Symbolic expressions of differences between earth radius

doi:10.11947/j.AGCS.2019.20180145

Abstract

Abstract:

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.

Key words: earth radius, difference extrema value, extrema value point, symbolic expression, CGCS2000

CLC Number:

P282

ZONG Jingwen, LI Houpu, BIAN Shaofeng, TANG Qinghui. Symbolic expressions of differences between earth radius[J]. Acta Geodaetica et Cartographica Sinica, 2019, 48(2): 238-244.

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