Published in Scientific Papers. Series "Journal of Young Scientist", Vol. 3
Written by Alina BUZILA, Bogdan Ioan CIOBAN, Marcela Ionela HANDRO, Adrian Serban PETRIC
The purpose of this paper is to present the methods of solving the basic geodetic problems. 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 correction to the ellipsoid determined by numerical integration. The problems in geodesy are usually reduced to two main cases: the direct problem, given a starting point and an initial heading, find the position after traveling a certain distance along the geodesic; and the inverse problem, given two points on the ellipsoid find the connecting geodesic and hence the shortest distance between them. Much of the early work on these problems was carried out by mathematicians—for example, Legendre, Bessel, and Gauss—who were also heavily involved in the practical aspects of surveying. If the Earth is treated as a sphere, the geodesics are great circles (all of which are closed) and the problems reduce to ones inspherical trigonometry. For a sphere the solutions to these problems are simple exercises in spherical trigonometry, whose solution is given by formulas for solving a spherical triangle.
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