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SOLUTIONS TO EXERCISE 10

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(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.