In studies of physical processes near planetary bow shocks, empirical models of the latter are usually used. While computational magneto-hydrodynamics (MHD) or kinetic models of bow shocks are often more accurate, their computationally extensive nature limits their applicability to routine analysis of large volumes of data. We suggest an analytical model of the bow shock position based on MHD calculations and accurate analytical solutions. The analytical expressions for the bow shock position and shape include the following parameters: The distance of the bow shock nose point from the planet, radii of curvature and bluntnesses of the shock surface at this point and a parameter describing the transition to the asymptotic downstream slope of the shock. It is shown that for an analytical description of the surface of the shock, it is sufficient to approximate its radius of curvature and bluntness in two perpendicular planes. Another parameter used in this model is the bow shock skewing angle, appearing when the interplanetary magnetic field directed at an angle with respect to the solar wind velocity. This parameter naturally vanishes when the magnetic field of the solar wind is directed either parallel or perpendicular to the velocity vector. The exact analytical solution for the asymptotic downstream slope of the MHD Mach cone is modified to take into account the skewing angle of the bow shock.

中文翻译：

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基于物理学的行星弓激波位置和形状的分析模型

在研究行星弓形冲击附近的物理过程时，通常使用后者的经验模型。虽然弓形激波的计算磁流体动力学（MHD）或动力学模型通常更准确，但它们的计算广泛性限制了其对大量数据进行常规分析的适用性。我们建议基于MHD计算和准确的解析解的弓形冲击位置解析模型。弓形激波位置和形状的解析表达式包括以下参数：弓形激波鼻点距行星的距离，曲率半径和该点的激波表面钝度，以及描述过渡到渐近下游坡度的参数的震惊。结果表明，对于冲击表面的分析描述，足以在两个垂直平面中近似其曲率半径和钝度。在该模型中使用的另一个参数是弓形激振偏斜角，当行星际磁场相对于太阳风速成一定角度时出现。当太阳风的磁场平行或垂直于速度矢量时，此参数自然消失。修改了MHD Mach锥的渐近下游斜率的精确解析解，以考虑到弓形冲击的偏斜角。当太阳风的磁场平行或垂直于速度矢量时，此参数自然消失。修改了MHD Mach锥的渐近下游斜率的精确解析解，以考虑到弓形冲击的偏斜角。当太阳风的磁场平行或垂直于速度矢量时，此参数自然消失。修改了MHD Mach锥的渐近下游斜率的精确解析解，以考虑到弓形冲击的偏斜角。