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Math Help - Radian Measure

  1. #1
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    Radian Measure

    Satellites that are used for satellite television must stay over the same point on Earth at all times, so that the receiving antenna is always pointed at the satellite . This is known as a geostationary orbit and requires an orbit at a distance of approximately 35 900 km above earth's surface.

    A) Explain how such a satellite could remain over the same point on earth as it orbits the planet. Answer, geosynchronous.

    b) How long would such an orbit require for one complete revolution of Earth? Answer: 24 H

    c) What is the angular velocity of such a satellite, in radians per second?

    This is what I got:

    1rev/24 h. 1 rev x 2 pi = 2 pi rads.
    24 H = 86 400 seconds.

    angular velocity = 2 pi rad/ 86 400 s
    = 0.0000727 pi rad/s


    I've tried to solve the problem, but I keep getting a different answer for the angular velocity. I get 0.0000727 rad/s, whereas the answer should be 0.000023 rad/s.
    Last edited by darksoulzero; November 22nd 2009 at 08:31 PM.
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  2. #2
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    Quote Originally Posted by darksoulzero View Post
    Satellites that are used for satellite television must stay over the same point on Earth at all times, so that the receiving antenna is always pointed at the satellite . This is known as a geostationary orbit and requires an orbit at a distance of approximately 35 900 km above earth's surface.

    A) Explain how such a satellite could remain over the same point on earth as it orbits the planet. Answer, geosynchronous.

    b) How long would such an orbit require for one complete revolution of Earth? Answer: 24 H

    c) What is the angular velocity of such a satellite, in radians per second?

    This is what I got:

    1rev/24 h. 1 rev x 2 pi = 2 pi rads.
    24 H = 86 400 seconds.

    angular velocity = 2 pi rad/ 86 400 s
    = 0.0000727 pi rad/s


    I've tried to solve the problem, but I keep getting a different answer for the angular velocity. I get 0.0000727 rad/s, whereas the answer should be 0.000023 rad/s.
    Looks like a typo:

    0.000023\ \frac{rad}{s} \bold{\color{red}\cdot \pi} = 0.0000727 \ \frac{rad}{s}
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  3. #3
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    Awesome, thanks. Hmm, I see, but what's the difference between rad/s and pi rad/ s?
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  4. #4
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    Quote Originally Posted by darksoulzero View Post
    Awesome, thanks. Hmm, I see, but what's the difference between rad/s and pi rad/ s?
    Pi, writen as \pi, is a constant number. If you have \pi as a part of a solution this constant number is a factor.
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  5. #5
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    Quote Originally Posted by darksoulzero View Post
    Awesome, thanks. Hmm, I see, but what's the difference between rad/s and pi rad/ s?
    Pretty much the difference between 1 rad/s and 3.141592... rad/s!
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