The article quotes Cathy Jordan,"Technically, what is going on is that the Earth, Sun and all the planets are orbiting around the center of mass of the solar sy

The article quotes Cathy Jordan,"Technically, what is going on is that the Earth, Sun and all the planets are orbiting around the center of mass of the solar system". I believe that the statement is a good approximation for the orbits of trans-Neptunian objects or any other orbiting object that is more than 40 AU from the Sun, but I think it is a bad approximation for Mercury, and not a good approximation for the Earth. When I say it's a bad approximation, I mean that it would be more accurate to say "the Earth and Mercury orbit the center of the Sun" than it is to say "the Earth and Mercury orbit the barycenter of the Solar System (center of mass)". Any comments by someone more qualified that me would be appreciated (I took about 6 courses in physics and 2 courses in astronomy in college and I graduated over 20 years ago).