 1 = 0.173 There is somewhat of a difference, about 10% or so. This level of inaccuracy is about the maximum tolerable error for this kind of measurement. (b) v = Hr and v = 47500 km/s, and H = 70 km/s/Mpc, so r = (47500 km/s) / (70 km/s/Mpc) = 680 Mpc (c) F = L/(4 * pi * r^2), so L = F * 4 * pi * r^2. F = 3 * 10^-13 W/m^2, so L = 3 * 10^-13 W/m^2 * 4 * 3.14 * (680 Mpc * 3.1 * 10^22 m/Mpc)^2 = 1.7 * 10^39 Watts The Sun's luminosity is 3.9 * 10^26 Watts. A Watt is 1 Joule/sec, so 3C 273 produces 1.7 * 10^39 Joules in one sec. That means the Sun has to shine, to equal that amount of energy, 1.7 * 10^39 J --------------- = 4.4 * 10^12 s; at 3.15 * 10^7 seconds per year, that's 3.9 * 10^26 J/s (4.4 * 10^12) / (3.15 * 10^7) = 140,000 years. |