Aligned magnetohydrodynamic solution for solar wind flow past the earth's magnetosphere

Exact numerical solutions of the magnetohydrodynamic equations for a perfect dissipation-less gas with aligned magnetic field are given for conditions representative of steady supersonic solar wind flow past an axisymmetric model of the earth's magnetosphere. The solution is based on use of a transformation that relates without approximation the equations of magnetohydrodynamics to those of gasdynamics of a pseudo gas that has an unusual equation of state. The results confirm the applicability of the previously existing gasdynamic solutions for the typically modest intensities of the interplanetary magnetic field that lead to Alfvén Mach numbers of about 10 or greater. For smaller values, however, significant effects are indicated with the flanks of the bow wave moving away from the earth and the nose moving toward the earth. The results are consistent with direct observations in space.