text: For an isothermal gaseous star, the pressure  is due to the kinetic pressure and radiation pressure
  whe
  * is the density
  * is the Boltzmann constant
  * is the mean molecular weight
  * is the mass of the proton
  * is the temperature of the star
  * is the Stefan–Boltzmann constant
  * is the speed of light
  The equation for equilibrium of the star requires a balance between the pressure force and gravitational force
  where  is the radius measured from the center and  is the gravitational constant. The equation is re-written as
  Introducing the transformation
  where  is the central density of the star, leads to
  The boundary conditions are
  For , the solution goes like