推导了以归化纬度、地心纬度解算子午线弧长的展开公式,同时又根据拉格朗日反演定理,得到了由子午线弧长反解归化纬度、地心纬度的直接公式。该组公式与子午线弧长正反解公式的大地纬度表达在结构形式上保持一致,进一步揭示了子午线弧长同3种纬度变量之间的内在联系。分析表明,基于归化纬度的子午线弧长解算与大地主题解算方法具有理论上的统一性,正反解精度均高于传统基于大地纬度的展开。
Formulas for direct solutions of meridian written by the reduced and geocentric latitudes respectively were derived by series expansion. Meanwhile, according to Lagrange inversion theorem, formulas for inverse solutions of the issue were also expressed in terms of the same latitudes. These two formulas were structurally consistent with that expressed by geodetic latitude ones. In these sets of formulas, internal connection between meridian and three different types of latitude were realized. Analysis and numerical calculation showed that the direct and inverse meridional solution with reduced latitude was of higher precision than that with geodetic latitude, and furthermore, there had a unified theory between meridian theory and classical geodetic problems expressed by reduced latitude.
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