Geoid

Lore & Background

The geoid is the equipotential surface of Earth's gravity field that coincides with mean sea level in the absence of tides, currents, and weather. It was first conceptualized by Carl Friedrich Gauss, who called it the 'mathematical figure of the Earth.' The geoid is irregular due to uneven mass distribution within and on Earth's surface, but its deviation from a reference ellipsoid is less than 200 meters total, far smoother than Earth's physical surface. For nearly 200 years, the geoid could not be precisely defined until satellite geodesy in the mid-20th century enabled accurate measurements. Mathematician Gladys West was the first to synthesize a high-fidelity geoid from satellite data.

Reader's Guide

The geoid is a critical concept in geodesy and geophysics, serving as the reference surface for orthometric heights, geopotential heights, and dynamic heights. It is essential for satellite-based global positioning systems, as GPS receivers measure heights relative to a reference ellipsoid and must correct to the geoid to obtain orthometric height. The geoid's determination relies on extensive gravitational measurements and calculations, including Stokes' integral formula and Bruns' formula. Modern approaches combine terrestrial gravimetry, satellite orbital perturbations, and satellite gravity missions. The geoid's shape reflects Earth's internal density variations, with rises where material is denser and gravitational pull stronger. Its practical importance extends to navigation, surveying, and understanding Earth's gravity field.

Did You Know?

• All points on the geoid have the same geopotential, and gravity acts perpendicular to it everywhere, apart from temporary tidal fluctuations.
• Mathematician Gladys West was the first person to synthesize a high-fidelity geoid from satellite data.
• GPS receivers on a ship may indicate height variations even at sea level because they measure height relative to a geocentric reference ellipsoid, not the geoid.