Abstract: Polytrope is often used to describe the internal structure of gaseous stars. For a stationary polytropes, the Lane-Emden equation can be obtained bycombing the hydrostatic equilibrium equation with the polytropic equation, and the internal structure of the star can be determined approximately by solving the equation. But for the more general cases, the star is in rotation. Hence the influence of rotation on the outer boundary and inner structure of the polytrope model is particularly important. This paper firstly substitutes the rotation into the hydrostatic equilibrium equation and combines the polytropic equation to obtain a differential equation that can describe the internal structure of the star in the case of rotation, and then considers the case of slow rotation, and uses the method of perturbation expansion and separation of variables to obtain a approximated solution. Finally, the outer boundary, internal density distribution and the relationship of mass and radius of the rotation polytrope are discussed through the approximated solution.

Key words: polytrope, rotation, internal structure