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Example

Determine the look angles and the range for the situation given below.

 latitude of the earth station (lE)=-20 deg, Longitude of earth station  (fE)=-30 deg, Longitude of sub satellite point fs=+30 deg; height = 35,786 km radiuses of earth = 6378.14 km. 

Solution:
f
E=-20 deg
lE=-30 deg
fs=+30 deg
Height = 35,786 km
Radius of earth = 6378.14 km.

From the equation                B = fE - fS
                                  
         B =  - 30 – (+30) =-60o

From the equation         Tan A  = - tan |B|/ sin lE
                                           
= -tan |-60|/sin(-20)
                                           
= tan 60/sin20
                                           
=  5.064
                                          
A= tan-15.064
                 Azimuth angle AZ=78.83 deg.

From the equation            Cos c = cos lE cos B
                                    
Cos c = cos(-60) cos (-20)
                                             
=o.4698
and therefore  sin c =0.8827
                  
RE + h =42164.14 km
      
d  = squrt(6375.642+42,164.142–2*6375.64 *42,164.14*0.4698)
          
= 39,571 km
From the equation Cos EI = (RE+ h/d)sin C
                                   
= 42.164.14 * 0.8827 / 39,571
                                   
= 0.9405 and therefore 

                  Elevation angle EI =18.86 deg.


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