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geopotential
surface
W= P = const.
P
N P
Q
spheropotential
surface
U= P = const.
P 0
geoid W= 0
N
Q 0
ellipsoid U= 0
Fig. 2.15. Geopotential and spheropotential surfaces
are often called geopotential surfaces ; the level surfaces of the normal gravity
field, the surfaces
U = constant ,
(2-284)
are called spheropotential surfaces .
We consider now the point P outside the earth (Fig. 2.15) and denote
the geopotential surface passing through it by
W = W P .
(2-285)
There is also a spheropotential surface
U = W P
(2-286)
of the same constant W P . The normal plumb line through P intersects this
spheropotential surface at the point Q , which is said to correspond to P .
We see that the level surfaces W = W P and U = W P are related to each
other in exactly the same way as are the geoid W = W 0 and the reference
ellipsoid U = W 0 . If, therefore, the gravity anomaly is defined by
g P
= g P
γ Q ,
(2-287)
as in Sect. 2.12, then all derivations and formulas of that section also apply
for the present situation, the geopotential surface W = W P replacing the
geoid W = W 0 , and the spheropotential surface U = W P replacing the
ellipsoid U = W 0 . This is also the reason why (2-271) applies at P as well
as at the geoid.
Note that P in Sect. 2.12 is a point at the geoid, which is denoted by P 0
in Fig. 2.15.
This situation will be taken up again in Chap. 8, in the context of Molo-
densky's problem.
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