The sun is stationary, it is the planets that move. The immense gravity of the sun is what is keeping us all in our correct places. That's why the planets keep on the same orbits. If the sun moved, then it would throw everything out of whack. Planets would be colliding. The solar system would not function as we know it. We are in the "sweet spot"- the perfect distance away from the sun. A little closer, we'd burn to a crisp. Farther away, we'd freeze to death. Move the sun, you move the planets and everything is haywire.