Geoscience Reference
In-Depth Information
are first and second numerical eccentricity. As introduced in (5-28),
p
=
√
X
2
+
Y
2
. Actually, there is no reason why these formulas are less popular
than the iterative procedure since there is no significant difference between
the two methods. Computation methods with neither iteration nor approx-
imation are, e.g., given by Sunkel (1977) and Zhu (1993).
5.6.2
Ellipsoidal, ellipsoidal-harmonic, and spherical
coordinates
Even if we have several times pointed out the different definitions, it is
very important to stress once more the need not to confuse the following
coordinate triples (see Fig. 5.6):
•
ellipsoidal coordinates:
ϕ, λ, h
;
•
ellipsoidal-harmonic coordinates:
β, λ, u
,
alternatively:
ϑ
ellipsoidal-harmonic
,λ,u
;
•
spherical coordinates:
ϕ, λ, r
, alternatively:
ϑ
spherical
,λ,r
.
The longitude
λ
is the same in all triples. The ellipsoidal coordinates latitude
ϕ
and longitude
λ
are sometimes also denoted
geodetic latitude
and
geodetic
z
s uE
+
2
2
P
P
h
#
Q
ell-har.
r
#
sph.
¯
'
'
F
1
F
2
x, plane
E= ab
-
uE
+
2
2
2
2
u
Fig. 5.6. Ellipsoidal, ellipsoidal-harmonic, and spherical coordinates
