Theoretical gravity
Encyclopedia
In geodesy
and geophysics
, theoretical gravity is a means to compare the true gravity on the Earth's surface with a physically smoothed model. The most common model of a smoothed Earth is the Earth ellipsoid
.
Despite of the fact that the exact density layers in the Earth's interior are still unknown, the theoretical gravity g of its level surface can be computed by a relative simple formula, which is called the International Gravity Formula. It refers to a mean Earth ellipsoid
, the parameters of which are set by international convention. It shows the gravity at a smoothed Earth's surface as a function of geographic latitude φ; the actual formula is
The term 0.0516323 is called gravity flattening (abbreviated β). As a physically defined form parameter it corresponds to the geometrical flattening
f of the earth ellipsoid.
Up to the 1960s, the formula either of the Hayford ellipsoid
(1924) or of the famous German geodesist Helmert (1906) was used. Hayford has an axis difference to modern values of , Helmert only . The Helmert formula is
A slightly different formula for g as a function of latitude is the WGS (World Geodetic System
) 1984 Ellipsoidal Gravity Formula:
The difference between the WGS-84 formula and Helmert's equation is less than 0.68 ppm
or .
Geodesy
Geodesy , also named geodetics, a branch of earth sciences, is the scientific discipline that deals with the measurement and representation of the Earth, including its gravitational field, in a three-dimensional time-varying space. Geodesists also study geodynamical phenomena such as crustal...
and geophysics
Geophysics
Geophysics is the physics of the Earth and its environment in space; also the study of the Earth using quantitative physical methods. The term geophysics sometimes refers only to the geological applications: Earth's shape; its gravitational and magnetic fields; its internal structure and...
, theoretical gravity is a means to compare the true gravity on the Earth's surface with a physically smoothed model. The most common model of a smoothed Earth is the Earth ellipsoid
Earth ellipsoid
An Earth ellipsoid is a mathematical figure approximating the shape of the Earth, used as a reference frame for computations in geodesy, astronomy and the geosciences...
.
Despite of the fact that the exact density layers in the Earth's interior are still unknown, the theoretical gravity g of its level surface can be computed by a relative simple formula, which is called the International Gravity Formula. It refers to a mean Earth ellipsoid
Earth ellipsoid
An Earth ellipsoid is a mathematical figure approximating the shape of the Earth, used as a reference frame for computations in geodesy, astronomy and the geosciences...
, the parameters of which are set by international convention. It shows the gravity at a smoothed Earth's surface as a function of geographic latitude φ; the actual formula is
The term 0.0516323 is called gravity flattening (abbreviated β). As a physically defined form parameter it corresponds to the geometrical flattening
Flattening
The flattening, ellipticity, or oblateness of an oblate spheroid is a measure of the "squashing" of the spheroid's pole, towards its equator...
f of the earth ellipsoid.
Up to the 1960s, the formula either of the Hayford ellipsoid
Hayford ellipsoid
The Hayford ellipsoid is a geodetic reference ellipsoid, named after the US geodesist John Fillmore Hayford , which was introduced in 1910. The Hayford ellipsoid was also referred to as the International ellipsoid 1924 after it had been adopted by the International Union of Geodesy and Geophysics...
(1924) or of the famous German geodesist Helmert (1906) was used. Hayford has an axis difference to modern values of , Helmert only . The Helmert formula is
A slightly different formula for g as a function of latitude is the WGS (World Geodetic System
World Geodetic System
The World Geodetic System is a standard for use in cartography, geodesy, and navigation. It comprises a standard coordinate frame for the Earth, a standard spheroidal reference surface for raw altitude data, and a gravitational equipotential surface that defines the nominal sea level.The latest...
) 1984 Ellipsoidal Gravity Formula:
The difference between the WGS-84 formula and Helmert's equation is less than 0.68 ppm
PPM
- Culture :*Peter, Paul and Mary, a 1960s folk music trio*Picture Postcard Monthly, a magazine for collectors of postcards*Please Please Me, the first album by The Beatles- Health :*Permanent pacemaker or artificial pacemaker...
or .
Literature
- Karl LederstegerKarl LederstegerKarl Ledersteger was an important geodesist and geophysicist.After studies of astronomy, mathematics and geodesy he worked in Germany and later in the National Survey of Austria. Later he set up the scientific department of the Federal Office for Metrology and Survey , Vienna...
: Astronomische und physikalische GeodäsiePhysical geodesyPhysical geodesy is the study of the physical properties of the gravity field of the Earth, the geopotential, with a view to their application in geodesy.-Measurement procedure:...
. Handbuch der Vermessungskunde Band 5, 10. Auflage. Metzler, Stuttgart 1969 - B.Hofmann-Wellenhof, Helmut Moritz: Physical Geodesy, ISBN 3-211-23584-1, Springer-Verlag Wien 2006.