

Satellite Earth Station Problem
Given an earth station that is located at 80.438 degrees west longitude and 37.229 degrees north latitude. Calculate its
look angle and range to a geosynchronous satellite whose subsatellite point is located at 121 degrees west longitude.
With the provided coordinates, our variables assignment is as follows:
γ = 52.78 degrees, and the satellite is visible to this earth station because γ < 81.30 degrees
cos (El) = sin (γ) / [1.02274  (0.31596 cos (γ))]^{1/2}
cos (El) = 29.69 degrees
Next, calculate the Azimuth Angle:
a =  l_{s}  l_{e}  = 40.56 degrees
c =  L_{e}  L_{s}  = 37.229 degrees
s = 0.5 ( a + c + γ ) = 65.28 degrees
α = 2 tan^{1}[ (sin (s  γ) sin (s  L_{e})) / (sin (s) sin (s  l_{e}  l_{s})) ]^{1/2}
α = 2 tan^{1}[ 0.268 ]^{1/2}
α = 54.74 degrees
With the subsatellite point at a southwesterly angle from the earth station the Azimuth is equal to the calculated angle, alpha, plus 180 degrees.
Az = 180 degrees + 54.74 degrees = 234.74 degrees
Finally, calculate the Range:
d = 42,242 [1.02274  0.301596 cos (0.605)]^{1/2}
d = 38,721km
Satellite key words: earth station, ES, UT, universal time, coordinates, north latitude and west longitude, look angle, distance,
range, geosynchronous, GEO, elevation angle, azimuth angle, orbit variables, radius, radian, visibility, clear sky, orbital rotation.
