Geodesy

The literal meaning of geodesy is “division of the Earth,” and it can therefore be said that at its most fundamental level, the subject is concerned with positioning on the surface of the Earth. More narrowly, the subject is understood to apply principally to applications with an extent or accuracy that demands a consideration of the true shape of the planet (in contrast with surveying, which may be more concerned with flat Earth approximations).

More broadly, however, geodesy necessarily encompasses the range of mathematical and scientific topics that relate to the determination of the shape and size of the Earth, its representation in coordinate terms and computations within these coordinate systems, map projections, positioning, and height determination techniques (in particular satellite-based systems). It can therefore be seen that geodesy is of direct relevance to geography in that it establishes the essential underlying coordinate reference systems for use in mapping and related spatial information activities.

This process can be thought of in a hierarchical fashion or as a logical sequence of required steps. First, one needs to know the shape and size of the [Page 1218]Earth, which one finds from several different types of observation. The surface that it is required to determine is known as the geoid, which is defined as that equipotential surface (one perpendicular to gravity) that most closely corresponds to mean sea level. Its long-wavelength components are generally found from an analysis of the perturbations of satellite orbits from the simple Keplerian model, since these are caused by major gravitational trends. Its short-wavelength components are determined principally from a combination of direct observations of gravity anomalies (on the surface, through airborne gravimetry, and from dedicated satellite missions) and analysis of satellite altimetry data over the oceans. The link between gravity and shape is one of the classical mathematical problems of geodesy, and much research is devoted to the optimization of the algorithms used.

The traditional method for the determination of Earth's size was by terrestrial observations of angles and distances. These were generally made in linked chains of triangulation that were sometimes carried out along a meridian with the specific intention of gaining information on Earth's size; more generally, these were carried out to provide a framework for mapping. While the results of these traditional geodetic observations may still in many parts of the world (and not necessarily the least developed) form an essential component of the coordinate framework, the primary techniques for the determination of the size of the Earth (i.e., determining the relative coordinate values for key global reference points) are space based. These include the following: (a) very long baseline interferometry (VLBI), in which pairs or sets of radio telescopes make mutual observations to extragalactic sources of radiation, and baselines are inferred from time delays; (b) satellite laser ranging (SLR), in which ground stations fire lasers that are returned by retroreflectors aboard satellites; (c) the global positioning system (GPS) or any other similar global navigation satellite system in which receivers make observations of electromagnetic signals broadcast by a system of orbiting satellites; and (d) Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS), in which the Doppler shift of a signal received at a dedicated satellite from a ground station is the fundamental measurable.

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