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#### First GRACE follow-on satellite completes construction - Phys.Org

The geoid is the shape that the surface of the oceans would take under the influence of Earth's gravity and rotation alone, in the absence of other influences such as winds and tides. This surface is extended through the continents . All points on the geoid have the same gravity potential energy . The force of gravity acts everywhere perpendicular to the geoid, meaning that plumb lines point perpendicular and water levels parallel to the geoid.

The geoid is the shape that the surface of the oceans would take under the influence of Earth's gravity and rotation alone, in the absence of other influences such as winds and tides. This surface is extended through the continents (such as with very narrow hypothetical canals). All points on the geoid have the same gravity potential energy (the sum of gravitational potential energy and centrifugal potential energy). The force of gravity acts everywhere perpendicular to the geoid, meaning that plumb lines point perpendicular and water levels parallel to the geoid.

Specifically, the geoid is the equipotential surface that would coincide with the mean ocean surface of Earth if the oceans and atmosphere were in equilibrium, at rest relative to the rotating Earth, and extended through the continents (such as with very narrow canals). According to Gauss, who first described it, it is the "mathematical figure of Earth", a smooth but highly irregular surface whose shape results from the uneven distribution of mass within and on the surface of Earth. It does not correspond to the actual surface of Earth's crust, but to a surface which can only be known through extensive gravitational measurements and calculations. Despite being an important concept for almost two hundred years in the history of geodesy and geophysics, it has only been defined to high precision since advances in satellite geodesy in the late 20th century. It is often described as the true physical figure of the Earth, in contrast to the idealized geometrical figure of a reference ellipsoid.

The surface of the geoid is higher than the reference ellipsoid wherever there is a positive gravity anomaly (mass excess) and lower than the reference ellipsoid wherever there is a negative gravity anomaly (mass deficit).

### GOCE: Geoid

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