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canonlybeusedfor
δ
g
so that
γ
u
and
γ
β
must be computed by the rigorous
formulas
(6-12).
The gravity potential
W
may be computed by the first equation of (6-
4); the gravitational potential
V
is obtained by subtracting the centrifugal
potential
ω
2
(
x
2
+
y
2
)
/
2; and the vector of gravitation is given by (6-5).
6.6
Gravity anomalies and disturbances compared
Suppose gravity
g
is to be computed at some point
P
outside the earth
(Fig. 6.4); we consider here only the
magnitude
of the gravity vector. This
is conveniently done by adding a correction to the normal gravity
γ
.From
Sect. 2.12 and later, we recall the two different kinds of such a correction,
g
−
γ
:
1. the
gravity disturbance δg
,inwhich
g
and
γ
both refer to the same
point
P
;
2. the
gravity anomaly
∆
g
,inwhich
g
refers to
P
, but
γ
refers to the
corresponding point
Q
, which is situated on the plumb line of
P
and
whose normal potential
U
is the same as the actual potential
W
of
P
,
that is,
U
Q
=
W
P
.
These two quantities are connected by
2
γ
0
R
∆
g
=
δg
−
N
P
;
(6-61)
this simple relation is sucient for moderate altitudes.
The gravity disturbance is used when the spatial position of
P
is given,
that is, its geocentric rectangular coordinates
x, y, z
are measured. With
GPS measurements of the position of the aircraft, the use of gravity distur-
bances is natural.
The use of gravity anomalies ∆
g
had been traditional. This is the case, for
instance, in airborne gravity measurements, where the height of the aircraft
P
W=
P
N
P
Q
U=
P
H
1
F
earth's
surface
Fig. 6.4. Gravity anomalies and disturbancies
