地球椭球向径和平均曲率半径的积分表达式  

Integral Expressions of Earth Ellipsoid Radius Vector and Mean Radius of Curvature

作　　者：宗敬文 李厚朴[1] 钟业勋 ZONG Jingwen;LI Houpu;ZHONG Yexun(Department of Navigation,Naval University of Engineering,Wuhan 430033,China;Key Laboratory of Environment Change and Resources Use in Beibu Gulf,Ministry of Education,Nanning Normal University,Nanning 530001,China;Guangxi Key Laboratory of Earth Surface Processes and Intelligent Simulation,Nanning Normal University,Nanning 530001,China)

机构地区：[1]海军工程大学导航工程系,湖北武汉430033 [2]南宁师范大学北部湾环境演变与资源利用省部共建教育部重点实验室,广西南宁530001 [3]南宁师范大学广西地表过程与智能模拟重点实验室,广西南宁530001

出　　处：《武汉大学学报（信息科学版）》2022年第7期1063-1070,共8页Geomatics and Information Science of Wuhan University

基　　金：国家自然科学基金(41671459,41871376,41771487);湖北省杰出青年科学基金(2019CFA086)。

摘　　要：引入地球向径积分平均值和地球平均曲率半径积分平均值的概念,借助计算机代数系统推导出了两者的符号表达式,并将它们表示为偏心率e的幂级数形式。将地球向径积分平均值和地球平均曲率半径积分平均值分别与平均球半径、等面积球半径、等距离球半径、等体积球半径这4种常用球体半径进行比较,研究表明地球向径积分平均值与4种常用球体半径间的差异更小。由于地球是一个旋转椭球体,向径与曲率半径是背离的,向径最大时,曲率半径最小,向径最小时,曲率半径最大,传统思维所认为的曲率半径并不能准确地代表地球半径平均值,因此在一定程度上,地球向径的积分平均值更能代表地球半径平均值。这些研究结果可为地球科学、空间科学、导航定位提供基础理论依据。Objectives:The Earth’s radial diameter and mean radius of curvature are the basic parameters commonly used in measurement and Earth science calculation.According to the requirements of Earth scien⁃ce and space science and some requirements,the Earth’s radial diameter,mean radius of curvature,mean radius of sphere,equal distance radius of sphere,equal area radius of sphere and equal volume radius of sphere are commonly used.The concept of integral mean values of ellipsoid radius vector and mean radius of curvature is introduced.With the application and development of space technology and computer technolo⁃gy in geodesy and cartography,it is of more important practical value to study the relationship between the Earth’s radial diameter and the common Earth radius.Methods:The symbolic expressions of them are de⁃duced by computer algebraic system and are expressed as the power series of eccentricity.We use the method that comparing the radial vector integral mean and the radius integral mean with the four common sphere ra⁃dius respectively.Results:The results shows that the difference between the radial integral mean and the four common sphere radii is smaller.Since the Earth is a rotating ellipsoid,the radial and the radius of cur⁃vature deviate.When the radial vector is the largest,the radius of curvature is the smallest.When the radial is the smallest,the radius of curvature is the largest.Conclusions:The radius of curvature considered by tra⁃ditional thinking cannot accurately represent the radius of the earth average values,to a certain extent,which means that integral mean value of ellipsoid radius vector is more representative of the average of the Earth’s radius.These research results can provide theoretical basis for Earth science,space science and navi⁃gation and positioning.

关 键 词：大地测量 地球向径积分表达式 平均曲率半径积分表达式 计算机代数系统 差异符号表达式 

分 类 号：P282[天文地球—地图制图学与地理信息工程]