The geometry of the earth - Physical Geodesy - page 171

Part I: Global reference systems after GPS

5.2 Introduction

Geodesy, as the theory of size and shape of the earth, is not a purely geo-
metrical science since the earth's gravity field, a physical entity, is involved
in many geodetic measurements, especially terrestrial ones.
The gravimetric methods are usually considered to constitute physical
geodesy in the narrower sense. The measurements of triangulation, leveling,
and geodetic astronomy, all make essential use of the plumb line, which,
being the direction of the gravity vector, is no less physically defined by
nature than its magnitude, that is, the gravity g . All determinations of the
geoid by various methods and its use as well as the use of deflections of the
vertical belong to physical geodesy, quite as well as the gravimetric methods.
Even in the age of GPS, we have many previous geodetic data which
continue to be useful and have to be understood in order to be optimally
combined with the new satellite data. In precise operations of engineering
geodesy such as tunnel surveying, the plumb line and deflections of the ver-
tical must be taken into account.
For an optimal understanding and use of local (or rather regional) geo-
detic datums, we must know their relation to a global geodetic system as
used in GPS. Therefore, it is appropriate to start with global geometry in a
rather elementary way.
A few introductory ideas may help in comprehending this subject. To
fix the position of a point in space, we need three coordinates. We can use,
and have used, a rectangular Cartesian coordinate system. This is the basic
geometric coordinate system. It may be easily converted computationally to
ellipsoidal coordinates ϕ, λ, h referred to any given reference ellipsoid.
For many special purposes, however, it is preferable to take what we have
called the natural coordinates : Φ (astronomical latitude), Λ (astronomical
longitude), and H (orthometric height), which directly refer to the gravity
field of the earth (Sect. 2.4). The height H may be obtained by geometric
leveling, combined with gravity measurements, and Φ and Λ are determined
by astronomical measurements.
As long as the geoid can be identified with an ellipsoid, the use of these
coordinates for computations is very simple. Since this identification is suf-
ficient only for results of rather low accuracy, the deviations of the geoid
from an ellipsoid must be taken into account. As we have seen, the geoid has
rather disagreeable mathematical properties. It is a complicated surface with
discontinuities of curvature. Thus, it is not suitable as a surface on which to
perform mathematical computations directly, as on the ellipsoid.