Sea level is lumpy: the true shape of Earth dips and bulges by 110 metres
Imagine the oceans at rest, free of currents and winds, extended under the continents. That surface, the geoid, is not a smooth ellipsoid. It rises and falls by up to about 110 metres relative to the reference shape GPS uses, because gravity varies across the planet. Measuring such things is the job of geodesy.
Geodesy, from a Greek word meaning division of the Earth, studies the planet's shape, orientation in space and gravity field, all of which change over time. Early thinkers pictured a flat Earth under a solid sky dome; two ancient clues pointed to a sphere instead, the round shadow Earth casts on the Moon during eclipses and the way the Pole Star sinks lower as a traveller heads south. Rotation flattens the planet into an equatorial bulge, while plate collisions and volcanism push the surface around against the pull of gravity.
Geodesists juggle three surfaces. The topography is the actual ground. The geoid is a physical level surface that can be located with instruments such as tide gauges, but it is too irregular to calculate with. So positions are computed on a reference ellipsoid, a smooth mathematical shape. The 1980 Geodetic Reference System fixed its equatorial radius at 6,378,137 metres and its flattening at 1 part in 298.257, and it underpins GPS positioning. Satellite receivers therefore report height above that ellipsoid unless software converts it using a geoid model.
Before satellites, countries used regional datums such as the North American Datum of 1927 or the European Datum of 1950, each fitted to local conditions, whose centres could sit hundreds of metres from Earth's true centre. Because GPS satellites orbit the centre of mass, that point naturally became the origin for modern coordinates, and many national mapping systems are giving way to global ones. Heights still need an anchor: vertical datums, such as the Amsterdam and Kronstadt datums, each pin zero to a reference benchmark, often a tide gauge.
Flat maps involve compromise, since a curved surface cannot be flattened without distortion. Conformal projections such as Universal Transverse Mercator preserve local angles, and the gap between map north and true local north is called meridian convergence. In a quirk of the field, surveyors point the x-axis north and the y-axis east, the reverse of the mathematical habit. Geodetic measurements underpin navigation, construction, satellite systems and even timekeeping.
Source: Geodesy
