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Example

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

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

Solution:
f_E=-20 deg
l_E=-30 deg
f_s=+30 deg
Height = 35,786 km
Radius of earth = 6378.14 km.

From the equation                B = f_E - f_S
                                           B =  - 30 – (+30) =-60^o

From the equation         Tan A  = - tan |B|/ sin l_E
                                            = -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 l_E cos B
                                     Cos c = cos(-60) cos (-20)
                                              =o.4698
and therefore  sin c =0.8827
                   R_E + 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 = (R_E⁺ 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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