Technically speaking, no celestial body in our solar system orbits around a single point. The barycenter thing only works with two bodies. When there are more than two bodies, such as in our solar system, the orbits become chaotic. Granted, the influence between planets is small, so they all appear to orbit their barycenters with the sun, but there are small perturbations to the orbits caused by the locations and masses of all the other bodies in the solar system.
Technically speaking, no celestial body in our solar system orbits around a single point. The barycenter thing only works with two bodies. When there are more than two bodies, such as in our solar system, the orbits become chaotic. Granted, the influence between planets is small, so they all appear to orbit their barycenters with the sun, but there are small perturbations to the orbits caused by the locations and masses of all the other bodies in the solar system.