ABSTRACT
A common problem is finding the shortest route across the Earth surface between two positions. Such trajectory is always a part of a geodesic (great circle, great ellipse) on the modelling globe surface. The geodesic is used by ship navigators attempting to minimize distances and the radio operators with directional antennae used to look for a bearing yielding the strongest signal. For many purposes, it is entirely adequate to model the Earth as a sphere. Actually, it is more nearly an oblate ellipsoid of revolution. The earth’s flattening is quite small, about 1 part in 300, and navigation errors induced by assuming the Earth is spherical do not exceed this, and so for many purposes a spherical approximation may be entirely adequate. On a sphere, the commonly used coordinates are latitude and longitude, likewise on a spheroid, however on a spheroid one has to be more careful about what exactly one means by latitude [Williams, 1996]. The spherical model is often used in cartographic projections creating the frame of the presented chart. The trajectory of the geodesic lines and the loxodrome looks different depending on the method of the projections given by the strict formulae. Thus, many map projections are invaluable in specialized applications.
