that the Earth was a sphere was dispelled by Sir Isaac Newton. In the first edition of Principia, published in 1687, Newton postulated that the Earth was slightly ellipsoidal in shape, with the polar radius about 27 kilometers shorter than the equatorial radius. Refinements in field geodesy techniques slowly increased the accuracy of these estimates, but it was not until the dawn of the space age that knowledge of the Earth’s size and shape improved significantly. Through the analysis of perturbations of satellite orbits, scientists first refined the ellipsoidal dimensions of the Earth and then discovered that the shape of the Earth, as represented by its gravity field, was much more complicated.

When geodesists talk about the shape of the Earth, what they actually mean is the shape of the equipotential surfaces of its gravity field. The equipotential surface that most closely approximates mean sea level is called the geoid. One of the major tasks of geodesy is to map the geoid as accurately as possible. An example of a highly accurate and precise geoid constructed using data from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite is shown in Figure 2.1 (Schiermeier, 2010; Floberghagen et al., 2011). Maps of the geoid provide information about the structure of the Earth’s crust and upper mantle, plate tectonics, and sea-level change. The geoid is needed to accurately determine satellite orbits and the trajectories of ballistic missiles. It also finds everyday use as the surface from which orthometric heights, the heights usually found on topographic maps, are measured. Improved knowledge of the gravity field can also be combined with GPS and/or inertial navigation sensors to produce a more accurate navigation system than can be provided by GPS alone.

NGA’s ongoing needs for geodesy stem primarily from work carried out by the former Defense Mapping Agency and include accurately and precisely determining the geoid, establishing accurate and precise coordinate systems (datums) and positions within them (e.g., World Geodetic System 1984; Merrigan et al., 2002), and relating different internationally used datums. In particular, NGA is responsible for supporting Department of Defense navigation systems, maintaining GPS fixed-site operations, and generating and distributing GPS precise ephemerides (Wiley et al., 2006).

Advances in geodesy are driven largely by continuing improvements to and expansion of space geodetic systems. New generations of GPS satellites are being deployed by the United States and several countries are developing global navigation satellite systems (GNSS), including the European Galileo, Chinese Compass, and Russian GLONASS systems. The use of GPS has become ubiquitous, with myriad civil and military applications. Improvements on the horizon include the development of less expensive and more accurate gravity gradiometry for determining the fine structure of the local gravity field and more accurate atomic clocks for measuring gravity and determining heights in the field.1

An important advance in geophysics that is relevant to NGA is the improvement in describing the Earth’s ever-changing magnetic field. The National Geophysical Data Center’s NGDC-720 model— compiled from satellite, ocean, aerial, and ground magnetic surveys—provides information on the field generated by magnetized rocks in the crust and upper mantle (Figure 2.2; Maus, 2010). This model is the first step toward producing a geomagnetic field model that would be useful for navigation.

Knowledge and Skills

Graduate study in geodesy encompasses the theory and modern practice of geodesy. Topics include the use of mathematical tools such as least-squares adjustment, Kalman filtering, and spectral analysis; the principles of gravity field theory and orbital mechanics; the propagation of electromagnetic waves; and the theory and operation of observing instruments such as GNSS receivers and inertial navigation systems. Modeling of observations to extract quantities of interest is a key technique learned by students. While course-only master’s degrees are available at some universities, most graduate degrees in geodesy require completion of a research project, some of which involve substantial amounts of computer programming. Graduates may carry out or manage research, and traditionally have a master’s or doctorate degree from a university specializing in geodesy and an undergraduate degree in a related field such as survey science, civil engineering, surveying

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1 Presentation by D. Smith, NOAA, to the NRC Workshop on New Research Directions for NGA, Washington, D.C., May 17-19, 2010.



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