- 43 - 
knowns, are necessary. Together with the 9 unknown station coordinates, the unique problem 
presents itself with 18 unknowns. The satellite position above the center of the triangle is now 
observed from 3 stations and the other two satellite positions from two stations each, leading 
to 7 rays or 14 observational equations. Again, 18 - 14 = 4 additional geometric parameters 
must be introduced into the solution. From the viewpoint of analytical photogrammetry, the geo 
metric feasibility of the photogrammetric satellite triangulation can be explained by the fact 
that the unknown ground stations and the unknown orientations of the cameras at these stations 
resemble the air stations in traditional aerial photogrammetry. The unknown satellite positions 
correspond to the relative control points of the model and the stars play the role of absolute 
control points, with the obvious limitations that they are at infinity and, therefore, do not con 
tribute to scale determination. Furthermore, a somewhat different geometrical interpretation 
of the triangulation problem is necessary in so far as the stars are used to determine the ele - 
ments of interior orientation together with the three rotational components of the exterior orien 
tation. The condition of intersection, as associated with any one satellite image, is used to de 
termine the translatory elements of the exterior orientations (the position coordinates of the ca 
mera stations). In this way we avoid the unfavorable correlation that exists between rotations 
and translations in aerial photogrammetric procedures. 
Approaching our problem in this way has two advantages : 
a - First, the problem of data reduction is rigorously solved by applying computer pro - 
grams developed for analytical block triangulation. 
b - Second, the results obtained from these programs will not only determine the most pro 
bable values for the station coordinates, but at the same time provide all the variance and co- 
variance matrices. Based on fictitious examples, it is, therefore, possible to design an opti 
mum system in terms of station distribution, desirable orbit figuration, and, very important, 
selection of location, necessary length and accuracy of a system of scale-supporting baselines. 
The strictly geometrical considerations must now be complemented by considering a 
significant physical phenomenon which exercises a decisive influence on the concept of the prac 
tical execution of stellar triangulation. 
The refraction problem as such enters into the method with only a second order effect. 
It can be shown that the refraction of an image outside the atmosphere can be computed as as - 
tronomical refraction minus a parallactic angle, which is extremely insensitive to an error in 
the astronomical refraction [7]. Nor does the refraction error enter significantly into the orien 
tation of a photogrammetric record, because the orientation is established with respect to the 
geometrically-known star catalog values. 
As a matter of fact, the basic concept of the photogrammetric star triangulation me - 
thod depends not only on the geometrical interpolation method of the photogrammetric measu - 
ring procedure, but equally on the fact that the satellite images are physically-significantly in 
terpolated into the astronomical refraction effect. Because of both the geometrical as well as 
the physical interpolation, this method is essentially free of bias errors. It is this fact which 
distinguishes the method in principle from other spatial triangulation methods, e. g.,from elec - 
tronic lengthmeasuring methods. 
In order to obtain a precise and bias-free result with the stellar-triangulation method, 
it is, however, necessary to recognize a basic shortcoming of the method as long as the prac - 
tical execution is carried out with a flashing-light satellite, as it was e. g., performed with the 
geodetic satellite ANNA. 
The reason, very simply, is that the random scintillation (shimmer) of a short-dura 
tion light flash limits its geometrical significance to plus or minus two to three seconds of arc, 
somewhat depending on the geographic location of the station [8]. It is true that with increasing 
aperture this effect can be reduced, but because the just-mentioned values are by no means ex 
treme, it appears that this phenomenon can only be coped with by statistical means - that is to 
say by producing and measuring a large number of photographic images. Present-day technolo- 
gys does not provide the means for producing the several hundred flashes necessary to assure 
geometric significance of the observed target direction.