site search by freefind

follow me


Figure of the Earth Geodetic Reference System
To describe the figure of the earth and its gravity field is the aim of geodesy.
There exist various typs of mathematical, physical und topographical earth models to describe the figure, shape and size of the earth.
Three definitions of "figure of the earth" [Moritz 1990, p. 1]:
A) The solid and liquid earth bounded by the physical earth's surface, or topographic surface, which is the surface which we see, on which we stand, walk, drive, and, occasionally, swim. It is highly irregular, even after some obvious smoothing which is always necessary to make it a smooth surface amenable to mathematical treatment, and also after some averaging with respect to time since this surface undergoes temporal variations (on the order of decimeter or more) because of tidal effects, etc.
B) The (part of the earth bounded by the) geoid, which is a level surface coinciding (somewhat loosely speaking) with the free surface of the oceans together with its continuation under the continents. It is the geoid above which "heights above sea level" are measured. A level surface is everywhere horizontal, that is, perpendicular to the direction of the plumb line. Level surfaces are surfaces of constant gravity potential W. , W = const. and the geoid is one of them, W = W0, denoting the constant geoid potential by W0. Again we are disregarding temporal (tidal) variations. Whereas the physical earth's surface, in its picturesque variety and beauty, is very irregular, the geoid is smoother and subject to a mathematical equation, W = W0; however, even the gravity potential W is far from being a simple mathematical function. Therefor, the geoid is referred to a much regular, "normal", surface which approximates the geoid while being more regular in an mathematical or physical sense. Thus we arrive at the concept of a
C) Normal earth, or reference earth, or earth model. Mathematically the simplest model is an ellipsoid of revolution, which therefor is practically almost exclusively used. Physically the best reference for describing the small, more or less elastic, temporal variations (free and forced oscillations such as earth tides), is a hydrostatic equilibrium figure. Figures of hydrostatic equilibrium for the earth are very close to ellipsoids, but do not exactly coincide with an ellipsoid as we shall have ample opportunity to see in this book. By the way, we are frequently not distinguishing between a figure and the surface bounding it; this is costumary and should not cause any confusion.