Geoid

The geoid is the shape that the <a href="/facts/Ocean/8W8lYgjD">ocean</a> surface would take under the influence of the <a href="/facts/Gravity_of_Earth/IXe9Bh8k">gravity of Earth</a>, including <a href="/facts/Gravitational_attraction/bqAN7DdQ">gravitational attraction</a> and <a href="/facts/Earth%2527s_rotation/mDbXcKUx">Earth's rotation</a>, if other influences such as winds and <a href="/facts/Tide/zNstvWPv">tides</a> were absent. This surface is extended through the <a href="/facts/Continent/Pysd9Sw8">continents</a> (such as might be approximated with very narrow hypothetical <a href="/facts/Canal/cm3cUj1x">canals</a>). According to <a href="/facts/Carl_Friedrich_Gauss/f4eSMBD7">Carl Friedrich Gauss</a>, who first described it, it is the "mathematical <a href="/facts/Figure_of_the_Earth/z1LvpVgd">figure of the Earth</a>", a smooth but irregular <a href="/facts/Surface/0XA8ce89">surface</a> whose shape results from the uneven distribution of mass within and on the surface of Earth. It can be known only through extensive gravitational measurements and calculations. Despite being an important concept for almost 200 years in the history of <a href="/facts/Geodesy/EJH0Te0m">geodesy</a> and <a href="/facts/Geophysics/ywVQ1sAQ">geophysics</a>, it has been defined to high precision only since advances in <a href="/facts/Satellite_geodesy/r9AAcApl">satellite geodesy</a> in the late 20th century.
The geoid is often expressed as a geoid undulation or geoidal height above a given <a href="/facts/Reference_ellipsoid/uD1C2sTU">reference ellipsoid</a>, which is a slightly flattened sphere whose <a href="/facts/Equatorial_bulge/8CIPWl0I">equatorial bulge</a> is caused by the planet's rotation. Generally the geoidal height rises where the Earth's material is locally more dense and exerts greater gravitational force than the surrounding areas. The geoid in turn serves as a reference <a href="/facts/Coordinate_surface/Mtd0q4SP">coordinate surface</a> for various <a href="/facts/Vertical_coordinate/HpaNYcWC">vertical coordinates</a>, such as <a href="/facts/Orthometric_height/IKeHex7L">orthometric heights</a>, <a href="/facts/Geopotential_height/uPSKWF1G">geopotential heights</a>, and <a href="/facts/Dynamic_height/r5yBTjDg">dynamic heights</a> (see <a href="/facts/Geodesy/EJH0Te0m">Geodesy#Heights</a>).
All points on a geoid surface have the same <a href="/facts/Geopotential/5LFGRzhT">geopotential</a> (the sum of <a href="/facts/Gravitational_energy/SJpNw6G5">gravitational potential energy</a> and <a href="/facts/Centrifugal_force/CWgvMw6w">centrifugal</a> potential energy). At this surface, apart from temporary tidal fluctuations, the <a href="/facts/Force_of_gravity/bqAN7DdQ">force of gravity</a> acts everywhere perpendicular to the geoid, meaning that <a href="/facts/Plumb_bob/eA2XJ6bp">plumb lines</a> point perpendicular and <a href="/facts/Bubble_level/fXQH69hY">bubble levels</a> are parallel to the geoid. 
Being an <a href="/facts/Equigeopotential/5LFGRzhT">equigeopotential</a> means the geoid corresponds to the <a href="/facts/Free_surface/NB0yMSxH">free surface</a> of water at rest (if only the Earth's gravity and rotational acceleration were at work); this is also a sufficient condition for a ball to remain at rest instead of rolling over the geoid.
Earth's gravity acceleration (the <a href="/facts/Vertical_derivative/2cmoCezd">vertical derivative</a> of geopotential) is thus non-uniform over the geoid.

Geoid open-in-new

Geoid