- 38 - 
d - To establish the necessary geometric fidelity for a system of world-wide tracking sta - 
tions for observing orbiting satellites. The data collected from these satellite observations will 
be ideally suited for analyzing gravimetric and related geophysical parameters. These parame 
ters, in turn, can then be used for determining the position of the center of mass and the ove - 
rail shape of the gravitational field of the earth associated with its mass distribution. 
Such results will support the establishment of a uniform system for both geometric and 
gravimetric data, which is desirable from the standpoint of basic geodetic theoretical conside 
rations and, in practice, necessary to provide information for anticipated navigational problems 
in connection with space explorations. 
In gravimetric geodesy difficulties in the classical theory are caused by the need for 
certàin information which, in practice, cannot be ascertained. The theory postulates that cer 
tain groups of observations are executed at the geoid, while in practice they obviously can only 
be made at points on the physical surface of the earth. Subsequent reductions depend on know 
ledge of the distribution of mass inside the crust of the earth. Further difficulties arise from 
the fact that the theory assumes that all masses of the earth are inside the geoid. The process 
of regularizing the earth affects the corresponding results in accordance with the postulated ty 
pe of mass transport. 
New ideas in gravimetric geodesy suggest that the determination of the geoid is an un- 
solvable problem and in practice an unnecessary operation. Nevertheless, the dilemma remains 
that the paucity and non-uniformity of the distribution of gravity measurements produces errors 
larger than those caused by the defects of the theoretical developments. In addition, the corre 
lation between the classic geometric triangulation results and the gravimetric data still depends 
on certain a priori accepted hypotheses. 
The ability to calculate the orbits of artificial satellites in terms of the potential is the 
basic significance of such vehicles for world-wide gravimetric geodesy. Because the partial 
derivatives of satellite orbit observations with respect to the positions of the specific tracking 
stations allow us to determine these positions relative to the center of mass, we are provided 
with a link between the gravimetrical and geometrical problems in geodesy. In practice, howe 
ver, there are errors in the relative positions of such tracking stations within the individual da 
tum. Also, rather strong correlation exists between the large number of perturbations, caused 
by the variations of the gravitational field and other geophysical phenomena, and the station po 
sition errors. To overcome the difficulties in deriving a solution to the gravimetric problem, it 
is necessary to obtain, as a first step, a geometric satellite solution such as was mentioned 
earlier. 
Considerable interest has been shown in the launching of a series of gravimetric sa - 
tellites. Also, valuable gravimetric data has already been obtained by the analysis of satellite 
orbits which were observed mainly by photogrammetric cameras [3]. Any forthcoming geode - 
tic satellite program will, therefore, include gravimetric satellites with optical beacons for 
photogrammetric triangulation in support of orbit determinations. (Compare flow chart, " Geo 
metry of Satellite Orbits " . 
The processes of data adjustment and analysis in satellite photogrammetry will depend 
on the acceptance of a reformation in a third ar&a of activity, which is concerned with modern 
mathematical statistics and amounts to a generalization of the classic least squares method. It 
is no longer sufficient to consider the purpose of an adjustment as a means of reducing obser - 
vational errors, but the ultimate goal is to make a set of measured quantities compatible with 
an economized mathematical model. The basic idea underlying this approach is that all quanti 
ties used in the construction of a specific mathematical model are assumed to be measured 
quantities, which in turn are considered to be samples of stochastic variables. By assigning to 
these variables in advance relative variances and co-variances between the limits of zero and 
infinity, the least squares method will provide unbiased estimates for all variables, even if