An ellipsoid is a three-dimensional geometric shape that serves as the mathematical model for representing Earth’s overall form in geodesy, cartography, and satellite navigation systems. Specifically, geodetic applications use a reference ellipsoid, an oblate spheroid generated by rotating an ellipse around its shorter axis, to approximate the Earth’s shape, which bulges slightly at the equator due to centrifugal forces from planetary rotation.
The Earth is not a perfect sphere; its equatorial radius exceeds its polar radius by approximately 21 kilometers. An ellipsoid defined by specific parameters, primarily the semi-major axis (equatorial radius) and flattening factor, provides a mathematically tractable surface for coordinate calculations while closely approximating Earth’s actual shape. Different reference ellipsoids have been developed throughout geodetic history to best fit various regions or global applications.
The WGS84 (World Geodetic System 1984) ellipsoid is the reference surface used by GPS and most global GNSS applications. Its parameters define a semi-major axis of 6,378,137 meters and a flattening of 1/298.257223563. Other commonly encountered ellipsoids include GRS80 (Geodetic Reference System 1980), which differs from WGS84 only slightly, and regional ellipsoids like Clarke 1866 (historically used in North America) or Bessel 1841 (used in parts of Europe and Asia).
Understanding the ellipsoid concept is essential for working with GNSS coordinates and heights. Geographic coordinates (latitude and longitude) are defined with respect to the ellipsoid surface, latitude measures the angle between the equatorial plane and a line perpendicular to the ellipsoid at a point, while longitude measures the angular distance east or west from the prime meridian. Ellipsoidal height (or height above ellipsoid) measures the distance along this perpendicular line from the ellipsoid surface to a point, which differs from elevation referenced to mean sea level (orthometric height) due to variations in Earth’s gravitational field.
