# Über die Berechnung der geographischen Längen und Breiten aus geodätischen Vermessungen

@article{BesselberDB, title={{\"U}ber die Berechnung der geographischen L{\"a}ngen und Breiten aus geod{\"a}tischen Vermessungen}, author={Friedrich Wilhelm Bessel and Charles F. F. Karney and Rodney E. Deakin}, journal={Astronomische Nachrichten}, volume={4}, pages={241} }

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 a transcription of F. W. Bessel, Astronomische Nachrichten 4(86), 241-254 (1825). The text follows the original; however the mathematical notation has been updated to conform to current conventions. Several errors have been corrected and the tables have been recomputed.]

## 15 Citations

Solving the Direct and Inverse Geodetic Problems on the Ellipsoid by Numerical Integration

- Mathematics
- 2012

Taking advantage of numerical integration, we solve the direct and inverse geodetic problems on the ellipsoid. In general, the solutions are composed of a strict solution for the sphere plus a…

An Algorithm for the Inverse Solution of Geodesic Sailing without Auxiliary Sphere

- MathematicsJournal of Navigation
- 2014

An innovative algorithm to determine the inverse solution of a geodesic with the vertex or Clairaut constant located between two points on a spheroid is presented. This solution to the inverse…

Research Article. Geodesic equations and their numerical solutions in geodetic and Cartesian coordinates on an oblate spheroid

- MathematicsArXiv
- 2016

It is concluded that a complete, stable, precise, accurate and fast solution of the problem in Cartesian coordinates is accomplished.

Solutions to the ellipsoidal Clairaut constant and the inverse geodetic problem by numerical integration

- Mathematics
- 2012

Abstract We derive computational formulas for determining the Clairaut constant, i.e. the cosine of the maximum latitude of the geodesic arc, from two given points on the oblate ellipsoid of…

Performance of a solution of the direct geodetic problem by Taylor series of Cartesian coordinates

- MathematicsJournal of Geodetic Science
- 2021

Abstract The direct geodetic problem is regarded on the biaxial and triaxial ellipsoid. A known solution method suitable for low eccentricities, which uses differential equations in Cartesian…

Calculating on a round planet

- GeologyInt. J. Geogr. Inf. Sci.
- 2017

This paper explores solutions that range from moderate measures to correct for map projection errors to radical revisions of standard practice that place all calculations on the ellipsoid.

Numerical determination of the geodesic curves: the solution of a two-point boundary value problem

- Mathematics
- 2018

In this paper, we suggest a simple iterative method to find the geodesic path on a surface parameterized byorthogonal curvilinear system between two given points based on solving Boundary Value…

Inverse geodetic problem for long distance based on improved Vincenty’s formula

- MathematicsJournal of Applied Geodesy
- 2022

Abstract Solutions of geodetic problem is an important technical problem in geodesy. Based on the comprehensive analysis of the characteristics of Bessel’s formula and Vincenty’s formula, an improved…

Superintegrability of Geodesic Motion on the Sausage Model

- Mathematics
- 2016

Reduction of the $\eta$-deformed sigma model on ${\rm AdS}_5 \times {\rm S}^5$ to the two-dimensional squashed sphere $({\rm S}^2)_{\eta}$ can be viewed as a special case of the Fateev sausage model…

An illustrated introduction to general geomorphometry

- Environmental Science
- 2017

Geomorphometry is widely used to solve various multiscale geoscientific problems. For the successful application of geomorphometric methods, a researcher should know the basic mathematical concepts…