

Satellite Look Angle Problem
The WESTAR III satellite is a geosynchronous satellite located at 91 degrees W longitude. Determine the look
angles to this WESTAR III satellite from an earth station near the city of Los Angeles California at 120 degrees W,
34 degrees N. Also, determine the latitude and longitude of the northern most and the westerly most point at which
the WESTAR III satellite is visible at a 10 degree elevation angle.
Solution:
a) In determining the lookangles to the geosynchronous satellite describe above:
Azimuth (Az):
a =  l_{s}  l_{e}  = 29 degrees
c =  L_{e}  L_{s}  = 34 degrees
s = 0.5 ( a + c + γ ) = 53.26 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}[ 0.169]^{1/2}
α = 44.75 degrees
Sense subsatellite position is southeast of the earth station,
Az = 180 degrees  α = 135.25 degrees
b) In finding the lat and long of the northern most point and westerly most point, set the elevation equal to 10 degrees and solve for gamma (γ).
cos (El) = sin (γ) / [ (1.023  0.302) cos (γ) ]^{1/2}
Let X = cos (γ)
[ 1  X^{2} ]^{1/2} = sin (γ)
A = 10.23
B = 0.302
C = cos (El) = 0.985
We get the following expression: 1  X^{2} = C^{2} (A  BX)
Which as written as a quadratic equation we get: X^{2}  BC^{2}X + (AC^{2}  1) = 0
Rewriting the equation into the quadratic formula we get: X = BC^{2} ± [ B^{2}C^{4}  4 (AC^{2}  1) ]^{1/2} / 2
X = (0.293 + 0.340) / 2
γ = cos^{1}X = 71.54 degrees
Therefore, the northern most point is where l_{e} is equal to l_{s} and L_{e} is equal to γ
Latitude = 71.54 degrees N
Longitude = 91.00 degrees W
Now, the westerly most point must lie on the equator, L_{e} = 0 degrees
cos (γ) = cos L_{e} cos (l_{s}  l_{e})
cos (γ) = 1 cos (l_{s}  l_{e})
γ =  l_{s}  l_{e} 
l_{e} = l_{s} ± γ
l_{e} = 91.00 degrees ± 71.54 degrees
So: l_{e} = 162.54 degrees or 19.46 degrees
This equates to the westerly most point of,
Latitude = 0 degrees N
Longitude = 162.54 degrees W
Satellite key words: earth station look angle, visible, line of sight, site, geosynchronous, elevation angle,
westar, coordinates, lat, long, satcom, absolute value, mathematical orbital computation, calculated, apogee,
perigee, spacecraft, velocity, eccentricity, angular limits, engineering dynamics, scientific notation.
