Series Expansion for Direct and Inverse Solutions of Meridian in Terms of Different Latitude Variables

doi:10.11947/j.AGCS.2016.20140575

Abstract

Abstract: 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.

Key words: meridian arc length, series expansion, geodetic latitude, reduced latitude, geocentric latitude

CLC Number:

P226

GUO Jiachun, LI Houpu, ZHUANG Yunling, LI Dajun, WU Yanlan. Series Expansion for Direct and Inverse Solutions of Meridian in Terms of Different Latitude Variables[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(5): 560-565.

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