Editing Geoid (section)

{{Short description|Ocean shape without winds and tides}}
{{Distinguish|text=[[geode]], a crystal-filled rock}}
{{Distinguish|text=[[GEOID]], a geocoding scheme}}
{{Geophysics}}
{{Geodesy}}
{{Use dmy dates|date=May 2022}}

The '''geoid''' ({{IPAc-en|ˈ|dʒ|iː|.|oɪ|d}} {{respell|JEE|oyd}}) is the shape that the [[ocean]] surface would take under the influence of the [[gravity of Earth]], including [[gravitational attraction]] and [[Earth's rotation]], if other influences such as winds and [[tide]]s were absent. This surface is extended through the [[continent]]s (such as might be approximated with very narrow hypothetical [[canal]]s). According to [[Carl Friedrich Gauss]], who first described it, it is the "mathematical [[figure of the Earth]]", a smooth but irregular [[surface]] whose shape results from the uneven distribution of mass within and on the surface of Earth.<ref name="Gauß1828">{{cite book | last=Gauß | first=C.F. | title=Bestimmung des Breitenunterschiedes zwischen den Sternwarten von Göttingen und Altona durch Beobachtungen am Ramsdenschen Zenithsector | publisher=Vandenhoeck und Ruprecht | year=1828 | url=https://books.google.com/books?id=tIg_AAAAcAAJ&pg=PA73 | language=de | access-date=2021-07-06 | page=73}}</ref> It can be known only through extensive gravitational measurements and calculations. Despite being an important concept for almost 200 years in the history of [[geodesy]] and [[geophysics]], it has been defined to high precision only since advances in [[satellite geodesy]] in the late 20th century.

The geoid is often expressed as a '''geoid undulation''' or '''geoidal height''' above a given [[reference ellipsoid]], which is a slightly flattened sphere whose [[equatorial bulge]] 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 [[coordinate surface]] for various [[vertical coordinate]]s, such as [[orthometric height]]s, [[geopotential height]]s, and [[dynamic height]]s (see [[Geodesy#Heights]]).

All points on a geoid surface have the same [[geopotential]] (the sum of [[gravitational energy|gravitational potential energy]] and [[centrifugal force|centrifugal]] potential energy). At this surface, apart from temporary tidal fluctuations, the [[force of gravity]] acts everywhere perpendicular to the geoid, meaning that [[plumb bob|plumb lines]] point perpendicular and [[bubble level]]s are parallel to the geoid. 
Being an [[equigeopotential]] means the geoid corresponds to the [[free surface]] 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 [[vertical derivative]] of geopotential) is thus non-uniform over the geoid.<ref name="BookGeodesyConcepts">''Geodesy: The Concepts.''  Petr Vanicek and E.J. Krakiwsky.  Amsterdam: Elsevier.  1982 (first ed.): {{ISBN|0-444-86149-1}}, {{ISBN|978-0-444-86149-8}}.  1986 (third ed.): {{ISBN|0-444-87777-0}}, {{ISBN|978-0-444-87777-2}}.  {{ASIN|0444877770}}.</ref>

[[File:Geoid undulation 10k scale.jpg|thumb|Geoid undulation in [[pseudocolor]], [[shaded relief]] and [[vertical exaggeration]] (10000 vertical scaling factor).]]
[[File:Geoid undulation to scale.jpg|thumb|Geoid undulation in pseudocolor, without vertical exaggeration.]]