On Deflection of the Vertical Components and Their Transformations

Abstract

The deflection of the vertical is an important parameter that combines both physical (astronomic) and geometric (geodetic) determined quantities. This paper introduces an alternative didactic approach based on rotations of three-dimensional right-handed local frames that simplifies such concepts as the derivation of Laplace’s equation and facilitates understanding of vertical deflection components and their transformations under different assumptions. Variations in deflections of the vertical as a consequence of geometric changes introduced by the future replacement of the North American Datum of 1983 (NAD 83) are also investigated.