geopotentialen

Geopotential refers to the potential energy per unit mass in the Earth’s gravity field. In a rotating frame, the geopotential W combines the gravitational potential V with the centrifugal potential Φ, so that the local gravity acceleration g is the gradient of W. Geopotential is therefore a scalar field whose level surfaces, called geopotential surfaces or equipotential surfaces, represent places where the gravity potential is the same.

Geopotential surfaces are central to geodesy. The geoid is the special geopotential surface that best fits mean sea level and extends through the continents. Elevations and heights are defined with respect to combinations of these surfaces: ellipsoidal height uses a smooth reference ellipsoid, orthometric height is measured above the geoid, and geopotential height converts W differences into heights by dividing by a standard gravity value. The concept of geopotential height is also used in meteorology, where it serves as a vertical coordinate for atmospheric pressure levels.

Practically, the Earth’s gravity field is modeled as a geopotential function W(r, θ, φ) that includes both the Earth’s gravitational potential and the centrifugal potential from rotation. It is commonly represented by spherical harmonic expansions with coefficients that encode mass distribution within the planet. Modern gravity field models, such as those derived from satellite missions, provide high-resolution maps of W and its derivatives, enabling precise determinations of geoid undulations, height systems, and dynamic topography.

Applications span geodesy, surveying, navigation, oceanography, and atmospheric science, reflecting the role of geopotential in linking gravity, height, and the shape of the Earth.