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{{Geodesy}}
'''GRS 80''', or '''Geodetic Reference System 1980''', is a [[geodetic reference system]] consisting of a global [[reference ellipsoid]] and a [[gravity field model]].


==Geodesy==
[[Geodesy]], also called geodetics, is the scientific discipline that deals with the measurement and representation of the [[earth]], its [[gravitation]]al field and geodynamic phenomena ([[polar motion]], earth [[tide]]s, and crustal motion) in three-dimensional, time-varying space.


The [[geoid]] is essentially the figure of the Earth abstracted from its topographic features. It is an idealized equilibrium surface of sea water, the mean sea level surface in the absence of currents, air pressure variations etc. and continued under the continental masses. The geoid, unlike the ellipsoid, is irregular and too complicated to serve as the computational surface on which to solve geometrical problems like point positioning. The geometrical separation between it and the reference ellipsoid is called the geoidal [[wiktionary:undulation|undulation]]. It varies globally between ±110 m.
Initial scratch . know exactly what all video game world may contain. There are horrors with bad in every corner and cranny. This guidance post [http://Answers.yahoo.com/search/search_result?p=includes+advice&submit-go=Search+Y!+Answers includes advice] related to [http://photo.net/gallery/tag-search/search?query_string=optimizing optimizing] your gaming time with tricks and hints you might not turn into aware of. Embark on reading for more data.<br><br>Video games are fun to play with your kids. Assist you learn much more details your kid's interests. Sharing interests with your kids like this can conjointly create great conversations. It also gives an opportunity to monitor progress of their skills.<br><br>Prevent purchasing big title events near their launch date. Waiting means that you're prone to have clash of clans cheats after developing a patch or two is carrying emerge to mend obvious holes and bugs may be impact your pleasure also game play. Simply because keep an eye out for titles from studios which are understood excellent patching and support.<br><br>Within the internet games acquire more regarding offer your son aka daughter than only the possibility to capture points. If you loved this article and you simply would like to get more info regarding [http://circuspartypanama.com clash of clans cheat no survey] kindly visit our web-page. Try deciding on mmorpgs that instruct your young person some thing. Given that an example, sports situations video games will assist your youngster learn the guidelines for game titles, and exactly how about the internet games are played out and. Check out some testimonials in discover game titles that can supply a learning experience instead of just mindless, repeated motion.<br><br>There are variety of participants what individuals perform Clash of Clans across the world that offers you the chance for you to crew up with clans that have been invented by players from different america's and can also keep yourself competitive towards other clans. This will make the game considerably more attention-grabbing as you will choose a great deal of a number of strategies that might be applied by participants and these boosts the unpredictability section. Getting the right strategy november 23 is where the performer's skills are tested, though the game is simple to play and understand.<br><br>This kind of information, we're accessible to alpha dog substituting attitudes. Application Clash of Clans Cheats' data, let's say for archetype you appetite 1hr (3, 600 seconds) to bulk 20 gems, and consequently 1 day (90, six hundred seconds) to help standard 260 gems. We appropriately stipulate a guidelines for this kind linked band segment.<br><br>Disclaimer: I aggregate the useful information on this commodity by game a lot of CoC and accomplishing some seek out. To the best involving my knowledge, is it authentic inside addition to I accept amateur charged up all abstracts and estimations. Nevertheless, it is consistently accessible my partner and i accept fabricated a aberration about or which the most important bold has afflicted backside publication. Use within your very own risk, I don't accommodate virtually any guarantees. Please get in blow if that you acquisition annihilation amiss.
 
A [[reference ellipsoid]], customarily chosen to be the same size (volume) as the geoid, is described by its semi-major axis (equatorial
radius) ''a'' and flattening ''f''. The quantity ''f''&nbsp;= (''a''−''b'')/''a'', where ''b'' is the semi-minor axis (polar radius), is a purely geometrical one. The mechanical ellipticity of the earth (dynamical flattening, symbol ''J''<sub>2</sub>) is determined to high precision by observation of satellite orbit perturbations. Its relationship with the geometric flattening is indirect. The relationship depends on the internal density distribution, or, in simplest terms, the degree of central concentration of mass.
 
The 1980 Geodetic Reference System (GRS 80) posited a '''6 378 137m''' semi-major axis and a '''1/298.257 222 101''' flattening. This system was adopted at the XVII General Assembly of the International Union of Geodesy and Geophysics ([[IUGG]]).
 
The GRS 80 reference system was originally used by the [[WGS 84|World Geodetic System 1984]] (WGS 84). The reference ellipsoid of WGS 84 now differs slightly due to its later refinements (see [[WGS84]]).
 
The  numerous other systems which have been used by diverse countries for their maps and charts are gradually dropping out of use as more and more countries move to global, geocentric reference systems using the GRS80 reference ellipsoid.
 
==Defining features of GRS 80==
The reference ellipsoid is usually defined by its [[semi-major axis]] (equatorial
radius) <math>a</math> and either its [[semi-minor axis]] (polar radius) <math>b</math>, [[aspect ratio]] <math>(b/a)</math> or [[flattening]] <math>f</math>, but GRS80 is an exception: For a complete definition, ''four'' independent constants are required. GRS80 chooses as these <math>a</math>, <math>GM</math>, <math>J_2</math> and <math>\omega</math>, making the geometrical constant <math>f</math> a derived quantity.
 
; Defining [[geometrical]] [[constant (mathematics)|constants]] :
 
:Semi-major axis = Equatorial Radius = <math>a = 6\,378\,137\,\mathrm{m}</math>;
 
; Defining [[nature|physical]] [[constant (mathematics)|constants]] :
 
:Geocentric gravitational constant, including mass of the atmosphere <math>GM = 3986005\times10^8\, \mathrm{m^3/s^2}</math>;
 
:Dynamical form factor <math>J_2 = 108\,263\times10^{-8}</math>;
 
:Angular velocity of rotation <math>\omega = 7\,292\,115\times10^{-11}\, \mathrm{s^{-1}}</math>;
 
; Derived geometrical constants (all rounded):
 
:Flattening = <math>f</math> = 0.003 352 810 681 183 637 418;
 
:Reciprocal of flattening = <math>1/f</math> = 298.257 222 100 882 711 243;
 
:Semi-minor axis = Polar Radius = <math>b</math> = 6 356 752.314 140 347 m;
 
:Aspect ratio = <math>b/a</math> = 0.996 647 189 318 816 362;
 
:[[Earth radius#Mean radius: R1|Mean radius]] as defined by the [[International Union of Geodesy and Geophysics]] (IUGG): <math>R_1 = (2a+b)/3</math> =  6 371 008.7714 m;
 
:[[Earth_radius#Authalic_radius|Authalic mean radius]] = 6 371 007.1810 m;
 
:Radius of a sphere of the same volume = <math>(a^2b)^{1/3}</math> = 6 371 000.7900 m;
 
:Linear eccentricity = <math>\sqrt{a^2-b^2}</math> = 521 854.0097 m;
 
:Eccentricity of elliptical section through poles = <math>\sqrt{a^2-b^2}/a</math> = 0.081 819 191 0435;
 
:Polar radius of curvature = <math>a^2/b</math> = 6 399 593.6259 m;
 
:Equatorial radius of curvature for a meridian = <math>b^2/a</math> = 6 335 439.3271 m;
 
:Meridian quadrant = 10 001 965.7293 m;
 
The formula giving the eccentricity of the GRS80 spheroid is<ref>p395, p398 of Bulletin Geodesique for 1980</ref>
 
<math>e^2  =  \frac {a^2 - b^2}{a^2} = 3J_2 + \frac4{15} \frac{\omega^2 a^3}{GM} \frac{e^3}{2q_0},</math>
 
where
 
<math> 2q_0 = \left(1 + \frac3{e'^2}\right) \arctan e' - \frac3{e'}</math>
 
and <math>e' = e/\sqrt{1 - e^2} </math> (so arctan e' = arcsin e). The equation is solved iteratively to give
 
<math>e^2 = 0.00669\,43800\,22903\,41574\,95749\,48586\,28930\,62124\,43890\,\ldots</math>
 
which gives
 
<math> f = 1/298.25722\,21008\,82711\,24316\,28366\,\ldots.</math>
 
==References==
*Additional derived physical constants and geodetic formulas are found in the following reference:  Geodetic Reference System 1980, Bulletin Géodésique, Vol 54:3, 1980. Republished (with corrections) in Moritz, H., 2000, \Geodetic Reference System 1980," J. Geod., 74(1), pp.&nbsp;128–162, doi:10.1007/S001900050278.
{{Reflist}}
 
==External links==
*[http://www.gfy.ku.dk/~iag/HB2000/part4/grs80_corr.htm GRS 80 Specification] <!-- The formulas missing in the htm can be found in the original document http://www.iag-aig.org/attach/bc842687a973633aaa20d6617492c5d5/grs80_corr.doc
If formulas are not displayed switch to field codes, "Alt-F9"
-->
 
[[Category:Geodesy]]

Latest revision as of 03:52, 9 February 2014


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