The geometry of the earth - Physical Geodesy - page 169

5 The geometry of the earth

5.1 Overview

This chapter consists of three parts.

Part I: Global reference systems after GPS
A fundamental task is to define a global reference system based on a reference
ellipsoid which is a good global representation of the earth and which should
ideally be characterized by the following properties: Its center coincides with
the geocenter (the earth's center of mass), its z -axisrepresentsasuitably
defined mean rotation axis of the earth, and the xz -plane is parallel to a
mean plane close to the Greenwich meridian. The reference ellipsoid itself is
defined to be an ellipsoid of revolution that globally approximates the geoid
best in some global sense.
Actually, such a geometric or physical definition cannot be absolutely ac-
curately and unambiguously realized; the final definition will always contain
an arbitrary conventional element.
To make things even more complicated, the earth is not a completely
rigid body. It can (again approximately!) be regarded as an elastic body
with a liquid core. It undergoes small more or less periodic changes. So it
must be referred to a mean ellipsoid that does not change with time.
All this will be taken for granted in the present introductory treatment.
We shall assume a well-defined geocentric reference ellipsoid with rigid di-
mensions, a fixed origin, and a time-invariant orientation - close to reality
but, in principle, conventionally adopted. For temporal changes in the earth's
body and rotation, the reader may be referred to Moritz and Mueller (1987).
Before the advent of satellite geodesy, a geocentric reference system could
not be realized. Thus, we had to work with a local geodetic system displaced
with respect to the geocenter by an unknown amount on the order of up to
a few hundred meters. Therefore, we must take into account a translation
(parallel shift) of the local reference ellipsoid with respect to a geocentric
system. This implies three translation parameters.
Note that “local” here is used in the sense of “regional”, i.e., for a country,
territory, or region, in contrast to “global”.
Usually, the orientation of a local reference system is accurately known
since the direction of the xyz -axes was accessible by astronomical measure-
ments quite accurately at least for the last two centuries. Thus, the orienta-
tion of a local geodetic datum is known to the order of 0 . 1 (arc seconds).