Comparison between the azimuths of astronomical and geodetic coordinates in Ghana

Abstract

Astronomic azimuths are bearings, which are referenced to the true north direction whereas geodetic azimuths are those referenced to a grid north direction. The difference between these two directions can be expressed through the deflection of the vertical. This deflection of the vertical refers to the difference between the normal to the geoid (Astronomic) and the normal to the ellipsoid (geodetic). The deflection of the vertical components are used to convert between astronomic and geodetic coordinates and azimuths using Laplace equations. This paper compares astronomic and geodetically derived coordinates at eight Laplace stations constituting twenty-eight baselines for which both geodetic and astronomic azimuths were derived. The comparison of azimuths shows that differences of 000°00'05.95" up to 000°23'06.93" exist between the two different versions of azimuths. These differences are not accounted for in application of the simplified Laplace equations under the assumptions made in their derivation. It is, thence, recommended that an alternative didactic approach based on rotations of three-dimensional right-handed local frames as used in Helmert’s coordinate transformations be explored for transformation between astronomic and geodetic coordinates.