Geoscience Reference
In-Depth Information
Varying the size and shape of the reference ellipsoid and its position with
respect to the earth changes only the coecients
δW
,
a
10
,
a
11
,
b
11
,and
a
20
,
leaving the other coecients practically invariant. Thus, the minimum of any
of the integrals (5-157), (5-158), (5-159) is obtained if all these coe
cients
are equal to zero. Now,
δW
= 0 means equal potential
U
0
=
W
0
;
a
10
=
a
11
=
b
11
= 0 means absolute position (coincident centers of gravity); and
a
20
=0
means equality of
J
2
or of
C
(
A
+
B
)
/
2.
Therefore, the equivalence of the physical definition by means of
M,W
0
,
−
A
,
ω
and of the condition of closest approximation in any of the forms
(5-148), (5-149), or (5-153) has been established. (It may be noted that
(5-158) contains no first-degree term, because of the factor (
n
C
−
1)
2
,and
that (5-159) contains no term of degree zero, so that these equations do not
determine the missing terms.)
−
Best-fitting ellipsoid and World Geodetic System
It should be remembered, however, that the mean earth ellipsoid, defined
in this manner, is not necessarily the best reference surface for practical
geodetic purposes. It is essentially defined empirically by means of empiri-
cal determinations of
GM, W
0
, etc. Its parameters will change with every
improvement in the quality or the number of the relevant measurements
(gravity, distances, etc.). Since an enormous amount of numerical data is
based on an assumed reference ellipsoid, it would be highly impractical to
change it very often, for this would involve repeated transformations of all
the data. It is much better to use a fixed reference ellipsoid with rigidly
assumed parameters, which can be more or less arbitrary if only they give
a reasonably good approximation. In this respect, the Geodetic Reference
System 1980 is still (2005) perfectly acceptable.
A certain amount of conflict exists between the interests of geodesists and
astronomers regarding the earth ellipsoid. The geodesist needs a permanent
reference surface, whereas the astronomer wants the best approximation of
the earth by an ellipsoid. A good compromise is to use a fixed geodetic
reference ellipsoid, but from time to time to compute the “best” corrections
to the assumed parameters for astronomical and other purposes. This has
been the practice of the IAG since 1974.
