Relative to what? Motion of any object is only valid when compared to something else.
The Sun orbits the center of the Milky Way Galaxy at about 225 Km/sec, and our Galaxy itself
has a motion in its Local Group of galaxies of about 100 Km/sec. Our Local Group, in turn,
has a speed of about 220 Km/sec relative to the Super Cluster it resides in, and there are
further layers of motion beyond that.
The Milky Way - Our Galaxy
Perhaps the best measure of the Sun's overall 'motion' is based on the observed Doppler Shift of the Cosmic Background Radiation (COBE). That measure indicates a motion of about 390 Km/sec for our Sun vs. the Universe as a whole.
Paul Walorski, B.A., Part-time Physics Instructor
'Restlessness and discontent are the first necessities of progress.'