"Some people say light is waves, and some say it's particles, so I bet light is some in-between thing that's both wave and particle depending on how you look at it. Am I right?" "YES, BUT YOU SHOULDN'T BE!"
It's called a barycenter, kids, a common center that both objects circle around. That common center happens to be inside the sun, but that's a topic for next week's class in this semester's AP Astrophysics program.
I don't think the barycentre is inside the sun? Wikipedia says on the barycentre article:
When the less massive object is far away, the barycenter can be located outside the more massive object. This is the case for Jupiter and the Sun; despite the Sun being a thousandfold more massive than Jupiter, their barycenter is slightly outside the Sun due to the relatively large distance between them.[2]