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Homework Help: Satellite period, which equation?

  1. Nov 23, 2007 #1
    1. The problem statement, all variables and given/known data

    I'm looking for the period of an orbiting object a certain height from the earth's surface, I am given this height. So I have the total radius of 6,5OO,OOO m, g = 9.81 m/s^2 and the mass of earth = 5.98*10^24 kg

    Please note that for this problem G is another constant than what it usually is.

    2. Relevant equations

    Here is where I am confused I do not know whether to use the T = (2[tex]\pi[/tex]r)/[tex]\sqrt{gr}[/tex]

    or the T[tex]^{2}[/tex] = (4[tex]\pi^{2}r^{3}[/tex])/(GM[tex]_{earth}[/tex])

    where G = 6.67*1O^-7

    3. The attempt at a solution

    K. So when I use the method of going with T = (2[tex]\pi[/tex]r)/[tex]\sqrt{gr}[/tex]

    I get about 5114 seconds for the period.

    when I use T[tex]^{2}[/tex] = (4[tex]\pi^{2}r^{3}[/tex])/(GM[tex]_{earth}[/tex])
    I get 52.13584223 seconds, which doesn't logically seem right but since G is different I don't know.

    does anyone know what the right method is?
     
  2. jcsd
  3. Nov 23, 2007 #2

    malawi_glenn

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  4. Nov 23, 2007 #3

    Dick

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    And your value for G is wrong. Though it's hard to really say until you put units on it.
     
  5. Nov 23, 2007 #4
    thx alot for that clarification. Still it doesn't make sense that its period would be 52 seconds here's my work.

    T(secs)^2 = (4(pi^2)(6,500,000^3 m))/((6.67*10^-7 N*m^2/kg^2)(5.98*10^24 kg))

    are the units for T in seconds? was it alright that I changed km to m for the radius?
     
  6. Nov 23, 2007 #5
    I'm using a different value for this problem
     
  7. Nov 23, 2007 #6

    Dick

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    G=6.67*10^(-11)*N*m^2/kg^2. Note the exponent.
     
  8. Nov 23, 2007 #7

    Dick

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    Is it an 'alternative universe' problem? Why would you use a different value for G? It's a 'universal constant'.
     
  9. Nov 23, 2007 #8
    you could say that. But either way I don't think it would have much difference for this equation than the plug and chug. Right now I want to know if I am calculating everything else right. I assume I am.
     
  10. Nov 23, 2007 #9

    Dick

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    The reason you getting 52 seconds is because you are putting in a value of G that is 10000 times too large. Other than that you are doing fine.
     
  11. Nov 23, 2007 #10
    thank you
     
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