2-4 Normal Section Azimuth and Geodesic

The normal sections at two different points on the surface of a biaxial ellipsoid are skewed, meaning they are neither parallel nor intersecting. Moreover, they cannot lie within a single mathematical plane. As a result, the normal section from point A to B does not coincide with the normal section from B to A, or the reverse normal section. Therefore, these two normal sections will have different azimuths. A geodesic is the shortest distance between two points on the surface of the ellipsoid. Neither the normal section nor the reverse normal section is geodetic. A geodesic is not a straight curve; it has two curvatures or torsions. All points along a geodesic satisfy Clairaut's equation (for proof, see Jekeli 2016). In this video, these concepts are explained with figures, and the mathematical formulae for computing the differences between the azimuths of the normal and reverse normal sections, as well as the normal section and the geodesic, are presented. Reference Jekeli C. (2016) Geometric Reference Systems in Geodesy, Lecture Notes, Ohio State University, Columbus, USA, hdl.handle.net/1811/77986