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Math Help - How to find the orbit time of this satellite?

  1. #1
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    How to find the orbit time of this satellite?

    A satellite is in a circular orbit H km above the earth surface.
    In how many hours does the satellite complete one orbit?

    The radius of the earth is 6370 km.

    H[km] = 289;

    Could someone please show me how to solve this
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  2. #2
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    Quote Originally Posted by m_i_k_o View Post
    A satellite is in a circular orbit H km above the earth surface.
    In how many hours does the satellite complete one orbit?

    The radius of the earth is 6370 km.

    H[km] = 289;

    Could someone please show me how to solve this

    HI

    The gravitational attraction between the satelite and the earth is the same as the centripetal force of the satelite so

    Let M be the mass of earth and small m be the mass of satelite .
    Note that omega=2pi/T

     \frac{GMm}{(R+H)^2}=m(R+H)(\frac{2\pi}{T})^2

    Rearranging ..

    T=\sqrt{\frac{4\pi^2(R+H)^3}{GM}}

    Now you know R , H , G (Gravitational constant) , Mass of the earth is not given but you can check it out in your book since i hv forgotten .

    Then substitute .
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  3. #3
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    Converting to hours

    To convert to hours I will just divide T by 360?
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  4. #4
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    Divide by 60 \times 60 = 3600
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by m_i_k_o View Post
    A satellite is in a circular orbit H km above the earth surface.
    In how many hours does the satellite complete one orbit?

    The radius of the earth is 6370 km.

    H[km] = 289;

    Could someone please show me how to solve this
    Kepler's Third law tells us that for a circular orbit:

    \tau^2=kr^3

    where \tau is the period of the orbit and r its' radius.

    For Geostationary orbit \tau_{geo}=24 hours, and r_{geo}=35786 km.

    So the period \tau_1 that we seek satisfies:

    \frac{\tau_1^2}{\tau_{geo}^2}=\frac{6659^3}{r_{geo  }^3}

    and the rest is arithmetic.

    CB
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