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Homework Help: Orbital period

  1. Dec 7, 2008 #1
    1. The problem statement, all variables and given/known data
    Mars orbits the sun at 1.52 Earth's orbital radius. What is the period of Mars in Earth years?


    2. Relevant equations
    ΣFc = mac


    3. The attempt at a solution
    I am unsure how to do this problem as this is the first "orbital period" question that I have encountered. Do I use the equation ΣFc = mac to solve this question, or is there another equation specifically for orbital periods that I don't know about?

    because if I go the ΣFc = mac route I get:

    ΣFc = mac
    Fg = m4(pie)^2r/T^2
    GMem/r^2 = m4(pie)^2(1.52)r/T^2
    GMe/r^2 = 4(pie)^2(1.52)r/T^2
    (GMe)(T^2) = 4(pie)^2(1.52)r^3
    T = √4(pie)^2(1.52)r^3/GMe

    This is my first orbital period question so I was just wondering would this be the correct way to solve it?
     
  2. jcsd
  3. Dec 7, 2008 #2

    fluidistic

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  4. Dec 8, 2008 #3
    So I should use the harmonic's law equation for this question?
     
  5. Dec 8, 2008 #4

    fluidistic

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    I think you can use the formula [tex]\frac{T_{\text {Earth}}}{a_{\text {Earth}}}=\frac{T_{\text {Mars}}}{a_{\text {Mars}}}[/tex] where [tex]T[/tex] is the period and [tex]a[/tex] is the semimajor axis of the orbit. I think that in your case you can consider [tex]a[/tex] as being the orbital radius.
     
  6. Dec 8, 2008 #5
    Oh okay, that makes this question so much easier :) thanks alot for the help.

    Oh and by the way for Tearth (the period), do I use the constant given for period of rotation given or do I use the constant given for period of orbit around the sun (both found on the Chart titled "Fundamental Constants and Physical Data")? I use the constant for period of orbit around the sun right?
     
    Last edited: Dec 8, 2008
  7. Dec 9, 2008 #6

    fluidistic

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    You're welcome!
    For [tex]T_{\text {Earth}}[/tex] I'd keep it like that. (I wouldn't plug any number instead of it). This way you will get [tex]T_{\text {Mars}}[/tex] in term of [tex]T_{\text {Earth}}[/tex] as they are asking you.
     
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