中国大地坐标系地球旋转椭球子午线弧长的严密精确解

由于椭球子午线弧长经典解存在3个缺陷,在大地测量学上会引入无法接受的误差.根据定积分的换元法,推导以大地纬度为自变量的地球旋转椭球子午线弧长精确解析解.按照2000中国大地坐标系、GRS 80和WGS 84所定义的2个基本椭圆常数（长半轴、短半轴）,给出相应3种椭球子午线弧长.以椭圆第一偏心率为自变量,将解析解与文献2]近似级数解做比较.研究结果表明,当椭圆第一偏心率较大时,文献2]近似级数解的误差较大.在Matlab R2009b语言中,开发了2套命令文件.解析解为子午线弧长计算的实用化和误差控制提供了理论依据.

Exact Rigorous Solution for Earth Rotating Ellipsoid Meridian Arc Length in China Geodetic Coordinate Svstem

The classical solution for the ellipsoid meridian arc length,which results in the unacceptable warp in geodesy,has 3 limitations.According to transforming element method of fixed integral,the precise analytic expression for earth rotating ellipsoid meridian arc length was deduced by considering the geodetic latitude an independent variable.By virtue of 2 basic elliptic constants(larger semi axis and smaller semi axis) defined by China Geodetic Coordinate System 2000(CGCS 2000),GRS 80 and WGS 84,three relevant ellipsoid meridian arc length were provided.Taking account of the elliptic first eccentricity as an independent variable,the analytic answer was compared with the approximate series solution of reference2].The research results make clear that the windage of approximate series solution of reference 2] becomes larger as the elliptic first eccentricity increases.Two sets of command files were compiled in Matlab R2009b language.The analytic solution can be the theoretical basis of its utility and error control in calculating the meridian arc length.