It is often stated, somewhat erroneously, that the planets orbit the Sun. This is nearly, but not quite true. What is true is that the Sun and the planets all orbit the common center of mass, or barycenter of the Solar System. The barycenter is sometimes within the Sun, and sometimes outside of it, depending almost entirely on the relative positions of the two most massive planets, Jupiter and Saturn (and to a much smaller degree on the relative positions of the two sub-giant planets Uranus and Neptune). When Jupiter & Saturn are on the same side of the Sun, the barycenter is outside of the Sun.

Of course, this has been known since the time of Newton, but has been sort of glossed over in many books. It has some interesting consequences. Kepler found some small discrepencies between the observations of Tycho Brahe and his (Kepler's) Law that the planets orbit the Sun in eliptical orbits. These discrepencies vanish (up to observational error) when the barycenter replaces the Sun at the focus of planetary orbits. Kepler was wise enough to ignore these discrepencies since he had no idea of their origin, which was not explained until the time of Newton. This is a great example of the way Science produces successively better approximations to the truth. Copernicus' Theory was less accurate than Kepler's Theory which was, in turn, less accurate than Newton's Theory. More recently, Einstein's Theory has been shown to be more accurate than Newton's Theory.