Ask A Scientist© Astronomy Archive

Author:      twilson
Does the Sun have any motion in respect to our solar system, or is it
completely stationary (no spin, etc.) with all of the other planets orbiting
around it?

Response #:  1 of 2 
Author:      hawley
The Sun not only spins on its axis but also travels around the center of our
galaxy in a big orbit.  And our galaxy is moving relative to other galaxies. 
Basically, everything is moving.

Response #:  2 of 2
Author:      rcwinther
If we neglect the motion of our solar system as a whole, then all of the
bodies in the solar system revolve around the center of mass of the solar
system.  The center of mass is an imaginary point that is determined by a
sort of averaging over the whole.  The solar system's center of mass lies
deep within the Sun (because the Sun contains the vast majority of the solar
system's mass) but not at its center.  Hence, the Sun also revolves about
this point; we say that it wobbles (in our case, almost entirely due to
Jupiter's pull on the Sun).  At the moment, looking for this sort of wobble
in other stars is our best bet for inferring the existence of planetary
systems around those stars.