Astronomers have used a different sort of distance
   indicator -- not Cepheids -- to measure the distance to the
   Coma cluster of galaxies.  They find for the galaxy NGC 4489 a
   distance modulus 

            (m-M) = 34.64 +/- 0.25.

   Spectra of the galaxy show that the hydrogen Balmer-alpha
   line appears at 672 nm instead of its rest wavelength of 656 nm.

      a)  What is the distance to NGC 4489 based on
          this distance modulus?

              
               (m - M)  =  5 log d  - 5

                             [(m - M) + 5] / 5
             ---->   d  =  10

                             [ 34.64 + 5]  /  5
                        =  10

                             7.928
                        =  10

                        =   85,000,000  pc     approx

                        =   85 Mpc      



      b)  What is the radial velocity of this galaxy?

               We can use the Doppler formula to find
               the radial velocity:

                              shift in wavelength
                  speed   =  ---------------------  *  c
                                 rest wavelength


                             (672 nm - 656 nm)
                          =  ------------------- *  (300,00 km/s)
                                 656 nm


                          =   7300  km/s       approx


      c)  Add this galaxy to your Hubble diagram.  What value
          for the Hubble constant do you derive now?


               The Hubble diagram now stretches from about
               0 Mpc to 85 Mpc, and from 0 km/s to 7300 km/s.
               If we draw a line from the origin to this 
               galaxy alone -- which passes close to many 
               of the other galaxies -- we find a slope of

                                     (7300 km/s  -  0 km/s)
                   Hubble const  =  -----------------------
                                       ( 85 Mpc  -  0 Mpc )


                                        86 km/s
                                  =   ----------
                                         Mpc