![]() the inverse geodesic problem or second geodesic problem, given A and B, determine s 12, α 1, and α 2.Īs can be seen from Fig.the direct geodesic problem or first geodesic problem, given A, α 1, and s 12, determine B and α 2.The two geodesic problems usually considered are: The connecting geodesic (from A to B) is AB, of length s 12, which has azimuths α 1 and α 2 at the two endpoints. Consider two points: A at latitude φ 1 and longitude λ 1 and B at latitude φ 2 and longitude λ 2 (see Fig. 1). It is possible to reduce the various geodesic problems into one of two types. ![]() N is the north pole and EFH lie on the equator. A geodesic AB on an ellipsoid of revolution. The adjustment of triangulation networks entailed reducing all the measurements to a reference ellipsoid and solving the resulting two-dimensional problem as an exercise in spheroidal trigonometry ( Bomford 1952, Chap. Every globally-shortest path is a geodesic, but not vice versa.īy the end of the 18th century, an ellipsoid of revolution (the term spheroid is also used) was a well-accepted approximation to the figure of the Earth. Short enough segments of a geodesics are still the shortest route between their endpoints, but geodesics are not necessarily globally minimal (i.e. This definition encompasses geodesics traveling so far across the ellipsoid's surface that they start to return toward the starting point, so that other routes are more direct, and includes paths that intersect or re-trace themselves. However, it is frequently more useful to define them as paths with zero geodesic curvature-i.e., the analogue of straight lines on a curved surface. A simple definition is as the shortest path between two points on a surface. There are several ways of defining geodesics ( Hilbert & Cohn-Vossen 1952, pp. Finally, if the ellipsoid is further perturbed to become a triaxial ellipsoid (with three distinct semi-axes), only three geodesics are closed. Furthermore, the shortest path between two points on the equator does not necessarily run along the equator. However, Newton (1687) showed that the effect of the rotation of the Earth results in its resembling a slightly oblate ellipsoid: in this case, the equator and the meridians are the only simple closed geodesics. ![]() If the Earth is treated as a sphere, the geodesics are great circles (all of which are closed) and the problems reduce to ones in spherical trigonometry. The solution of a triangulation network on an ellipsoid is therefore a set of exercises in spheroidal trigonometry ( Euler 1755). A geodesic is the shortest path between two points on a curved surface, analogous to a straight line on a plane surface. The figure of the Earth is well approximated by an oblate ellipsoid, a slightly flattened sphere. The study of geodesics on an ellipsoid arose in connection with geodesy specifically with the solution of triangulation networks.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |