Geography Reference
In-Depth Information
M
KL
:= 1
2 G MN ( D K G NL + D L G KN
2 × 2 × 2
D N G KL )
R
K, L, M
∈{
1 , 2
}
.
In addition to this ID card, we here present the central characteristics of the geodetic ellipsoidal
system: see Table 8.1 , “Geodetic Reference System 1980” (Bulletin Geodesique, 58, pp. 388-398,
1984) versus “World Geodetic Datum 2000” (Journal of Geodesy, 73, pp. 611-623, 1999).
Tab l e 8 . 1
“Geodetic Reference System 1980” versus “World Geodetic Datum 2000”
Moritz ( 1984 )
Grafarend and Ardalan ( 1999 )
(“zero frequency tide geoid”)
Semi-major axis A 1
6,378,137m
6,378,136.602
±
0.053m
Semi-minor axis A 2
6,356,752.3141m
6,356,751.860
±
0.052m
Relative eccentricity
0.00669438002290
0.00669439798491
) /A 1
Absolute eccentric ity
E 2 =( A 1
A 2
±
521,854.0097m
521,854.674
0.015m
= A 1
A 2
Axis difference A 1
A 2
21,384.686m
21,384.742m
Flattening F =( A 1
A 2 ) /A 1
0.00335281068118
0.00335281969240
Inverse flattening
298.257222101
298.256420489
F 1 = A 1 / ( A 1
A 2 )
8-1 General Mapping Equations
Setting up general equations of the mapping “ellipsoid-of-revolution to plane”: azimuthal
projections in the normal aspect (polar aspect).
There are again two basic postulates which govern the setup of general equations of mapping the
ellipsoid-of-revolution E
A 1 ,A 2 of semi-major axis A 1 and semi-minor axis A 2 , which are charac-
terized by A 1 >A 2 , to a tangential plane T E
A 1 ,A 2 attached to a point X ∈ T E
A 1 ,A 2 .Letthe
tangential plane be covered by polar coordinates
{
α, r
}
. Then the following postulates are valid.
Postulate.
The polar coordinate α , which is also called azimuth , is identical to the ellipsoidal longitude, i.e.
α = Λ .
End of Postulate.
 
Search WWH ::




Custom Search