Question

A communications satellite is in a synchronous orbit that is 3.09×107m directly above the equator. The satellite is located midway between Quito, Equador, and Belem, Brazil, two cities almost on the equator that are separated by a distance of 3.48×106m. Calculate the time it takes for a telephone call to go by way of satellite between these cities. Ignore the curvature of the earth.

Answer 1

Given that :

Heigth of the orbit above the equator h = 3.09*10^7 m

Seperation between the two cities d = 3.48*10^6 m

Let S be the total distance traveled by signal.

So that the distance between Belem (or Quito) to satellite is S/2 .

Therefore from geometry we can write

                   S / 2 = ? [ (h)² + (d / 2)² ]
                            

                             = ? [ (3.09 x 10⁷)² + (3.48 x 10⁶ / 2)² ]
                            

                            = 3.095 x 10⁷ m
                          

                          S = 6.19 x10⁷ m

The time taken by electromagnetic wave to travel a totaldistance S is
                  t = S / c
                    

                    = (6.19 x10⁷ m) / (3 x 10⁸ m/s)
   

                    = 0.206 s

Please rate positive it is correct