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Problem geostationary satellite

  1. Sep 11, 2008 #1

    fluidistic

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    1. The problem statement, all variables and given/known data
    At what height (from the ground of the Earth) must be placed a geostationary satellite?


    2. Relevant equations



    3. The attempt at a solution I'm not sure I understand well the question. I guess they are asking for a satellite in such a position that he would not deviate from the point over the ground it is situated. Well, I believe that the height doesn't matter at all and what matters is the velocity you put the satellite in orbit that matters. But the answer of the question is [tex]3.58 \cdot 10^5 \text{km}[/tex]. I have no idea of how to get the solution. Do you have an idea?
     
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  3. Sep 11, 2008 #2

    Redbelly98

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    They mean that the orbital period is 1 day, so that the satellite is always directly over the same place on Earth.

    Also, assume a circular orbit. What equations do you know that apply to:
    1. gravity
    2. circular motion
     
  4. Sep 11, 2008 #3

    fluidistic

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    Hmm... I guess they want me to use [tex]F_c=m_ca_c=m_c\frac{v^2}{r}[/tex]. Also [tex]F_c=\frac{Gm_cM_E}{r^2}[/tex] which led me to conclude that [tex]r=\frac{GM_E}{v^2}[/tex]. But the velocity is unknown so I'm stuck. At last I could calculate it but only in function of the altitude (using the formula [tex]v=\omega r[/tex]) which is precisely what I'm looking for...
     
  5. Sep 12, 2008 #4

    alphysicist

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    What is [itex]\omega[/itex] for this satellite?
     
  6. Sep 12, 2008 #5

    Redbelly98

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    You're on the right track. What happens if you substitute [itex]v=\omega r[/itex] into the previous equation here?
     
  7. Sep 12, 2008 #6

    fluidistic

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    Oh... Thanks to both! I didn't think about replacing [tex]v[/tex] by [tex]\omega r[/tex]!
     
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