The Earth isn't obiting the Sun, it is orbiting the solar system's center mass, most of the solar system's mass in in the Sun so we appear to be orbiting the sun but in reality the Sun and the planets are orbiting a point that is close to the Sun's surface. If you were looking at the sun from another star, it would appear to wobble because it is orbiting a point that is sometimes below it's surface and other times it is above the surface depending on where Jupiter is.