Geodesy: Earth’s Shape, Gravity Field, and GPS Positioning

Geodesy is the scientific study of the size and shape of the Earth, its gravitational field, and the precise determination of point locations on the planet’s surface. This branch of Earth science also investigates temporal variations in the planet’s shape and point positions resulting from tides, rotation, and plate tectonic movements. Geodetic measurements depend critically on positional data from satellite-based global positioning systems (GPS), gravity measurements, and radar altimetry over ocean basins. The science of measuring Earth’s dimensions likely began with Eratosthenes in ancient Greece, who measured the distance between Alexandria and Aswan in Egypt and calculated the planet’s curvature from his observations.

One branch of geodesy focuses on measuring the Earth’s gravity field and the geoid, which is defined as the surface of equal gravitational potential. A person’s weight—the pull of Earth’s gravity—would be identical at every point on this hypothetical surface. However, because Earth contains internal density irregularities, the geoid itself is irregular in shape. The geoid exhibits a roughly elliptical form that is slightly flattened at the poles as a result of planetary rotation, and this shape is approximated by a mathematical surface known as the reference ellipsoid.

Variations in geoid height relative to the reference ellipsoid are termed geoid height, often reaching 30–50 feet (tens of meters) in many regions. Such variations reflect lateral differences in mass distribution within Earth’s interior, including mantle convection and crustal thickness changes. Smaller, temporary geoid variations may arise from ocean tides or wind-driven changes in ocean mass distribution. Consequently, precise geoid models are essential for converting GPS-derived heights into meaningful orthometric heights used in engineering and mapping.

All geodetic measurements require a consistent reference frame, which may be astronomical (celestial) or inertial in nature. Many geodetic observations are made between different surface points, and these terrestrial measurements prove valuable for detecting surface deformation, such as motion along active faults. Regional geodetic networks rely on the art of triangulation, first developed by Dutch scientist Gemma Frisius in the 16th century. Triangulation employs precise angular and distance measurements between points in a network or grid to track temporal changes in grid geometry, thereby quantifying surface deformation.

Space geodesy utilizes satellite positioning techniques in which GPS satellites transmit microwave signals encoded with the satellite’s position and the exact transmission time. Ground-based GPS receivers capture and decode these signals, then calculate the distance to each satellite by multiplying the signal travel time by the microwave propagation speed through the atmosphere. The initial calculation places the receiver anywhere on a sphere centered on the satellite, but this ambiguity is resolved because the receiver is known to lie on Earth’s surface. By processing signals from multiple GPS satellites simultaneously, the receiver determines its unique position where the calculated spheres intersect at a single point on the surface.

Standard GPS positioning achieves accuracies of a few feet (one meter or less), which can be enhanced using differential GPS (DGPS). In DGPS, a stationary receiver at a known location transmits corrections to a roving receiver, significantly reducing common errors such as atmospheric delays and satellite clock biases. Furthermore, advanced techniques such as multireceiver interferometric GPS and kinematic GPS improve positional measurements to the submillimeter level. This exceptional precision has revolutionized observations of surface deformation needed to predict earthquakes and volcanic eruptions, and it supports precise navigation, surveying, and guidance systems in civil engineering, agriculture, and autonomous vehicles.

In addition to GPS, modern space geodesy employs Very Long Baseline Interferometry (VLBI) , which uses radio signals from distant quasars to measure Earth’s rotation and tectonic plate motions with millimeter accuracy. Satellite Laser Ranging (SLR) and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) provide complementary data for monitoring global sea level rise, ice sheet mass balance, and post-glacial rebound. These techniques collectively enable the realization of the International Terrestrial Reference Frame (ITRF) , which underpins all high-precision geodetic and geophysical applications.

Geodynamics—the study of Earth’s internal and surface movements—relies heavily on repeated geodetic measurements to model mantle convection, lithospheric deformation, and earthquake cycle processes. For example, continuous GPS networks along plate boundaries detect slow interseismic strain accumulation, which helps assess seismic hazard. Similarly, tide gauge and satellite altimetry data are combined with geoid models to separate absolute sea level change from vertical land motion, a critical factor in climate change research.

FURTHER READING: Turcotte, Donald L., and Gerald Schubert. Geodynamics. 2nd ed. Cambridge: Cambridge University Press, 2002.