The paper presents a magnetohydrodynamic (MHD) model for the interaction between the solar wind and the Earth's magnetic field. It examines how the governing equations can be approximated by the simpler equations of classical Chapman-Ferraro theory combined with gas dynamics, and presents numerical results for various cases. The magnetosphere boundary and distant tail are represented by tangential and contact discontinuities, while the bow wave is modeled as a fast MHD shock wave. The connectivity of interplanetary and geomagnetic fields, and the asymptotic directions of the wake and shock waves at large distances from Earth, are discussed in terms of properties of these discontinuities. Detailed numerical results for the location of the bow wave and the density, velocity, and temperature of the flow between the bow wave and the magnetosphere are presented for Mach numbers 5, 8, and 12 for γ = 5/3 and 2. The calculated position of the bow wave is shown to agree with observations from shadowgraph photographs of supersonic flow past a model magnetosphere in the Ames Supersonic Free-Flight Wind Tunnel. Results are also presented that illustrate the distortion of the interplanetary magnetic field in the region between the bow and the magnetosphere for cases where the magnetic field in the incident stream is inclined at 45° and 90° to the free-stream direction. The paper discusses the fundamental equations of MHD for the steady flow of a non-dissipative perfect compressible gas, including the continuity equation, the momentum equation, and the energy equation. It also presents the properties of various types of discontinuities, including tangential, contact, and rotational discontinuities, and shock waves. The paper examines the behavior of weak shock waves and their relation to gas dynamics. It also discusses the application of MHD equations to the geophysical problem of the interaction between the solar wind and the geomagnetic field, including the asymptotic directions of shock waves and wakes, and the relation between hydromagnetic and gasdynamic flows. The paper concludes that the results of gasdynamic calculations provide a useful approximation for MHD flows when the ratio of sound speed to Alfvén speed is substantially greater than unity.The paper presents a magnetohydrodynamic (MHD) model for the interaction between the solar wind and the Earth's magnetic field. It examines how the governing equations can be approximated by the simpler equations of classical Chapman-Ferraro theory combined with gas dynamics, and presents numerical results for various cases. The magnetosphere boundary and distant tail are represented by tangential and contact discontinuities, while the bow wave is modeled as a fast MHD shock wave. The connectivity of interplanetary and geomagnetic fields, and the asymptotic directions of the wake and shock waves at large distances from Earth, are discussed in terms of properties of these discontinuities. Detailed numerical results for the location of the bow wave and the density, velocity, and temperature of the flow between the bow wave and the magnetosphere are presented for Mach numbers 5, 8, and 12 for γ = 5/3 and 2. The calculated position of the bow wave is shown to agree with observations from shadowgraph photographs of supersonic flow past a model magnetosphere in the Ames Supersonic Free-Flight Wind Tunnel. Results are also presented that illustrate the distortion of the interplanetary magnetic field in the region between the bow and the magnetosphere for cases where the magnetic field in the incident stream is inclined at 45° and 90° to the free-stream direction. The paper discusses the fundamental equations of MHD for the steady flow of a non-dissipative perfect compressible gas, including the continuity equation, the momentum equation, and the energy equation. It also presents the properties of various types of discontinuities, including tangential, contact, and rotational discontinuities, and shock waves. The paper examines the behavior of weak shock waves and their relation to gas dynamics. It also discusses the application of MHD equations to the geophysical problem of the interaction between the solar wind and the geomagnetic field, including the asymptotic directions of shock waves and wakes, and the relation between hydromagnetic and gasdynamic flows. The paper concludes that the results of gasdynamic calculations provide a useful approximation for MHD flows when the ratio of sound speed to Alfvén speed is substantially greater than unity.