text: Assuming isothermal sphere has some disadvantages. Though the density obtained as solution of this isothermal gas sphere decreases from the centre, it decreases too slowly to give a well-defined surface and finite mass for the sphere. It can be shown that, as ,
  where  and  are constants which will be obtained with numerical solution. This behavior of density  gives rise to increase in mass with increase in radius. Thus, the model is usually valid to describe the core of the star, where the temperature is approximately constant.