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| | My name is Asa from Greenleigh studying Graduate School. I did my schooling, secured 77% and hope to find someone with same interests in Backpacking.<br><br>Review my blog [http://www.youtube.com/watch?v=aON41nbKcPQ John Chow] |
| '''Geopotential''' is the potential of the [[Earth]]'s [[gravity field]]. For convenience it is often defined as ''minus'' the [[potential energy]] per unit [[mass]], so that the gravity vector is obtained as the [[gradient]] of this potential, without the minus.
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| For [[geophysical]] applications, gravity is distinguished from gravitation. Gravity is defined as the resultant of [[gravitation]] and the [[centrifugal force (fictitious)|centrifugal force]] caused by the [[Earth's rotation]]. The [[Sea level|global mean sea surface]] is close to one of the equipotential surfaces of the geopotential of gravity. This equipotential surface, or surface of constant geopotential, is called the [[geoid]].
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| For the purpose of satellite [[orbital mechanics]], the geopotential is typically described by a series expansion into [[spherical harmonics]] ([[spectral]] representation). In this context the geopotential is taken as the potential of the gravitational field of the Earth, that is, leaving out the centrifugal potential.
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| Solving for geopotential (Φ):
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| :<math>\Phi(h) = \int_0^h g\,dz\ </math><ref>Holton, James R. ''An Introduction to Dynamic Meteorology''. 4th ed. Burlington: Elsevier, 2004. Print.</ref>
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| :<math>\Phi = \int_0^z \left[ \frac{Gm}{(a+z)^2} \right] dz</math>
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| Integrate to get
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| :<math>\Phi = Gm \left[\frac{1}{a} - \frac{1}{a+z} \right]</math>
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| where:
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| :G=6.673x10<sup>-11</sup> Nm<sup>2</sup>/kg<sup>2</sup> is the gravitational constant,
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| :m=5.975x10<sup>24</sup> kg is the mass of the earth,
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| :a=6.378x10<sup>6</sup> m is the average radius of the earth,
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| :z is the height in meters
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| :Φ is the geopotential at height z, which is in units of [m<sup>2</sup>/s<sup>2</sup>] or [J/kg].
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| ==See also==
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| * [[Geoid]]
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| * [[Physical geodesy]]
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| * [[Geopotential height]]
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| * [[Geopotential model]]
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| ==References==
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| {{Reflist}}
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| {{Geophysics-stub}}
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| [[Category:Gravimetry]]
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My name is Asa from Greenleigh studying Graduate School. I did my schooling, secured 77% and hope to find someone with same interests in Backpacking.
Review my blog John Chow