Shock waves in a self-gravitating gas

The CCW method (see Chester, 1854; Chisnell, 1955; Whitham, 1958) has been used to investigate the propagation of diverging shock waves through an ideal gas under its own gravitation having an initial density distributionρ0 =ρ′ exp(−λr , whereρ′ is the density at the plane/axis/origin, respectively, for plane, cylindrical, and spherical symmetry of the shock and, λ is non-dimensional constant, for the two situations: viz., (i) when the shock is weak and (ii) when it is strong, simultaneously. Analytical relations for shock velocity and shock strength have been obtained. Expressions for the pressure, the density and the particle velocity immediately behind the shock have been derived. Their numberical estimates for plane and cylindrical symmetry of the shock, have been computed.