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Short Grade 12 Gravitational Problem

  1. Jan 22, 2012 #1
    The Question
    The Planet V has a year lasting 360 days. In the same star system is the Planet X. The Planet X has half the mass and triple the radius. A planet X year would be approximately _____ days



    The attempt at a solution

    Givens:
    Tv= 360days
    Tx= ?
    mv = mv
    mx = 1/2mv
    rv = rv
    rx = 3rv


    I derived a formula that incorporates time.
    From which v = sqrt ( GM/r )
    since T = 2pir / v

    sub v into that formula and you get:

    T = sqrt (4 pi^2 r^ 3 / GM )

    with that I had two sets of values, Vulcan and X:
    I plugged them into the formula and arranged for a common values such as Mv.
    Then I subbed Mv from one formula into another.

    This is what results:

    8pi^23rv^3 / GTx^2 = 4pi^2rv^3/ GTv^2

    through cancellations I ended up getting:

    Tx = sqrt ( (2)(3)^3(360)^2 )
    which was that amount of days.

    Not sure if this method would be the correct way to go with this question or not.
     
  2. jcsd
  3. Jan 22, 2012 #2

    SammyS

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    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Do you mean that the radius of the orbit of planet X is triple that of planet V ?

    Does the mass of the planet matter? Is the M in the equation, v = sqrt ( GM/r ), the mass of the planet, or the mass of some other object?

    Use the subscript, X2, & superscript, X2, buttons above the "Go Advanced" message box.
     
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