Geoscience Reference
In-Depth Information
z
#
= const
u
P
z
u
O
#
¯
E
xy - plane
F
1
F
2
y
x
z
P
uE
2
+
2
sin
#
¸
¸
= const
y
x
Fig. 1.10. Ellipsoidal-harmonic coordinates: view from the front (top)
and view from above (bottom)
ellipsoid,
ϑ
is the complement of the “reduced latitude”
β
of
P
with respect
to this ellipsoid (the definition is seen in Fig. 1.10), i.e.,
ϑ
=90
◦
−
β
,and
λ
is the geocentric longitude in the usual sense.
It should be carefully noted that in spherical harmonics
ϑ
is the polar
distance, which is nothing but the complement of the
geocentric
latitude,
whereas in ellipsoidal-harmonic coordinates
ϑ
is the complement of the
re-
duced
latitude denoted by
β
.
The ellipsoidal-harmonic coordinates
u, ϑ, λ
are related to
x, y, z
by
x
=
√
u
2
+
E
2
sin
ϑ
cos
λ,
y
=
√
u
2
+
E
2
sin
ϑ
sin
λ,
(1-150)
z
=
u
cos
ϑ,
