Well, they orbit each other, don't they? [Edit, well, to be precise, they are both orbiting the barycenter, which, given the great mass of the sun, is much closer to the center of the sun than the center of the earth]
For the Earth-Sun system, the center of mass is only shifted a few 100 km towards the earth, but the radius of the sun is 695500 km. So the offset is less than 1/1000 of the radius of the sun.
That wibble-wobbles around much faster than I would have expected.
It looks like Jupiter is way faster than I thought it was. My guestimate for gas giant orbits was skewed towards Uranus/Neptune (84/165 years), but Jupiter orbits in only 12!. It's crazy how close Jupiter is to us.
