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Concept
Figure of the Earth
Summary
Figure of the Earth is a term of art in geodesy that refers to the size and shape used to model Earth. The size and shape it refers to depend on context, including the precision needed for the model. A sphere is a well-known historical approximation of the figure of the Earth that is satisfactory for many purposes. Several models with greater accuracy (including ellipsoid) have been developed so that coordinate systems can serve the precise needs of navigation, surveying, cadastre, land use, and various other concerns.
Earth's topographic surface is apparent with its variety of land forms and water areas. This topographic surface is generally the concern of topographers, hydrographers, and geophysicists. While it is the surface on which Earth measurements are made, mathematically modeling it while taking the irregularities into account would be extremely complicated.
The Pythagorean concept of a spherical Earth offers a simple surface that is easy to deal with mathematically. Many astronomical and navigational computations use a sphere to model the Earth as a close approximation. However, a more accurate figure is needed for measuring distances and areas on the scale beyond the purely local. Better approximations can be made by modeling the entire surface as an oblate spheroid, using spherical harmonics to approximate the geoid, or modeling a region with a best-fit reference ellipsoid.
For surveys of small areas, a planar (flat) model of Earth's surface suffices because the local topography overwhelms the curvature. Plane-table surveys are made for relatively small areas without considering the size and shape of the entire Earth. A survey of a city, for example, might be conducted this way.
By the late 1600s, serious effort was devoted to modeling the Earth as an ellipsoid, beginning with Jean Picard's measurement of a degree of arc along the Paris meridian. Improved maps and better measurement of distances and areas of national territories motivated these early attempts. Surveying instrumentation and techniques improved over the ensuing centuries.
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