Solar wind flow about the terrestrial planets 1. Modeling bow shock position and shape

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Abstract
General technique for modeling the position and shape of planetary bow waves are reviewed. A three‐parameter method was selected to model the near portion (i.e.,x′ > −1 Rob) of the Venus, earth, and Mars bow shocks and the results compared with existing models using 1 to 6 free variables. By limiting consideration to the forward part of the bow wave, only the region of the shock surface that is most sensitive to obstacle shape and size was examined. In contrast, most other studies include portions of the more distant downstream shock, thus tending to reduce the planetary magnetosphere in question to a point source and constrain the resultant model surfaces to be paraboloid or hyperboloid in shape to avoid downstream closure. It was found by this investigation that the relative effective shapes of the near Martian, Cytherean, and terrestrial bow shocks are ellipsoidal, paraboloidal, and hyperboloidal, respectively, in response to the increasing bluntness of the obstacles that Mars, Venus, and earth present to the solar wind. The position of the terrestrial shock over the years 1965 to 1972 showed only a weak dependence on the phase of the solar cycle after the effects of solar wind dynamic pressure on magnetopause location were taken into account. However, the bow wave of Venus was considerably more distant around solar maximum in 1979 than at minimum in 1975–6 suggesting a solar cycle variation in its interaction with the solar wind. Finally, no significant deviations from axial symmetry were found when the near bow waves of the earth and Venus were mapped into the aberrated terminator plane. This finding is in agreement with the predictions of gas dynamic theory which neglects the effects of the IMF on the grounds of their smallness. Farther downstream where the bow wave position is being limited by the MHD fast mode Mach cone, an elliptical cross section is expected and noted in the results of other investigations.