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Circular Motion of Satellite

  1. Feb 22, 2009 #1
    1. The problem statement, all variables and given/known data
    This is an question from (NZ) NCEA Scholarship Physics practise paper.
    Calculate the height of geostationary satellite and hence calculate the lattidue of a satellite dish that must be placed vertical to point at it.
    2. Relevant equations
    Earth's rotational velocity = 465.1 m/s
    therefore v of satellite = 465.1 m/s
    using Fc = Fg
    (mvsqr)/r = (GMm)/r
    vsqr = GM/r
    r = GM/vsqr

    3. The attempt at a solution
    Working so far from me:
    geostationary satellite = satellite that orbits at of Earth's rotational velocity.
    Earth's rotational velocity = 465.1 m/s
    therefore v of satellite = 465.1 m/s
    using Fc = Fg
    (mvsqr)/r = (GMm)/r
    vsqr = GM/r
    r = GM/vsqr
    = 1.8439x10pwrof9
    therefore height of geostationary satellite from surface = r - radius of earth
    = 1.8439x10pwrof9 - 6.39x10pwrof6
    = 1.8375x10pwrof9 m
    = 1.84 x 10pwrof9 m (3s.f.)
    (I'm not very sure about the answer, it's quite rediculous)

    And i'm having a problem with the second part of the question.
    Please help :3
     
    Last edited: Feb 22, 2009
  2. jcsd
  3. Feb 22, 2009 #2

    gabbagabbahey

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    Careful, a geostationary satellite orbits at the same angular frequency (or period) as Earth's rotation, not the same velocity.


    You mean mv2/r=GMm/r2 right?:wink:
    [/QUOTE]
     
  4. Feb 22, 2009 #3

    tiny-tim

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    Welcome to PF!

    Hi TofuManiac! Welcome to PF! :smile:

    For the second part, start by saying in words what the diagram would look like.

    Remember that if the dish is vertical, then the direction of the satellite must be horizontal :wink:
     
  5. Feb 23, 2009 #4
    Thanks man, I totally forgot the most important fact about the geostationary satellite XD

    Working:
    so period of orbit = 24hr = 86400s
    using derived formula - T = sqroot((4 pi^2 r^3)/(GM))
    r comes down to 42250474.3m
    therefore height of satellite from ground = 42250474.3 - 6.37x10^6 = 3.60x10^7m (3s.f.)

    To Tiny-tim = thanks for the help too XD
    Cheers :3
     
    Last edited: Feb 23, 2009
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