Geoscience Reference
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|| 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,
(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)
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