Where,
g
e
= Normal gravity at the equator
= 978032.67714 mgal
k = 0.00193185138639
e
2
= 0.00669437999013.
B.5 THE EARTH GRAVITATIONAL MODEL
The Earth Gravitational Model (EGM) of the WGS 84 is a spherical harmonic expan
sion of the earth s gravitational potential and is defined complete through degree (n)
and order (m) 180, comprising 32.755 coefficients. However, only the coefficients
through n = m = 18 are unclassified
3
.
Accuracy values are not available for all the WGS 84 EGM coefficients; however, an error
covariance matrix is available only for coefficients through n = m = 41, which were
determined from the weighted least squares solution.
B.6 THE GEOID
In addition to the earth s geometric surface or figure, the WGS 84 geoid, as the equi
potential figure of the earth (also approximately by mean sea level over the oceans), is
defined as
so many meters above (+N) or below ( N) the WGS 84 ellipsoid, where "N"
is known as geoidal height or undulation.
The worldwide geoidal heights were calculated using the WGS 84 EGM through n = m
= 180, and they can also be depicted as a contour chart (showing deviations from the
WGS 84 ellipsoid) or as a grid of desire density. Figure B 2 shows a worldwide WGS
84 geoid chart developed from a worldwide 1 degree x 1 degree grid using the
unclassified EGM coefficients through n = m = 18.
The Root Mean Square (RMS) geoidal height for WGS 84, taken worldwide, is 30.5
meters and the error ranges from +2 to +6 meters (1s). The accuracy of the WGS 84
geoid is better than +4 meters over approximately 93% of the globe.
B.7 RELATIONSHIP WITH LOCAL GEODETIC DATUMS
Counting islands and/or other "astro" datums, the number of local geodetic datums
available for MC&G; requirements and applications exceeds several hundred. If the
inherent technical difficulties of dealing with these numerous local datums, e ach
defined with its own specifications and basic limitations, are considered in daily usage,
the picture is just too complex and almost chaotic.
B 5
<< < GO > >>