Everything about Figure Of The Earth totally explained
The expression
figure of the Earth has various meanings in
geodesy according to the way it's used and the precision with which the Earth's size and shape is to be defined. The actual topographic surface is most apparent with its variety of land forms and water areas. This is, in fact, the surface on which actual
Earth measurements are made. It isn't suitable, however, for exact mathematical computations because the formulas which would be required to take the irregularities into account would necessitate a prohibitive amount of computations. The topographic surface is generally the concern of topographers and hydrographers.
The
Pythagorean concept of a
spherical Earth offers a simple surface which is mathematically easy to deal with. Many astronomical and navigational computations use it as a surface representing the Earth. While the sphere is a close approximation of the true figure of the Earth and satisfactory for many purposes, to the geodesists interested in the measurement of long distances—spanning continents and oceans—a more exact figure is necessary. Closer approximations range from modelling the shape of the entire Earth as an
oblate spheroid or an oblate ellipsoid to the use of
spherical harmonics or local approximations in terms of local
reference ellipsoids. The idea of a planar or flat surface for Earth, however, is still acceptable for surveys of small areas as local
topography is more important than the curvature. Plane-table surveys are made for relatively small areas and no account is taken of the curvature of the Earth. A survey of a city would likely be computed as though the Earth were a plane surface the size of the city. For such small areas, exact positions can be determined relative to each other without considering the size and shape of the total Earth.
In the mid- to late- 20th century, research across the geosciences contributed to drastic improvements in the accuracy of the Figure of the Earth. The primary utility (and the motivation for funding, mainly from the military) of this improved accuracy was to provide geographical and gravitational data for the
inertial guidance systems of
ballistic missiles. This funding also drove the expansion of geoscientific disciplines, fostering the creation and growth of various geoscience departments at many universities.
Ellipsoid of revolution
Since the Earth is in fact flattened slightly at the poles and bulges somewhat at the equator, the geometrical figure used in geodesy to most nearly approximate the shape of the Earth is an
ellipsoid of revolution. The ellipsoid of revolution is the figure which would be obtained by rotating an ellipse about its shorter axis. An ellipsoid of revolution describing the figure of the Earth is called a
reference ellipsoid.
An ellipsoid of revolution is uniquely defined by specifying two dimensions. Geodesists, by convention, use the semimajor axis and
flattening. The size is represented by the radius at the equator—the semimajor axis—and designated by the letter
. The shape of the ellipsoid is given by the flattening,
, which indicates how closely the ellipsoid approaches a spherical shape. The difference between the reference ellipsoid representing the Earth and a sphere is very small, only one part in 300 approximately.
For such a
flattened ellipsoid, the polar radius of curvature is larger than the equatorial
» ,
even though the Earth's surface is closer to the Earth's centre at the poles than at the equator. Conversely, the equator's vertical radius of curvature is smaller than the polar
» .
This circumstance has formed the basis for attempts to determine the flattening of the mean
Earth ellipsoid by so-called
grade measurements.
Historical Earth ellipsoids
The reference ellipsoid models listed below have had utility in geodetic work and many are still in use. The older ellipsoids are named for the individual who derived them and the year of development is given. In 1887 the English mathematician Col
Alexander Ross Clarke CB FRS RE was awarded the Gold Medal of the Royal Society for his work in determining the figure of the Earth. The international ellipsoid was developed by
John Fillmore Hayford in 1910 and adopted by the International Union of Geodesy and Geophysics (IUGG) in 1924, which recommended it for international use.
At the 1967 meeting of the IUGG held in Lucerne, Switzerland, the ellipsoid called GRS-67 (
Geodetic Reference System 1967) in the listing was recommended for adoption. The new ellipsoid wasn't recommended to replace the International Ellipsoid (1924), but was advocated for use where a greater degree of accuracy is required. It became a part of the GRS-67 which was approved and adopted at the 1971 meeting of the IUGG held in Moscow. It is used in Australia for the Australian Geodetic Datum and in South America for the South American Datum 1969.
| Reference ellipsoid name |
Equatorial radius (m) |
Polar radius (m) |
Inverse flattening |
Where used |
| Modified Everest (Malaya) Revised Kertau |
6,377,304.063 |
6,356,103.038993 |
300.801699969 |
|
| Timbalai |
6,377,298.56 |
6,356,097.55 |
300.801639166 |
|
| Everest Spheroid |
6,377,301.243 |
6,356,100.228 |
300.801694993 |
|
| Maupertuis (1738) |
6,397,300 |
6,363,806.283 |
191 |
France |
| Everest (1830) |
6,377,276.345 |
6,356,075.413 |
300.801697979 |
India |
| Airy (1830) |
6,377,563.396 |
6,356,256.909 |
299.3249646 |
Britain |
| Bessel (1841) |
6,377,397.155 |
6,356,078.963 |
299.1528128 |
Europe, Japan |
| Clarke (1866) |
6,378,206.4 |
6,356,583.8 |
294.9786982 |
North America |
| Clarke (1880) |
6,378,249.145 |
6,356,514.870 |
293.465 |
France, Africa |
| Helmert (1906) |
6,378,200 |
6,356,818.17 |
298.3 |
| Hayford (1910) |
6,378,388 |
6,356,911.946 |
297 |
USA |
| International (1924) |
6,378,388 |
6,356,911.946 |
297 |
Europe |
| NAD 27 |
6,378,206.4 |
6,356,583.800 |
294.978698208 |
North America |
| Krassovsky (1940) |
6,378,245 |
6,356,863.019 |
298.3 |
Russia |
| WGS66 (1966) |
6,378,145 |
6,356,759.769 |
298.25 |
USA/DoD |
| Australian National (1966) |
6,378,160 |
6,356,774.719 |
298.25 |
Australia |
| New International (1967) |
6,378,157.5 |
6,356,772.2 |
298.24961539 |
|
| GRS-67 (1967) |
6,378,160 |
6,356,774.516 |
298.247167427 |
|
| South American (1969) |
6,378,160 |
6,356,774.719 |
298.25 |
South America |
| WGS-72 (1972) |
6,378,135 |
6,356,750.52 |
298.26 |
USA/DoD |
| GRS-80 (1979) |
6,378,137 |
6,356,752.3141 |
298.257222101 |
|
| NAD 83 |
6,378,137 |
6,356,752.3 |
298.257024899 |
North America |
| (1984) |
6,378,137 |
6,356,752.3142 |
298.257223563 |
Global GPS |
| IERS (1989) |
6,378,136 |
6,356,751.302 |
298.257 |
|
| IERS (2003) |
6,378,136.6 |
6,356,751.9 |
298.25642 |
Global ITRS |
The GRS-80 (Geodetic Reference System 1980) as approved and adopted by the IUGG at its Canberra, Australia meeting of 1979 is originally defined based on the equatorial radius (semi-major axis of Earth ellipsoid)
, total mass
, dynamic form factor
and angular velocity of rotation
, making the inverse flattening
a derived quantity. The minute difference in
seen between GRS-80 and WGS-84 was produced by inaccurate numerical evaluation from the defining constants...
Some of the above ellipsoid models are actually
geodetic datums: for example, while GRS-80 defines only the geometric shape of its ellipsoid and a normal gravity field formula to go with it, WGS-84 defines a complete geodetic reference system realized in the terrain. Similarly, the older ED-50 (
European Datum 1950) is based on the Hayford or International Ellipsoid.
Note that the same ellipsoid may be known by different names, and it's best to mention the values for full identification.
More complicated figures
The possibility that the Earth's equator is an ellipse rather than a circle and therefore that the ellipsoid is triaxial has been a matter of scientific controversy for many years. Modern technological developments have furnished new and rapid methods for data collection and since the launch of
Sputnik 1, orbital data have been used to investigate the theory of ellipticity.
A second theory, more complicated than triaxiality, proposed that observed long periodic orbital variations of the first Earth satellites indicate an additional depression at the south pole accompanied by a bulge of the same degree at the north pole. It is also contended that the northern middle latitudes were slightly flattened and the southern middle latitudes bulged in a similar amount. This concept suggested a slightly pear-shaped Earth and was the subject of much public discussion. Modern geodesy tends to retain the ellipsoid of revolution and treat triaxiality and pear shape as a part of the
geoid figure: they're represented by the spherical harmonic coefficients
, respectively, corresponding to degree and order numbers 2.2 for the triaxiality and 3.0 for the pear shape.
Geoid
It was stated earlier that measurements are made on the apparent or topographic surface of the Earth and it has just been explained that computations are performed on an ellipsoid. One other surface is involved in geodetic measurement: the
geoid. In geodetic surveying, the computation of the geodetic coordinates of points is commonly performed on a
reference ellipsoid closely approximating the size and shape of the Earth in the area of the survey. The actual measurements made on the surface of the Earth with certain instruments are however referred to the
geoid. The ellipsoid is a mathematically defined regular surface with specific dimensions. The geoid, on the other hand, coincides with that surface to which the oceans would conform over the entire Earth if free to adjust to the combined effect of the Earth's mass attraction (
gravitation) and the centrifugal force of the Earth's rotation. As a result of the uneven distribution of the Earth's mass, the geoidal surface is irregular and, since the ellipsoid is a regular surface, the separations between the two, referred to as geoid undulations, geoid heights, or geoid separations, will be irregular as well.
The
geoid is a surface along which the gravity potential is everywhere equal and to which the direction of gravity is always perpendicular. The latter is particularly important because optical instruments containing levelling devices are commonly used to make geodetic measurements. When properly adjusted, the vertical axis of the instrument coincides with the direction of gravity and is, therefore, perpendicular to the geoid. The angle between the
plumb line which is perpendicular to the geoid (sometimes called "the vertical") and the perpendicular to the ellipsoid (sometimes called "the ellipsoidal normal") is defined as the
deflection of the vertical. It has two components: an east-west and a north-south component.
Earth rotation and Earth's interior
Determining the exact figure of the Earth isn't only a
geodetic operation or a task of
geometry, but is also related to
geophysics. Without any idea of the
Earth's interior, we can state a "constant density" of 5.515 g/cm³ and, according to theoretical arguments (see
Leonhard Euler,
Albert Wangerin, etc.), such a body rotating like the Earth would have an
flattening of 1:230.
In fact the measured flattening is 1:298.25, which is more similar to a sphere and a strong argument that the
Earth's core is
very compact. Therefore the
density must be a function of the depth, reaching from about 2.7 g/cm³ at the surface (rock density of
granite, limestone etc. — see regional
geology) up to approximately 15 within the inner core. Modern
seismology yields a value of 16 g/cm³ (
iron or hydrogen) at the center of the earth.
Global and regional gravity field
Another implication to the physical exploration of the Earth's interior is the
gravity field which can be measured very exactly at the surface and by
satellites. The true
vertical doesn't correspond to the theoretical one (in fact the
deflection amounts from 2" to 50") because the
topography and all
geological masses are slightly disturbing the gravity field. Therefore the gross structure of the
earth's crust and mantle can be determined by geodetic-geophysical models of the subsurface.
Earth's curvature
Since the Earth isn't exactly spherical, its
curvature varies with location.
Further Information
Get more info on 'Figure Of The Earth'.
|
External Link Exchanges
Do you know how hard it is to get a link from a large encyclopaedia? Well we're different and will prove it. To get a link from us just add the following HTML to your site on a relevant page:
<a href="http://figure_of_the_earth.totallyexplained.com">Figure of the Earth Totally Explained</a>
Then simply click through this link from your web page. Our crawlers will verify your link, extract the title of your web page and instantly add a link back to it. If you like you can remove the words Totally Explained and embed the link in article text.
As long as your link remains in place, we'll keep our link to you right here. Please play fair - our crawlers are watching. Your site must be closely related to this one's topic. Any kind of spamming, dubious practises or removing the link will result in your link from us being dropped and, potentially, your whole site being banned. |
