Ssuppose that radio astronomers measure emission from
a cloud of gas not at the expected wavelength of

   lambda_0 = 21.106 cm

but instead at a slightly longer wavelength of 

   lambda   = 21.109  cm



      Q:  Why might the wavelength be slightly longer?

            If the atoms are moving away from us as they emit
            the radio waves, then the Doppler shift will 
            increase the wavelength that we observe.



      Q:  What can you deduce about that cloud of hydrogen?

            For non-relativistic speeds, the size of the Doppler
            shift is

                delta_lambda         v
               --------------   =   ---
                 lambda_0            c


            Here, delta_lambda is (21.109 - 21.106) = 0.003 cm,
            so we have

                   v        0.003 cm
                  ---  =   ----------  =  0.000142
                   c       21.106 cm


            So the cloud must be moving away from us at 

                   v   =  0.000142 c  =  42.6 km/s