Geoscience Reference
In-Depth Information
|| z
n
n'
-
¸
»
-
¸
´
P
'
¸
Fig. 2.13. The deflection of the vertical as illustrated by means of a
unit sphere with center at
P
define the direction of the plumb line
n
or of the gravity vector
g
,canbe
determined by astronomical measurements. The ellipsoidal coordinates (or
geodetic coordinates in the sense of geographical coordinates on the ellip-
soid) given by the direction of the ellipsoidal normal
n
have been denoted
by
ϕ
and
λ
- these coordinates should not be confused with the ellipsoidal-
harmonic coordinates of Sect. 1.15 ! It is evident that this
λ
is identical with
the geocentric longitude (and also with the ellipsoidal-harmonic longitude).
Thus,
geoidal normal
n
, astronomical coordinates Φ
,
Λ;
(2-229)
ellipsoidal normal
n
, ellipsoidal coordinates
ϕ, λ .
From Fig. 2.13, we read
ξ
=Φ
− ϕ,
(2-230)
η
=(Λ
−
λ
)cos
ϕ.
It is also possible to compare the vectors
g
and
γ
at the same point
P
.Then
we get the
gravity disturbance vector
δ
g
=
g
P
−
γ
P
.
(2-231)