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Math Help - satellite, find time it takes a call between two cities.

  1. #1
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    satellite, find time it takes a call between two cities.

    A communications satellite is in an orbit that is 4.10 x 10^7 m directly above the equator. Consider the moment when the satellite is located midway between Quito, Equador, and Belem, Brazil; two cities almost on the equator that are separated by a distance of 3.40 x 10^6 m.

    Find the time it takes for a telephone call to go by the way of satellite between these cities. Ignore the curvature of the earth.

    in seconds.

    heres what I believe it looks like: http://img518.imageshack.us/img518/6439/46101437mc6.png

    also, i know that electromagnetic waves propagate through a vacuum at a speed given by c = 3.00 x 10^8

    i wasn't sure why the equation would not be one of the given distances d/c.

    Anyone who can explain this one please.
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  2. #2
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    Quote Originally Posted by rcmango View Post
    A communications satellite is in an orbit that is 4.10 x 10^7 m directly above the equator. Consider the moment when the satellite is located midway between Quito, Equador, and Belem, Brazil; two cities almost on the equator that are separated by a distance of 3.40 x 10^6 m.

    Find the time it takes for a telephone call to go by the way of satellite between these cities. Ignore the curvature of the earth.

    in seconds.

    heres what I believe it looks like: http://img518.imageshack.us/img518/6439/46101437mc6.png

    also, i know that electromagnetic waves propagate through a vacuum at a speed given by c = 3.00 x 10^8

    i wasn't sure why the equation would not be one of the given distances d/c.

    Anyone who can explain this one please.
    This is nearly a trick question: You have to "harmonize" all given distances.

    I take as a distance unit 10^6\ m

    Let a denote the distance of the satellite above the equator: a = 41 \cdot 10^6 \ m

    Let g denote the distance on the ground between Quito and Belem: g = 3.4 \cdot 10^6\ m

    The communication signal is running from Quito via satellite to Belem. Use Pythagorean Theorem to calculate the distance s of the signal:

    s = 2 \cdot \sqrt{\left(\frac12 \cdot 3.4 \cdot 10^6 \right)^2 + \left(41 \cdot 10^6\right)^2}

    And now calculate the time needed by the signal to cover the distance s.
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  3. #3
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    okay i get 82070457.53 for s, the distance.

    now i tried using the formula i had to divide s by c = 3.00 x 10^8

    to get a final answer of about .274 seconds.

    Thankyou!
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