火星高斯投影应用分析
Application Analysis of Mars Gauss Projection

以我国的火星探测计划为出发点，在以椭球面作为火星数学表面的前提下，研究了复变函数表示的高斯投影理论和方法在火星投影分带及平面坐标计算中的应用。比较了两种椭球间高斯投影幂级数展开式的数值形式差异，并对火星高斯投影长度变形进行了理论分析和计算，在此基础上初步提出了火星地图的分带方案。以7种经差为例，讨论了在赤道边缘处的火星高斯投影平面坐标误差及变形规律，将其与地球传统椭球进行对比分析。结果表明，从原理上讲地球投影理论完全适用于火星，这对高斯投影在火星上的工程应用是具有重要意义的。
Taking China’s Mars exploration program as the starting point, on the premise of taking the ellipsoid surface as the mathematical surface of Mars, the application of the Gaussian projection theory and method expressed by the complex function in the Mars projection banding and the calculation of plane coordinates is studied. The numerical form differences of the power series expansion of Gauss projection between two kinds of ellipsoids are compared, and after the theoretical analysis and calculation of the length deformation of the Mars Gauss projection, the banding scheme of the map of Mars is preliminarily proposed on this basis. Taking seven kinds of longitudinal differences as examples, we discuss the plane coordinate errors and deformation laws of Mars Gauss projection at the equatorial edge, and compare and analyze them with the traditional ellipsoid of the Earth. The results show that in principle the Earth projection theory is completely applicable to Mars, which is of great significance for the engineering application of Gauss projection on Mars.