海洋测绘2023，Vol.43Issue(6)：70-76,7.DOI:10.3969/j.issn.1671-3044.2023.06.016
子午线弧长正反解表达式3种形式的解析
Analysis of three forms of direct and inverse expressions of meridian arc length
摘要
Abstract
In order to analyze the influence of different expressions on the computational efficiency,three expressions of the meridian arc length are given in this paper.The expansion coefficients are rewritten as the third flattening n.The truncation errors of different forms of meridian arc length are calculated and analyzed,the appropriate terms are selected and the practical formulas of the expansion are given.The results show that the coefficients in the direct and inverse of the meridian arc length based on n have fewer digits in the numerical value,more concise form,and are more convenient for popularization and application.When the accuracy of the direct expression is millimeter,the expansion only needs to keep the first four items.When the inverse solution accuracy is 0.000 1",the expansion only needs to keep the first four items to satisfy the accuracy.For the three expressions,the double-angle form has higher computational efficiency.Therefore,it is recommended to use the double-angle form in the process of the positive and negative solutions of the meridian arc length.关键词
大地测量/子午线弧长/第三扁率/截断误差/3种表达式Key words
geodetic surveying/meridian arc length/the third flattening/truncation error/three expressions分类
天文与地球科学引用本文复制引用
张晓平,焦晨晨,李厚朴,边少锋,张思远..子午线弧长正反解表达式3种形式的解析[J].海洋测绘,2023,43(6):70-76,7.基金项目
国家优秀青年科学基金(42122025) （42122025）
国家自然科学基金(41971416 （）
42074010) （）
中国地质大学(北京)学科发展研究基金(2022XK207). （北京）
