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kets before the method was adapted for rocket testing in Peenemünde (Germany) and later in 
many other countries. 
Professor Väisälä suggested the same principle in the Sitzungsberichte der Finnischen 
Akademie der Wissenschaften 1946 under the title " An Astronomical Method of Triangulation " [6]. 
There are various ways to demonstrate the geometric feasibility of the method. Väisälä's ap 
proach allows a very elegant presentation of the basic geometric principles, but leads to a cum 
bersome data reduction method, especially if the corresponding triangulation consists of an ap 
preciable number of triangles and redundant information has to be treated. The reasoning in 
Väisälä's paper is : two conjugate rays emerging from the endpoints of a base line define a pla 
ne in space whose spatial orientation can be computed from the measured direction cosines of 
the two rays. If two such planes containing the base line are observed, the direction of the base 
line can be computed as the line in which the two planes intersect. (Compare Fig. la). 
It is now readily seen that two base lines originating from a specific station will form 
a spatially oriented triangle if the two lines under consideration are intersected with a plane 
which contains neither of the two lines and the orientation of which is known. As outlined befo 
re, each direction is determined from the intersection of two planes. Consequently, five planes 
are necessary and sufficient for establishing a unique solution for a spatially-oriented station 
triangle.(Compare Fig. lb). Any one of these planes contains two stations and a specific satel 
lite position. Therefore, five satellite positions are required introducing 5x3= 15 unknown 
coordinates. Together with the 3x3=9 unknown station coordinates, the problem has 24 un 
knowns. Each satellite observed from two stations gives rise to 2 rays or 4 equations ; conse - 
quently, 24 minus 5x4 = 4 independent geometrical parameters must be given. They are e. g. , 
the arbitrarily chosen coordinates for one of the stations and the length of one side of the trian 
gle, determining the scale of the triangulation. It is obvious that the just described principle 
can be applied to any number of triangles forming a three-dimensional triangulation scheme. Of 
interest is the fact that three of the five planes can be formed with only one satellite position if 
the location of the satellite is chosen so that its sub-point is about in the center of the triangle 
to be determined (Compare Fig. lc). In such a case, only 3 satellite positions, leading to 9 un-