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Homework Help: Period of a planet.

  1. Mar 18, 2005 #1
    In the figure the blue planet has a period of 1 year and an average distance from the sun of 1.73 x 1011 meters. If the average distance from the sun for the red planet is 1.39 x 1011 meters, what is its period to the nearest hundredth of a year?

    So I thought maybe they through in the information on the blue planet to confuse me, so disregarding that information, I used the formula:

    T=(2pi/square root of GM)*r^3/2
    where G=6.67e-11 and M is the mass of the sun=2.0e30kg

    Unfortunately, this isn't correct, and I don't see where I am supposed to incorporate the information about the blue planet with the red planet.
     

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  3. Mar 18, 2005 #2
    Maybe you are not supposed to use the values for M and G in this problem. Just write the expressions of T for the two planets and eliminate [tex]\sqrt(GM)[/tex].
     
  4. Mar 18, 2005 #3
    Kepler's Third Law!!
     
  5. Mar 18, 2005 #4

    SpaceTiger

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    Did you learn Kepler's Law? All you need is a proportionality.
     
  6. Mar 18, 2005 #5
    Right, the period T is proportional to r^3/2 (Kepler's 3rd law), but I am still unsure how to relate the two planets using this concept.
     
  7. Mar 18, 2005 #6

    SpaceTiger

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    If

    [tex]x^m \propto y^n[/tex]

    then, if you have two systems that fit the proportionality:

    [tex]\frac{x_1^m}{x_2^m}=\frac{y_1^n}{y_2^n}[/tex]

    This applies to all values of m and n.

    Proportionality just implies that there is some constant out front. If you have a test case with which to determine that constant, that's all you need.
     
  8. Mar 18, 2005 #7
    T^2/a^3=const for all planets orbiting the same massive object.
     
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