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.
Answered by:
Paul Walorski, B.A., Part-time Physics Instructor
'For the sake of persons of ... different types, scientific truth should be presented in different forms, and should be regarded as equally scientific, whether it appears in the robust form and the vivid coloring of a physical illustration, or in the tenuity and paleness of a symbolic expression.'