To generate a set of orbital elements for a satellite, one must know the
position and velocity at some given time. These are X,Y,Z,XDOT,YDOT,ZDOT, and T.
Knowing the azimuth and elevation, the direction cosines of a line to the
satellite can be determined. The intersection of this line with the known
location of the NAVSPASUR fence (a vertical plane), determines the location of
the satellite. The velocity components are more difficult to measure, and in
fact not enough information is known to determine all three. They can be
determined however, if the orbit is assumed circular. In a circular orbit, a
satellite always flies tangential to the earth's surface and its height uniquely
determines the total velocity, the vector sum of all three components. These
two constraints plus the measured doppler shift allow solving for the three
velocity components. The assumption of circularity holds well for orbital
eccentricity < .01, which includes the majority of satellites. An orbital
prediction program was written to predict the future fence crossings once a
Keplerian element set is generated, and can be used with element sets received
from NORAD as well.
