Yes it is, our solar system is orbiting the galaxy at a considerable speed, at 230 kilometres per second (143 miles per second), or 514,000 miles per hour. The Sun's orbit around the Milky Way takes about 225–250 million years to complete, which is known as a galactic year or cosmic year.The Sun is not moving and the retained form proves this ! Forgive the pun , this isn't a tail !