Discussion on the orthometric height realization

Abstract

Abstract In the theory of the orthometric height, the mean value of gravity along the plumbline between the geoid and the earth's surface is defined as the integral mean. To determine the mean gravity from the gravity observations realized at the physical surface of the earth, the actual topographical density distribution and vertical change of gravity with depth have to be known. In Helmert's (1890) definition of the orthometric height, the assumption of the linear change of normal gravity is used adopting the constant topographical density distribution. The mean value of gravity is then approximately evaluated so that the observed gravity of a point at the earth's surface is reduced to the mid‐point of the plumbline by Poincare‐Prey's gravity gradient. To avoid the problems related to the determination of mean gravity, Molodensky (1945) formulated the different concept. In his theory of the normal height, the mean value of the normal gravity along the ellipsoidal normal between the ellipsoid surface and...