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A Satellite Phone Call

  1. Feb 28, 2014 #1
    1. The problem statement, all variables and given/known data
    A communications satellite is in a synchronous orbit that is 3.33×107 m 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 3.30×106 m. Calculate the time it takes for a telephone call to go by way of satellite between these cities. Ignore the curvature of the earth.

    2. Relevant equations

    Time= Speed / distance
    Speed of Sound: 340.29 m/s
    a^2 + b^2 = c^2

    3. The attempt at a solution

    So, I started by drawing what was going on and it turned into a equilateral triangle which I made into two right triangles.

    I divided the distance between Quito and Belem in half (3.30 E 6)/2 = 1,650,000 m and I solved for the distance between Quito and the Satellite by using Pythagorean theorem: c^2=b^2+a^2
    c^2 = (1,650,000)^2 + (3.33 E 7)^2​
    c^2 = (2.72 E 12) + (1.108 E 15)​
    Sqrt(c^2) = Sqrt((2.72 E 12) + (1.108 E 15))​
    c = 5.49 E 13 m​
    C is the distance from Quito to the Satellite and so then, the distance from the Satellite and Belem would also be 5.49 E 13 m. Which would mean the total distance that the call would have to travel is 1.0989 E 14 m.

    The formula for Speed is Speed=Distance/Time which can be rewritten as Time=Distance/Speed. The speed of sound constant is 340.29 m/s.
    t= (1.0989 E 14) / (340.29)​
    t= 3.2293 E 11 seconds​

    This answer is incorrect and I am not really sure where I went wrong.

    Any help would be greatly appreciated C:
  2. jcsd
  3. Feb 28, 2014 #2


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    Staff Emeritus
    Science Advisor
    Homework Helper

    You don't use sound to communicate with satellites in orbit.

    Also, look carefully at the time to make the call: 3.23E11 sec.

    That's over 10,000 years, quite a long time to wait for a response.
    Last edited: Feb 28, 2014
  4. Feb 28, 2014 #3
    Cannot be correct. 1.108 E 15 is much greater than 2.72 E 12, so the result should not be much different from 3.33 E 7.
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