Define "star"
I'm beginning to believe there is not much that differentiates jupiter from the sun… Or any of the other planets for that matter..
If you subscribe to the helical model, the sun is actually like the head of a comet, and we, the 'planets' are like the tail of that "comet".
..And that "comet" has a helical motion around an even bigger "comet", called the milky way.. But I digress…
Not many people understand that jupiter does not 'orbit' the sun.
They are essentially a binary system, 'orbiting' each other in a helical pattern through space.