The distance from the Sun to its Center-of-Mass with the 
Earth is
                     mass of Earth
               d  =  -------------  *  1 AU       (approximately)
                     mass of Sun



                      5.98 x 10^(24) kg   
                  =  ------------------  *  1.5 x 10^(11) m
                      1.99 x 10^(30) kg


                  =   4.51 x 10^5  m


  The speed of the Sun in its motion around its Center-of-Mass
with the Earth is approximately

  


                     distance        2 * pi * 4.51 x 10^5  m
       speed    =   ----------  =   -------------------------
                      time             1.0 * (3.15 x 10^7) s


                =    0.09  m/s