Revolution

The Sun does revolve around the Milky Way on an almost circular orbit with a speed of about 220km/s. The Sun completes one revolution in about 230 million years. The Milky Way also moves - we are moving towards or nearest neighbour the Andromeda galaxy and both the Milky Way and Andromeda (which make up most of what we call the 'Local Group of galaxies') are moving towards the Virgo Cluster which is our nearest cluster of galaxies. Nothing seems to stand still at all

Rotation

The sun certainly does rotate ,it has a rotational period of about 25 days. This is apparent if you have ever used a telescope to project images of the sun onto a piece of white card so that you can see the sunspots. If you do this over several days, the sunspots appear to move across the face of the sun. Not only does the sun rotate, but it also orbits the centre of our galaxy, completing one orbit every 226 million years or so.

What I Think !

Hey i think the scientists had a tough job to find whether the run is rotating.I have a simple idea

Why not we just observe some spots on the sun and then make a note of it and see if the spots/identifications appear again. Simple ! But I'm sure the scientists must have found some flaw in this method !