Q:  How large would the shift in wavelength
      of the hydrogen Balmer alpha line be due
      this orbital motion?  The rest wavelength
      of Balmer alpha is 656 nm.


          The maximum shift would be

                       radial velocity
             shift  =  ---------------  *  (rest wavelength)
                       speed of light


                         466 m/s
                    =  ---------------  *  (656 nm)
                       300,000,000 m/s


                    =   0.0010 nm


          That's a small shift!