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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 sub-satellite point is located at 121 degrees west longitude.

With the provided coordinates, our variables assignment is as follows:


Earth Station Latitude = Le
Earth Station Longitude = le
Satellite Longitude = ls
Elevation Angle = El
Azimuth Angle = Az
Range = d


Solution:

Calculate the Elevation Angle:

cos (γ) = cos (Le) • cos (ls - le)

cos (γ) = cos (37.229) • cos (121 - 80.438)

cos (γ) = (0.796)(0.760)

cos (γ) = 0.605


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 = | ls - le | = 40.56 degrees

c = | Le - Ls | = 37.229 degrees

s = 0.5 ( a + c + γ ) = 65.28 degrees

α = 2 tan-1[ (sin (s - γ) sin (s - |Le|)) / (sin (s) sin (s - |le - ls|)) ]1/2

α = 2 tan-1[ 0.268 ]1/2

α = 54.74 degrees

With the sub-satellite 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.


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