Geoid

A geoid is a close representation or physical model of the figure of the Earth. According to C.F. Gauss, it is the "mathematical figure of the Earth", in fact, of the gravity field. It is that equipotential surface (surface of fixed potential value) which coincides on average with mean sea level.

Related Topics:
Figure of the Earth - C.F. Gauss - Gravity - Sea level

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The geoid surface is more irregular than the ellipsoid of revolution often used to approximate the shape of the physical Earth, but considerably smoother than Earth's physical surface. While the latter has excursions of +8,000 m (Mount Everest) and −11,000 m (Mariana Trench), the geoid varies by only about ±100 m about the reference ellipsoid of revolution.

Related Topics:
Ellipsoid - Mount Everest - Mariana Trench

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Because the force of gravity is everywhere perpendicular to the geoid (being an equipotential surface), sea water, if left to itself, would assume a surface equal to it—even through the continental land masses if sea water were allowed to freely penetrate them, e.g., by tunnels. In reality it can not, of course; still, geodesists are able to derive the heights of continental points above this imaginary, yet physically defined, surface by a technique called spirit levelling.

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When travelling by ship, one does not notice the undulations of the geoid; the local vertical is always perpendicular to it, and the local horizon tangential to it. A GPS receiver on board may show the height variations relative to the (mathematically defined) reference ellipsoid, the centre of which coincides with the Earth's centre of mass, the centre of orbital motion of GPS satellites.

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