Introduction

There has been a renewed interest in Geometric Geodesy due to the advent of commercial and private applications of the U.S. military's Global Positioning System. Traditionally, the study of geometric geodesy was motivated by the political needs of mapping and surveying of the entire Earth's surface. Today, the motivation for studying geometric geodesy comes from scientific needs where precise point positioning play an important role.

Surveyors working over small regions typically assume the territory to be defined over a flat surface. For larger, national and global surveys, the curvature of the Earth must be taken into account. This curvature can be described utilizing principles of geometry and trigonometry. Geometric geodesy thus falls under the guise of applied geometry.

In a very rudimentary way, we can say that the Earth has the shape of a sphere. But due to the planet's spin, it bulges at the equator and is flattened slightly at the poles. A better term to use for the shape of the Earth is that of an ellipsoid of rotation. There has been considerable work done (mostly in the latter 19th century and early 20th century) in the area of theoretical physics on the topic of figures of equilibrium.

Additionally, considerable geodetic surveying work has been done which considers the geometric implications of the ellipsoid. Lines lying on this ellipsoid of rotation are no longer great circles, which is the case for spheres. On an ellipsoid, or any curved surface for that matter, the curve connecting two points in the shortest distnce is called the geodesic curve. The study of these kinds of curves falls into the mathematical subdiscipline of differential geometry.

Geometric Geodesy confines itself to the study of coordinate systems and angular and linear relationships of geodesic curves on ellipsoids of rotation which best approximate the shape of the whole planet or parts thereof. These mathematically defined surfaces are called datums.

Resources

Hard Copy

• Geometric Geodesy Specifically

• Bomford, G., Geodesy, 4th Ed., Oxford Univ. Press, Oxford, 1980. (especially Chapter X therein.)
• Brunner, F. K. (ed.), Advances in Positioning and Reference Frames, Springer-Verlag, Berlin, 1998.
• Helmert, F. R., Die Mathematischen und Physikalischen Theorieen der Höheren Geodäsie, 2 vols., Teubner, Leipzig, 1880 (reprinted by Minerva, Frankfurt am Main, 1962).
• Hoffmann-Welenhof, B. and H. Lichtenegger, Global Positioning System, 4th ed., Springer-Verlag, Berlin, 1997.
• Hooijberg, M., Practical Geodesy Using Computers, Springer Verlag, Berlin, 1997.
• Jordan-Eggert, Jordan's Handbook of Geodesy, Two vols., U. S. Army Map Service, Washington, D.C., 1962.
• Leick, A., GPS Satellite Surveying, 2nd ed., John Wiley & Son, New York, 1995.
• Rapp, R. H., Geometric Geodesy, two vols., Ohio State University, 1982 (may have received more recent revisions).
• Rüeger, J. M., Electronic Distance Measurement, Springer Verlag, 1996.

• Texts on Differential Geometry

• Kreyzig, E., Differential Geometry, Dover Publications, New York, 1991 (reprint of a U. of Toronto 1963 edition).
• Struik, D. J., Lectures on Classical Differential Geometry, Addison Wesley, New York, 1960 (reprinted by Dover).

• Texts on Figures of Equilibrium

• Chanrasekhar, S., Ellipsoidal Figures of Equilibrium, Yale U. Press, New Haven, 1969.
• Jardetsky, W. S., Theories of Figures of Celestial Bodies, Interscience, New York, 1958.
• Kopal, Z., Figures of Equilibrium of Celestial Bodies, U. of Wisconsin Press, Madison, 1960.
• Lyttleton, R. A., The Stability of Rotating Liquid Masses, Cambridge U. Press, Cambridge, 1953.

Internet

Geodetic Datum Overview

AUSLIG's Coordinates, Datums and Ellipsoids

Sam Wormley's Maps and mapping (from Iowa State U.)

The Applied Geodesy Page

Local

Mars topographic mapping based on the Mars Observer Laser Altimeter (MOLA)