关键词: 子午线弧长, 第三扁率, 高斯超几何函数, 泰勒级数, 误差估计

Abstract:

A more concise formula of the meridian arc length was obtained by introduced two new parameters: the third flattening and the Gauss hypergeometric function. From another perspective, the simplified formula is also can be explained by a Taylor series expansion. By this, we got error estimate of the formula in terms of the Lagrange form of the remainder. For numerical verification of the error estimate theory, application example was presented by using the WGS84 data. The results show that experimental data are consistent with the error estimate theory and the simplified formula is more precise than the standard one.

Key words: Meridian Arc Length, the Third Flattening, Gauss Hypergeometric Function, Taylor Series, Error Estimate