Back to Notes_on_Map_Geometry_and_Projections

**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.

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**

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

- The
**Topographic Surface**(not shown) is the natural surface of Earth we walk on and which holds most of the features we like to show on maps.

Imagine an even more irregular line drawn meandering about the Geoid line, some times on the out side (land surface), some time inside (sea floor surface or depressions). - The
**Geoid**, some times also referred to as**Spheroid**, is a surface of equi-potential gravitational force at Mean Sea Level (MSL). This is the surface the oceans would take on if there would be no influence by tides and wind pressure and constant sea water temperature. This surface is defined by a constant gravity value, so it also exists beneath land masses.

The Geoid (MSL) has several important properties which led to it being used as "mapping reference surface": (1) it can physically be found through measurement and (2) it is the sink of all land surface water. The latter makes it useful as "Height Datum". **WGS84**is a mathematically defined best fitting ellipsoidal replacement surface for the Geoid, the currently accepted international geocentric ellipsoid.

It has been derived from measurements such that its center coincides with Earth's gravitational center and its surface best fits Earth's Geoid.

Advantage: WGS84, with best current knowledge, complements the physical ascpects of satellite navigation. Satellites orbit about Earth's gravitational center. For example, GPS measurements directly correspond to the definition of this Ellipsoid.

Disadvantage: In some places the deviation between the Geoid and the WGS84 ellipsoid (called 'Geoid Undulation') is larger than in comparable locally defined ellipsoids (e.g. AGD84). This leads to the requirement of major corrections of GPS derived heights to meet MSL defined heights.**AGD84**, an example of a locally best fitting ellipsoid, having been used until 31-12-1999 as mapping datum in Australia. Since 1-1-2000 Australia also uses WGS84 for GPS compatibility reasons.

AGD84's center is offset from Earth's gravitational center by about 200m. Maps based on AGD84 compared to those based on WGS84 show features at coordinate locations different by also about 200m. Using maps and GIS data from both epochs (before and after 1-1-2000) requires special care. (Brisbane 'South Bank' park may show on the north side of the River)

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