In this paper the Chisnell2 Chester1 Whitham3 (CCW1-3) method has been used to study the isothermal propagation of cylindrical hydromagnetic diverging shock waves in self gravitating rotating gas in presence of constant axial magnetic field. Assuming density decreasing atmosphere and exploring magnetic field as weak and strong, the analytical expressions have been derived for both weak and strong shocks and finally the effects of overtaking disturbances behind the flow on the motion of shock have also been included