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SOLUTIONS TO EXERCISE 10
(a) The difference between the rest wavelength (656.3 nm) and the observed wavelength (789.0 nm) is 789.0 - 656.3 = 122.7 nm. Using the Doppler equation, delta(lambda) v 122.7 v ------------- = --- so ----- = ------------- and v = 6.1 * 10^4 km/s. lambda c 656.3 3 * 10^5 km/s (b) Using Hubble's law of universal expansion, we know v = Hr ; so r = v/H. We'll use the current best measurement of H = 70 km/s/Mpc to get the distance r = (61000 km/s) / (70 km/s/Mpc) = 867 Mpc. Note that to be rigorous, the relativistic Doppler equation should be used to compute the redshift of Abell 2218, and then applied to a cosmological distance formula. That calculation is left as an exercise to the reader. (c) Since one parsec = 3.3 light years, a light beam that travels 867 Mpc would go for (867 * 10^6 pc) * (3.3 ly/pc) = 2.9 * 10^9 years. The light left the cluster before plant life first appeared on Earth's surface. |