19 
It can be seen that five translations in combination 
with six or seven rotations are necessary to correct for the 
following influences: proper motion of stars; their radial 
velocity; precession and nutation of the earth's axis; annual 
and diurnal aberration; parallax; astronomical refraction; 
earth rotation; and polar motion. 
After computing the Z vectors for all stars measured 
on a specific plate, the parameters simulating the photo- 
grammetric bundle, as shown in Figure 6, are computed by a 
least squares solution, allowing for weighting of the star 
coordinates as well as for the corresponding plate measure 
ments. The introduction of three sets of (cc,u),r) orienta 
tion elements is necessary to detect and account for any 
possible camera movements during the observational period, 
which typically spans a period of about 20 minutes. These 
sets correspond, respectively, to star images taken before, 
during, and after the satellite passage. In essence each 
such reduction is a camera calibration and, therefore, the 
method provides, in addition to its use for satellite triangu 
lation, the means to calibrate aerial cameras. It is being 
used for this purpose by the Coast & Geodetic Survey in its 
effort to develop a precision aerial photogrammetric trian 
gulation system. 
It may be of special interest to inspect the distortion 
model which involves both radial and decentering distortion, 
the latter in accordance with Conrady's results derived by 
ray tracing. Figure 3 shows schematically the situation for 
a specific radial distance d. In order to provide more 
flexibility for the mathematical model, the point of origin 
of these distances has been separated from the principal 
point, an approach which appears especially advantageous 
for the calibration of wide-angle systems. Furthermore, it 
is possible to correct the astronomical refraction coefficients 
when the angle of view covers an extended range in zenith 
distance. 
After obtaining the parameters simulating the photo 
grammetric bundle it is a straightforward procedure to 
reduce the measured coordinates of the satellite images to 
fictitious images whose locations correspond to the principle 
of central perspective. 
However, before these coordinates can be introduced into 
the final triangulation it is necessary to add further 
corrections, the purpose of which is to apply