|
|
| (One intermediate revision by one other user not shown) |
| Line 1: |
Line 1: |
| {{Unreferenced|date=September 2007}}
| | 37 yrs old Quality Assurance Manager Lashua from Chatham, likes to spend some time physical exercise (aerobics weights), clash of clans hack and archery. Recommends that you just visit Laponian Area.<br><br>Feel free to visit my blog post ... [https://www.facebook.com/pages/Clash-Of-Clans-Hack-2014/1394375284161983 clash of clans hack android] |
| '''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.
| |
| | |
| 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]].
| |
| | |
| 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.
| |
| | |
| Solving for geopotential (Φ):
| |
| :<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>
| |
| :<math>\Phi = \int_0^z \left[ \frac{Gm}{(a+z)^2} \right] dz</math>
| |
| | |
| Integrate to get
| |
| :<math>\Phi = Gm \left[\frac{1}{a} - \frac{1}{a+z} \right]</math>
| |
| | |
| where:
| |
| :G=6.673x10<sup>-11</sup> Nm<sup>2</sup>/kg<sup>2</sup> is the gravitational constant,
| |
| :m=5.975x10<sup>24</sup> kg is the mass of the earth,
| |
| :a=6.378x10<sup>6</sup> m is the average radius of the earth,
| |
| :z is the height in meters
| |
| :Φ is the geopotential at height z, which is in units of [m<sup>2</sup>/s<sup>2</sup>] or [J/kg].
| |
| | |
| ==See also==
| |
| * [[Geoid]]
| |
| * [[Physical geodesy]]
| |
| * [[Geopotential height]]
| |
| * [[Geopotential model]]
| |
| | |
| ==References==
| |
| {{Reflist}}
| |
| | |
| {{Geophysics-stub}}
| |
| [[Category:Gravimetry]]
| |
37 yrs old Quality Assurance Manager Lashua from Chatham, likes to spend some time physical exercise (aerobics weights), clash of clans hack and archery. Recommends that you just visit Laponian Area.
Feel free to visit my blog post ... clash of clans hack android