Barycenter

This is phrased wrong. Jupiter orbits the edge of the sun, a barycenter, instead of the actual center of the sun. This makes it sound like Jupiter and the sun are orbiting the same thing.

Nothing in the solar system orbits the center of the sun. Everything in the solar system has an influence on the barycenter, often causing it to lay outside the sun. Jupiter just influences it the most.

One of my favorite facts: the mass of all the objects in the solar system, besides the Sun, amount to 0.2% and the Sun itself makes up the other 99.8%.