常用地球半径差异符号表达式

Symbolic expressions of differences between earth radius

对测量和地球科学计算中5种常用地球半径进行了全面系统的比较,借助计算机代数系统推导出常用地球半径之间的差异最值点及其对应的最值和它们之间相等点大地纬度的符号表达式,并将其表示为偏心率e的幂级数形式,最后以CGCS2000椭球为例,将各个常用地球半径的差异明确到数值上。结果表明,常用地球半径之间差异在纬度为90°时存在最大值,在纬度为0°时存在最小值,平均曲率半径与等距离球半径间差异最大,平均曲率半径与平均球半径间差异最小。这些结果可为地球科学、空间科学、导航定位相关研究提供理论依据。

A systematic and comprehensive comparison of the five commonly used earth radius in geodesy and cartography is carried out, and the differences between the most common points of the earth’s radius, their corresponding maximum values, and the latitudes of equal points between themare derived with the help of computer algebraic systems. The symbolic expressionsare expressed as a power series of the first eccentricity. Taking the CGCS2000 ellipsoid as an example, the differences between the commonly used earth radii are clarified to numerical values. The results show that the difference between the commonly used Earth radii has a maximum at 90 degrees and a minimum at 0 degrees. The difference between the average radius of curvature and the equidistant sphere radius is the biggest, and the difference between the average radius of curvature and the average sphere radius is the smallest. These results can provide theoretical basis for relative research in earth science, space science, navigation and positioning.