Strong spherical shock in a self-gravitating gas

The Chisnell-Chester-Whitham method has been used to investigate the propagation of strong diverging spherical shock waves through a self-gravitating gas having an initial density distribution ϱ0=βr-w, where r is the distance from the origin,β andw are constants. Analytical expressions for shock velocity and shock strength have been obtained. It is observed that the casew =A + 2, whereA = 8γ[2γ/(γ - 1) + + √2γ/(γ - 1)2 + √2γ(γ - 1)]-1 and γ is the adiabatic index of the gas, corresponds to the shock moving with constant strength. An increase inw from 0 toA + 2 reduces the shock velocity, whereas, for further increase in w fromA + 2 to 3, the shock velocity increases. Finally, the expressions for the pressure, the density and the particle velocity immediately behind the shock have been obtained.