A method of high-precision calculating the normal height as the coordinate line`s length at an arbitrary distances from the Earth

Abstract

The authors highlight some special issues of the theory of heights. In establishing a global system of normal heights, one of the key matters is the final choice of a system of altitudes to represent elevation marks. In addition to proving the advantages of the mentioned system, it is necessary to eliminate some “white spots” within itself. In 2004, a more accurate way of calculating normal heights as the length of a coordinate line in a spheroidal system was considered. Simultaneously with this, in the papers by foreign researchers, methods of "practically accurate" calculation of the orthometric height were developed, which is associated with increasing knowledge of the earth`s crust upper layers structure. At studying the normal height, it is required to develop methods of its high-precision calculation and explore the properties of various options for setting the corresponding curvilinear integral. An expression is obtained for the normal height as a segment of the coordinate line of the spheroidal system; the one obtained in 2004, which contained inaccuracies, was corrected. The proposed method can be applied at an arbitrary distance from the reference ellipsoid.