Stars orbit each other, but not in a way like a planet orbits a star. A planet orbits a star that is standing still (not counting how the entire solar system is going around a galaxy center). When stars orbit each other, they are both equally large that it is not possible for one to orbit each other. read more
A gaseous planet cannot be bigger than a star, because they are made of mostly the same elements. If the planet is big enough, it would begin the process of fusion and become a star itself. Therefore, for a star to orbit a planet, it must be a planet made of heavier elements. read more
A star can orbit around another star in what is called a binary system. Technically, one star isn't orbiting the other -- they are orbiting each other. read more