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Geostationary satellite orbit radius as a multiple of Earth radius.

  1. Mar 19, 2016 #1
    1. The problem statement, all variables and given/known data
    Okay, so the question seems really simple so I don't know what I'm missing

    A satellite orbits at a fixed point above the Earth's equator. Assuming the earth has uniform
    density, radius R, and angular frequency of rotation, omega
    Find an expression for eta, such that the orbital radius of the satellite is expressed as eta R

    2. Relevant equations
    Below

    3. The attempt at a solution
    Centripetal force= gravitational force

    mr(omega)^2=GMm/r^2
    r^3=GM/(omega)^2
    But I honestly have no idea how to incorporate the Eaths radius. Every time I try it cancels.

    Thanks in advance :)
     
  2. jcsd
  3. Mar 19, 2016 #2
    When calculating mass of the earth you can use density and radius of the earth so it doesn't cancel out.
     
  4. Mar 19, 2016 #3
    Absolute star! Thank you!!
     
  5. Mar 19, 2016 #4
    Sorry - Ive just had a thought. That will give me an expression in terms of R^3, not R. This produces the same problem as I had before
     
  6. Mar 19, 2016 #5
    I don't understand the problem exactly. Any function dependent on R is actually an expression in terms of R so if you obtain a term with R^3 (you should) don't worry because it means that radius of the sattelite is not dependent on R linearly .
     
  7. Mar 19, 2016 #6

    gneill

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    Staff: Mentor

    There are two different radii involved: One is the radius of the Earth and the other the radius of the orbit. The volume is calculated using the Earth radius R, while the satellite orbit is a multiple of R. Replace the radius in your satellite force balance with ##\eta R##.

    Can you show more details of your workings?
     
  8. Mar 19, 2016 #7
    Ohh, sorry I did not see the part that asks you to write the sattalite radius as eta R. I think you should use @gneill 's argument.
     
  9. Mar 19, 2016 #8
    Ah okay - I think I've got it now. Thank you. Of course- would you like me to upload a photo of my working? (For some reason Latex doesn't work on my computer)
     
  10. Mar 19, 2016 #9

    gneill

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    Staff: Mentor

    You can upload a photo if it's easily legible.
    What machine/browser are you using?
     
  11. Mar 19, 2016 #10
    How do I inset a photo? I can't see the button- The only one i can find is the one requiring a URL

    A macbook air and safari
     
  12. Mar 19, 2016 #11

    gneill

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    Staff: Mentor

    You can UPLOAD an image file. Check out the UPLOAD button at the bottom right of the reply edit panel.

    Ah. I'm not familiar with safari, so I can't help you there.
     
  13. Mar 19, 2016 #12
    Thank you- please excuse my handwriting.

    My laptop is a mystery- I've had many people try to download latex, but no one has had any luck
     

    Attached Files:

  14. Mar 19, 2016 #13

    gneill

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    Staff: Mentor

    Your solution looks good.

    PF's LaTeX does not require any extensions or software to be added to your browser or machine. It's a feature that's managed externally. It may, however, require that certain character set capabilities exist in the browser. You might try testing another browser just to see if it's a browser issue. I think there's versions of Chrome and Firefox for mac.

    Edit: You might check your browser version against the supported versions at the Mathjax website.
     
    Last edited: Mar 19, 2016
  15. Mar 19, 2016 #14

    tony873004

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    Science Advisor
    Gold Member

    Your solution looks good. To do Latex, type this
    Code (Text):

    \eta  = \sqrt[3]{{\frac{{4G\rho \pi }}{{3\omega ^2 }}}}
     
    and put tex tags around it.
     
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