- 41 
Even if we assume that bias errors, resulting from the physical characteristics of the 
classic angle measuring instruments, are sufficiently eliminated, and even if we pretend that 
propagation effects, often referred to by such terms as refraction, scintillation, etc. are 
-well enough understood so as not to cause intolerable biases on the correspondingly corrected 
measured angles, classic geodetic triangulation is still confronted with a situation requiring ra 
ther complex theoretical considerations, the geometrical contents of which generally necessi 
tate the a priori acceptance of certain hypotheses. 
Aside from these physical problems, there is the unavoidable limitation of the length 
of the line of sight between specific points on or close to the physical surface of the earth. 
Practical geodesy suffers not only from the inability to establish intercontinental ties, but is 
forced to establish its basic so-called first-order reference systems as a mesh of all too nu - 
merous triangles. The undesirability of this situation is not in the number of points so*determi- 
ned, as clearly evidenced by the necessity to create even more control by filling in with second 
and third-order nets, but in the basically unfavorable laws of error propagation existing in any 
extended triangulation scheme which is based solely on angular measurements. The geometry 
of such a triangulation system can be established with only limited accuracy. 
Satellite triangulation by photogrammetric means gives promise of overcoming some 
of the basic difficulties encountered in classic geodetic triangulation. Foremost is the fact that 
such a triangulation, being independent of the direction of gravity, is free of any a priori geo 
physical hypothesis. Because of the exceedingly large dimensions of its individual figures, sa 
tellite triangulation encompasses the whole earth with a relatively small number of triangles 
and closes its spatial triangulation in all three dimensions, thus providing sufficient geometri 
cal strength to prevent unfavorable error propagation. 
The rigorous geometrical determination of a selected number of non-intervisible points 
on the physical surface of the earth, can be accomplished by a process of spatial triangulation 
using auxiliary target points sufficiently elevated above the surface of the earth. 
The creation of light signals, which can be seen over long distances, is possible with 
the help of artificial satellites. Because of the unavoidable motion of such targets, precise di 
rection measurements can presently only be carried out by photogrammetric means. The pho - 
togrammetric method, because of the physical and chemical nature of its numerous components 
and operations, lacks in absolute metric accuracy and in reproducibility of its procedures. If 
measuring results of extremely high absolute accuracy are to be obtained by photogrammetric 
techniques, the only possible approach is to use the photogrammetric method as a tool of inter 
polation. 
The reference system into which the direction to a sufficiently elevated target point can 
be interpolated is obviously the right ascension-declination system. 
This reference system is attractive from the geodetic standpoint because one of its axes 
is by definition parallel to the rotation axis of the earth. From a quantitative standpoint, a prac 
tically unlimited number of reference points are available. From a qualitative-standpoint, at 
least 30, 000 stars, as cataloged e.g., in the Boss General Catalog, are presently determined 
with an accuracy of about half a second of arc (one sigma level) and a large group of these (ti 
me-stars), collected in the FK-4 and N-30 catalogs, considerably better. From the fact that 
these fixed stars are for all practical purposes at infinity, it follows that their direction coor - 
dinates are insensitive to translations and, therefore, cannot be used for any scale determina - 
tion. 
It is now of interest to consider the problem of the geometric feasibility of a three-di 
mensional triangulation system based on incomplete direction measurements, incomplete becau 
se of the non-intervisibility of the ground stations [5]. 
The use of star photography for calibrating photogrammetric cameras is a proven con 
cept, especially with astronomers. The use of the star background for orienting cameras in 
connection with the triangulation of additionally recorded target point was, in the 1930's, sue - 
cessfully used by Hoppman and Lohman for trajectory measurements of shelles and small roc