Reference Ellipsoid
A reference ellipsoid is a mathematically defined surface that approximates the shape of the Earth as an oblate spheroid. It serves as the geometric foundation for geodetic datums and coordinate systems, enabling the calculation of geographic positions on Earth's irregular surface.
Overview A reference ellipsoid is a smooth mathematical surface defined by rotating an ellipse about its minor axis, producing an oblate (flattened) spheroid that closely approximates the Earth's overall shape. Because the Earth is not a perfect sphere—it bulges slightly at the equator due to rotational forces—ellipsoids provide a more accurate geometric model for computing positions, distances, and areas on the Earth's surface than a simple sphere.
Defining Parameters
An ellipsoid is fully defined by two parameters: the semi-major axis (a), which is the equatorial radius, and either the semi-minor axis (b), the polar radius, or the flattening ratio (f = (a-b)/a). The GRS 80 ellipsoid, used by both WGS 84WGS 84WGS 84 (World Geodetic System 1984) is the global geodetic reference system used by GPS and most modern mapping appli... and NAD 83NAD 83NAD 83 (North American Datum of 1983) is the horizontal geodetic datum used for surveying, mapping, and navigation ac..., has a semi-major axis of 6,378,137 meters and a flattening of 1/298.257222101. Historically, many ellipsoids were fitted to specific regions of the Earth; for example, the Clarke 1866 ellipsoid was optimized for North America and the Bessel 1841 for Europe and parts of Asia.
Role in Coordinate Systems
Every geographic coordinate system is based on a reference ellipsoid. Latitude and longitude values describe positions on the ellipsoid surface, and ellipsoidal height measures the distance above or below the ellipsoid along its normal. The choice of ellipsoid affects the calculated positions of all points, and using coordinates from one ellipsoid with a datumDatumA geodetic datum is a mathematical model that defines the size, shape, and orientation of the Earth, serving as the r... based on another introduces systematic errors. Map projectionMap ProjectionMap projections are mathematical transformations that convert the three-dimensional surface of the Earth onto a two-d... formulas also depend on ellipsoid parameters for accurate transformation from geographic to projected coordinates.
Relationship to the Geoid
The ellipsoid is a smooth mathematical approximation, while the geoidGeoidThe geoid is the equipotential surface of Earth's gravity field that best approximates global mean sea level. It serv... is the actual equipotential surface of Earth's gravity field, which undulates above and below the ellipsoid by up to 100 meters. The separation between the geoid and ellipsoid, called geoid undulation, must be accounted for when converting between GPSGPSThe Global Positioning System (GPS) is a satellite-based navigation system operated by the U.S. Space Force that prov...-derived ellipsoidal heights and orthometric heights (elevations above mean sea level).
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