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A practical and very common problem is the terrestrial pointing of earthbased parabolic antennas to satellites (e.g., geostationary communication satellites) and extragalactic radio sources [e.g., very long baseline interferometry (VLBI)]. Greater aiming accuracy is required for the exact pointing of optical instruments to stars or, using narrow-beam-laser ranging devices, pointing them to retroreflectors in orbiting space platforms. In all these cases the presumption is made that the earth-based tracking instruments have an altazimuth mounting. Therefore, the primary objective is to determine the spatial-object azimuth and altitude (for definitions see e.g., Mueller, p.) at some instant t. These two parameters are the socalled look angles in the terminology popularized by scientists and engineers specializing in the electrical/electronic field.
To improve the accuracy of the calculation of the look angles, the spherical
approximation of the earth is replaced by an oblate ellipsoid of revolution.
This approach eliminates errors introduced by spherical geometry and, con-
sequently, discrepancies due to differences in definition between geocentric
and geodetic parameters (i.e., zenith distances and latitudes). Fig.3 illus-
trates the advantage of using an ellipsoidal model of the earth. The value
of the geodetic zenith distance z (referred to the normal to the ellipsoid) is
more accurate than z' because the location of the observer at point P is
closer to its true location on the earth surface by the mere fact that the
earth more accurately resembles a flattened ellipsoid than a sphere. In the
~,= f ='= o-# ='= o+# ~'= o-#
]~c~ ' NW
FIG.2. Azimuth Calculation as Function of Subsatellite Point Location with Re-
spect to Earth Station
FIGURE NOT TO SCALE
(Geodetic Zenith)
,,/ / of ellipsoid at
I~P oint P.
// ~ Reference
/ Ellipsoid
,= a "'"_,~ r D
~ Geod
