| Summary: The direct and inverse problems of the geodesic on an ellipsoid are fundamental geodetic operations and because of the computational difficulties in solving both geodetic problems, geodeticists and mathematicians have been constantly striving to develop new solutions. In this thesis, it is also aimed to compare flight routes on sphere and ellipsoid used in air traffic with the shortest routes calculated using different approaches provided by geodesy and cartography disciplines. For this purpose, 17 flight routes with flight distances ranging from 400 to 1400 km were investigated. The ellipsoidal geodetic problem solution has made with five selected methods and the most appropriate method was selected by comparing the methods in terms of accuracy. By the way, the length of the flight route calculated from the sum of the distances between the route s intermediate points. The length of the flight route has calculated on the great elliptical arc. When the results were analysed; according to geodesic curve, the distance was varied maximum 0.19% on gauss sphere, maximum 0.03% on authalic sphere and 0.26% in the others. When the flight route was compared to the geodesic curve, the distance increments has been determined at varying rates from 3.91% and 25.68% (median 6.7%) on ellipsoid surface and 4.08% to 26.05% (median 6.9%) in the three-dimensional space |
