Geography Reference
In-Depth Information
x
∗
,y
∗
,z
∗
}
in an Earth fixed equatorial reference system
f
0
The transformation of Cartesian coordinates
{
=
{
in the
elliptic reference system is described by the following rela-
tions.
f
1
0
,f
2
0
,f
3
0
}
into Cartesian coordinates
{
x, y, z
}
⎡
⎤
⎡
⎤
⎡
⎤
x
y
z
x
y
z
Δx
Δy
Δz
⎣
⎦
=R
T
(
δα, δβ, Δλ
)
⎣
⎦
+
⎣
⎦
,
(J.86)
R
T
δα, δβ
(
Δλ
)=
=R
3
(
Δλ
)R
2
(
δβ
)R
1
(
δα
)=
⎡
⎤
cos
Δλ
sin
Δλ δβ
cos
Δλ
+
δα
sin
Δλ
−
⎣
⎦
.
=
sin
Δλ
cos
Δλ δβ
sin
Δλ
−
δα
cos
Δλ
(J.87)
δβ
δα
1
The numbers that follow below have been determined in the
Ph.D. Thesis of B. Eitschberger (Bonn 1978). The terms
{
Δλ, δα, δβ
}
define the orientation parameters, and the
terms
{
Δx, Δy, Δz
}
define the translation parameters.
14
◦
53
42
,δα
=0
.
16
,δβ
=0
.
10
,
Δλ
=
−
(J.88)
Δ
x
=
−
5
.
9cm
,Δy
=
−
2
.
4cm
,Δz
=1
.
8cm
.
(J.89)
J-33 Form Parameters of a Surface Normal Triaxial Ellipsoid: Earth,
Moon, Mars, Phobos, Amalthea, Io, Mimas
The following is a list of reference figures of the Earth, the Earth's moon, and other celestial
bodies which are pronounced
triaxially
(Table
J.3
).
As an example, we illustrate by Fig.
J.7
an azimuthal mapping of the triaxial ellipsoid of the
Earth, which is equidistant along the meridian parameterized by polar coordinates of type (
J.90
)
referred to the elliptic integral
E
(
·,π/
2). Compare with the Diploma Thesis of
Mueller
(
1991
).
α
= arctan
1
E
12
tan
Λ
,
−
E
12
sin
2
Λ
E
E
13
−
.
r
=
A
1
1
E
12
sin
2
Λ
1
− E
12
sin
2
Λ
,
π
2
−
(J.90)
Search WWH ::
Custom Search