Two Integrals of Geodetic Lines in Oblate Ellipsoidal Coordinates

Abstract

The manuscript establishes a series expansion of the core integral that relates changes in longitude and latitude along the geodetic line in oblate elliptical coordinates, and of a companion integral which is the path length along this line as a function of latitude. The expansion is a power series in the scaled (constant) altitude of the trajectory over the surface of the ellipsoid. Each term of this series is reduced to sums over inverse trigonometric functions, square roots and Elliptic Integrals. The aim is to avoid purely numerical means of integration.