Neither Venus nor the moon have a significant dipole magnetic field, and their atmospheres are exposed to the solar wind and the interplanetary magnetic field. As the solar wind ions penetrate the atmosphere, photo and charge-exchange ionization reactions alter the density and velocity of the ion stream. A collisionless reacting hydromagnetic model is used to describe the flow of atmospheric and solar wind ions normal to the interplanetary magnetic field. Because of the ionization reactions, the mass flow increases along the ion stream lines, and the usual adiabatic invariant, P⊥/nB, is not constant. The supersonic solutions obtained show that E/B decreases with penetration of the solar wind into an atmosphere. A critical penetration optical depth, τs, at which a hydromagnetic shock forms, is determined as a function of the ion generation rate in the ionosphere and the ratio of the photon flux to the solar wind flux. Recombination is taken into account and used to establish a minimum optical depth at which a hydromagnetic shock can be maintained in an isothermal atmosphere. In the case of Venus (CO2 atmosphere), the hydromagnetic shock forms for 10−9 < τs < 2 × 10−4, i.e., above the usual Chapman layer. The exact value of τs is strongly dependent on the value of the scale height which is used. For the moon, the lunar atmospheric optical depth is less than that required for the formation of a hydromagnetic shock.