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.
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