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Geostationary Satellite and Orbiting Satellite problem

  1. May 12, 2014 #1
    1. The problem statement, all variables and given/known data
    A satellite GeoSAT is in a circular geostationary orbit of radius RG above a point P on the equator. Another satellite ComSAT is in a lower circular orbit of radius 0.81RG. At 7 P.M. on January 1, ComSAT is sighted directly above P. On which day among the following can ComSAT be sighted directly above P between 7 P.M. and 8 P.M. ??
    (a) Jan 3
    (b) Jan 9
    (c) Jan 15
    (d) Jan 21

    2. The attempt at a solution
    I am sorry but I am unable to think of any possible way to solve this problem. Will Keplar's equations help?? :confused: I am totally confused!! Please help!!
    For your assistance, the answer given is January 9.
     
    Last edited: May 12, 2014
  2. jcsd
  3. May 12, 2014 #2

    phyzguy

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    What is the period of a geosynchronous orbit with radius RG? Using Kepler's laws, what is the period of an orbit with radius 0.81 RG?
     
  4. May 18, 2014 #3
    Umm...would that help?? :/
     
  5. May 18, 2014 #4

    phyzguy

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    Yes, it will help - that's why I asked the questions. Can you answer them?
     
  6. May 19, 2014 #5
    Well, the formula to be applied can be.....
    T2/R3 = (4 * π2) / (G * M)

    where M= 5.98x1024 kg i.e. the mass of the Earth.
    Would it help now??
     
  7. May 19, 2014 #6
    The above formula is for geosynchronous as I found out.... but the question tells about geostationary orbit.....
     
  8. May 19, 2014 #7

    phyzguy

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    Geosynchronous and geostationary really mean the same thing. Do you know what a geostationary orbit is? If you do, you should be able to tell me the period of a geostationary orbit without doing any calculations.
     
  9. May 19, 2014 #8
    As Wikipedia states, the time period can be
    T = 2π √(r3/μ)

    What say??
     
  10. May 19, 2014 #9
  11. May 19, 2014 #10
    Yeah it's 24 hours! :tongue:
     
  12. May 19, 2014 #11

    phyzguy

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    OK, good. It's actually 23 hours and 56 minutes, but 24 hours is probably close enough. So if the period of the satellite at radius R = RG is T = 24 hours, and if we know from what you wrote earlier that
    [tex]\rm \frac{T^2}{R^3} = constant[/tex]
    then what is T when R = 0.81RG?
     
  13. May 19, 2014 #12

    D H

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    You don't need to know M or G. What you need to do is to answer phyzguy's questions.

    What's the period of a geostationary satellite?
    What do Kepler's laws say about the period of a satellite? Hint: Only one law says anything about the period.

    From that, what is the period of that satellite whose orbital radius is 0.81 RG?
     
  14. May 19, 2014 #13
    oh okay got it now..... so all I have to do is to find out the periods for both the satellites and then calculate the time difference to get the number of days, right?
     
  15. May 19, 2014 #14

    phyzguy

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    Right.
     
  16. May 19, 2014 #15

    D H

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    There's more to it than that. The satellite will be directly overhead after an integral number of orbits.

    Here's what you need to solve for: For what integers N is the time needed to make N orbits between M days and M days plus one hour, where M is another integer?
     
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