In this article, the authors study the structure of the solutions for the Euler-Poisson equations in a bounded domain of Rⁿ with the given angular velocity and n is an odd number. For a ball domain and a constant angular velocity,
both existence and non-existence theorem are obtained depending on the adiabatic gas constant $\gamma$. In addition, they obtain the monotonicity of the radius of the star with both angular velocity and center density. They also prove that the radius of a rotating spherically symmetric star, with given constant angular velocity and constant entropy, is uniformly bounded independent of the central density. This is different to the case of the non-rotating star.