Geodesy

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File:RotEarth.gif??? Determining the Size and Shape of Earth: [[1]]

(Source of picture: unknown. Please claim ownership.)

A thought Model: Explosions creates gases and dust. The 'Big Bang' is thought to be the largest explosion we know off creating imense amounts of stellar gases and dust. Gases and dust like all matter particles posess attraction properties. The result is that gases and dust accumulate in lumps, over time forming what we know as stellar gas/dust clouds, stars and planets. Each of these compounding the attraction forces into what we now for example perceive as 'gravity' on Earth. The accumulation process, although initially at random, proceeded locally in randomly preferred directions. This together with the increasing gravity at local centres forced the process to become rotational. Galaxies, Stars and planets are rotating as a result around their local gravitational center, being modified by new gases and dust from exploding stars over time.

Keeping our thought on the lump of matter we call Earth, being of uniform material and gravitational forces alone, Earth would be an almost perfect sphere of quite enormous size. Since Earth rotates on it's own about an axis we call 'polar axis' or 'earth axis', one more force is created: a Centrifugal Force (outward), pulling against the gravitational force (inward). Since the centrifugal force grows with the distance away from the rotation center (Earth's rotational axis), it's pull is smalles at the poles (zero) and largest at the equator, distorting the perfect sphere to what we could call an 'Ellipsoid' (think an ellipse rotated about it's short axis).

Futher, Earth, in particular its crust, is not composed of uniform material. There are accumulations of material, the continents and their plates, and ocean basins. Each accumulation of material or lack of it alters the shape of the field of gravitational forces. The gravitational force field of Earth is further modified by the variation of density of material at a more local level. Iron ore bodies create a stronger attraction force than salt domes. (Useful in geological exploration for mineral deposites).

All this, including planetary tides, create a shape of Earth of imense complexity, too complex for exact gedodetic and mapping applications describing it mathematically.

We are left with using 'best approximations' for the size and shape of Earth in practical use. (See 'Geodesy for the layman' as html[2] or as pdf [3].)

Since the shape and size of Earth can be approximately determined based on measurement, the quality and spatial distribution of these influence the exactness of such approximations. In order to obtain an exact result an infinate number of local measurements with zero measurement error would be needed; a nearly impossible task. With passing time, more measurments become available at technological higher measurement accuracy leading to refinements of the definition of Shape and Size of Earth. Various sets of sch approximations of the shape of Earth (the Ellisoid / Spheroid) have been derived in the past and present and various more will be established and used in future.


[A bit of History]

The original idea of Earth being a near spherical rotating body goes even further back in time than the above link shows; to my knowledge this idea originated in ancient babylonian times well before.


What Geodesy delivers for Mapping and GIS

Geodetic surveys deliver through measurment and computation the definition of the SIZE and Shape of EARTH in form of a mathematical description of a best fitting Ellipsoid (Spheriod is another name for this), best fitting to Earth's Geoid in general or for selected regions (e.g. contries or continents).

This is achieved through defining parameters for an ellipse thought to be rotating about its short axis (polar axis). Two parameters are defined: the 'major semi axis (a)' and a measure relating to the 'minor semi axis (b)' in form of what is called the ellipsiodal 'flattening (f)'.

You find these parameters in *.prj files for example as

GEOGCS["GRS 1980(IUGG, 1980)",DATUM["unknown",SPHEROID["GRS80",6378137,298.257222101]],PRIMEM["Greenwich",0],UNIT["degree",0.0174532925199433]]

Semi major Axis a = 6378137.0 metres Flattening 1/f = 298.257222101

or for a UTM map projection covering Eastern Australia also using GRS80:

PROJCS["UTM Zone 55, Southern Hemisphere",GEOGCS["GRS 1980(IUGG, 1980)",DATUM["D_unknown",SPHEROID["GRS80",6378137,298.257222101]],PRIMEM["Greenwich",0],UNIT["Degree",0.017453292519943295]],PROJECTION["Transverse_Mercator"],PARAMETER["latitude_of_origin",0],PARAMETER["central_meridian",147],PARAMETER["scale_factor",0.9996],PARAMETER["false_easting",500000],PARAMETER["false_northing",10000000],UNIT["Meter",1]]


f is defined as f = (a-b)/a where b = minor semi axis length

The data above is valid for the ellipsoid called GRS80 as accepted by IUGG (International Union of Geodesy and Geophysics [4]) as of 1980, currently widely in use (2009).


For some more Ellispoid definitions in use in past and at present see [5] or the list below:

Name, Major semi axis a, flattening as 1/f, Delta a, Delta f

Airy, 6377563.396, 299.3249646, 573.604, 0.11960023

Australian National, 6378160.0, 298.25, -23.0, -0.00081204

Bessel 1841, 6377397.155, 299.1528128, 739.845, 0.10037483

Bessel 1841 (Nambia), 6377483.865, 299.1528128, 653.135, 0.10037483

Clarke 1866, 6378206.4, 294.9786982, -69.4, -0.37264639

Clarke 1880, 6378249.145, 293.465, -112.145, -0.54750714

Everest, 6377276.345, 300.8017, 860.655, 0.28361368

Fischer 1960 (Mercury), 6378166.0, 298.3, -29.0, 0.00480795

Fischer 1968, 6378150.0, 298.3, -13..0, 0.00480795

GRS 1967, 6378160.0, 298.247167427, -23.0, -0.00113048

GRS 1980, 6378137, 298.257222101, 0.0, -0.00000016

Helmert 1906, 6378200.0, 298.3, -63.0, 0.00480795

Hough, 6378270.0, 297.0, -133.0, -0.14192702

International, 6378388.0, 297.0, -251.0.0, -0.14192702

Krassovsky, 6378245.0, 298.3, -108.0, 0.00480795

Modified Airy, 6377340.189, 299.3249646, 796.811, 0.11960023

Modified Everest, 6377304.063, 300.8017, 832.937, 0.28361368

Modified Fischer 1960, 6378155.0, 298.3, -18.0, 0.00480795

South American 1969, 6378160.0, 298.25, -23.0, -0.00081204

WGS 60, 6378165.0, 298.3, -28.0, 0.00480795

WGS 66, 6378145.0, 298.25, -8.0, -0.00081204

WGS-72, 6378135.0, 298.26, 2.0, 0.0003121057

WGS-84, 6378137.0, 298.257223563, 0.0, 0.0

(Source: [6])


For an Australian view about differences between coordinate systems and their underlying Ellipsoid choice see [7].

For a nice overview about "Geodetic Datums and Coordinates" see [8] or explore any of the links on the left of either of these two links.


Summary

File:Geoids.jpg

The above sketch (a polar cross section) explains a few of the surfaces involved in geodetic approaches and in Mapping:


This page may contain inconsistencies and errors. Please correct or complain to --Gngdowid 04:53, 25 December 2009 (UTC)



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