The calculation of longitude and latitude from geodesic measurements
F. W. Bessel (K\"onigsberg Observatory), Charles F. F. Karney (Sarnoff, Corp.), Rodney E. Deakin (RMIT)
TL;DR
This paper presents a series-based method for calculating longitude and latitude from geodesic measurements on an oblate ellipsoid, including tables and corrections to previous work.
Contribution
It provides an updated, clearer, and corrected series solution for the geodesic problem on an oblate ellipsoid with supporting tables.
Findings
Series method simplifies geodesic calculations.
Tables facilitate practical computation.
Corrections improve accuracy of previous solutions.
Abstract
The solution of the geodesic problem for an oblate ellipsoid is developed in terms of series. Tables are provided to simplify the computation. [This is an English translation of F. W. Bessel, Astronomische Nachrichten 4(86), 241-254 (1825). The mathematical notation has been updated to conform to current conventions and, in a few places, the equations have been rearranged for clarity. Several errors have been corrected, a figure has been included, and the tables have been recomputed.]
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