| 地球椭球向径和平均曲率半径的积分表达式 |
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| 引用本文： | 宗敬文,李厚朴,钟业勋.地球椭球向径和平均曲率半径的积分表达式[J].武汉大学学报(信息科学版),2022,47(7):1063-1070. |
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| 作者姓名： | 宗敬文 李厚朴 钟业勋 |
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| 作者单位： | 1.海军工程大学导航工程系，湖北 武汉，430033 |
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| 基金项目： | 国家自然科学基金41671459国家自然科学基金41871376国家自然科学基金41771487湖北省杰出青年科学基金2019CFA086 |
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| 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。
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| 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 |
| 收稿时间： | 2020-02-27 |
Integral Expressions of Earth Ellipsoid Radius Vector and Mean Radius of Curvature |
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| Affiliation: | 1.Department of Navigation, Naval University of Engineering, Wuhan 430033, China2.Key Laboratory of Environment Change and Resources Use in Beibu Gulf, Ministry of Education, Nanning Normal University, Nanning 530001, China3.Guangxi Key Laboratory of Earth Surface Processes and Intelligent Simulation, Nanning Normal University, Nanning 530001, China |
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| Abstract: | 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 technology 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 deduced 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 radius 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 curvature 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 traditional 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 navigation and positioning. |
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