Geodesy

Geodesy (also called geodetics) is the science of measuring and representing Earth’s geometry, gravity, and spatial orientation in three-dimensional space as these change over time. When applied to other astronomical bodies—like planets or their moon systems—it is known as planetary geodesy. Professionals in this field are called geodesists or geodetic surveyors.

Using highly precise observations, geodesy forms the scientific foundation for mapping, navigation, and positioning. It also supports infrastructure development (including construction), natural resource management, mineral exploration, and geophysics. Its measurements underpin modern geospatial reference frames used in transportation, satellite systems, global trade, and timekeeping. Geodynamic phenomena—such as crustal motion, tides, and polar motion—are studied through global and national control networks, space geodesy and terrestrial geodetic techniques, and the use of datums and coordinate systems.

The word “geodesy” comes from the Ancient Greek *geodaisia*, meaning “division of Earth,” and the field began in pre-scientific antiquity. Early ideas about Earth’s shape held it to be flat, with the heavens as a physical dome above. Two early arguments for a spherical Earth were that lunar eclipses appear as circular shadows and that Polaris appears lower in the sky as a traveler moves south.

Geodesy originally focused on measuring and understanding Earth’s geometric shape, orientation in space, and gravitational field; it now also applies to other Solar System bodies. Earth’s shape largely results from rotation (causing an equatorial bulge) and geological processes like plate collisions and volcanism, resisted by gravity. This applies to the solid surface, the liquid surface (dynamic sea surface topography), and the atmosphere. The study of Earth’s gravitational field is called physical geodesy.

The geoid is Earth’s figure abstracted from its topography—an idealized equilibrium surface of seawater at mean sea level, free of currents and air pressure variations, extended under continents. Unlike a reference ellipsoid, the geoid is irregular and too complex for solving geometrical problems like point positioning. The separation between the geoid and a reference ellipsoid is called geoidal undulation, varying globally between ±110 meters based on the GRS 80 ellipsoid.

A reference ellipsoid, usually chosen to match the geoid’s volume, is defined by its semi-major axis (equatorial radius) *a* and flattening *f*, where *f* = (*a* − *b*)/*a* and *b* is the semi-minor axis (polar radius). The mechanical ellipticity (dynamical flattening, symbol *J₂*) is determined precisely from satellite orbit perturbations. Its link to geometrical flattening is indirect and depends on Earth’s internal density distribution—essentially, how mass is concentrated toward the center.

The 1980 Geodetic Reference System (GRS 80), adopted by the International Union of Geodesy and Geophysics, uses a semi-major axis of 6,378,137 meters and a flattening of 1:298.257. GRS 80 forms the basis for GPS positioning and is widely used outside geodesy. Many older mapping and charting systems are becoming obsolete as countries shift to global, geocentric reference systems based on the GRS 80 ellipsoid.

The geoid is a “realizable” surface—it can be consistently located on Earth using simple measurements from physical objects like a tide gauge—and is thus considered a physical surface. The reference ellipsoid, however, has many possible instantiations and is not readily realizable, making it an abstract surface. The third primary surface of geodetic interest—Earth’s topographic surface—is also realizable.

Points in 3D space are most conveniently described by three Cartesian coordinates: X, Y, and Z. Since satellite positioning began, such coordinate systems are typically geocentric, with the Z-axis aligned to Earth’s rotation axis (conventional or instantaneous). Before satellite geodesy, coordinate systems tied to a geodetic datum aimed to be geocentric, but their origins often differed from the geocenter by hundreds of meters due to regional plumbline deviations. Regional datums like ED 50 (European Datum 1950) or NAD 27 (North American Datum 1927) used ellipsoids that best fit the geoid within their areas, minimizing vertical deflections there. Because GPS satellites orbit the geocenter, that point naturally becomes the origin of a coordinate system defined by satellite geodesy. Geocentric coordinate systems in geodesy fall into two classes: inertial reference systems, where axes keep their orientation relative to fixed stars (or ideal gyroscopes), with the X-axis pointing to the vernal equinox.