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Math Help - finding the radius problem

  1. #1
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    Question finding the radius problem

    Hi i have a question: The radius of the Earth is approximately m and the acceleration due to gravity at the Earth’s surface is approximately 9.81 ms-2. If the acceleration due to gravity at the surface of the planet Mercury is approximately 3.59 ms-2 estimate the radius of Mercury. You may assume Newton’s Law of Gravitation but you do not require the value of the Gravitational constant in this law - list the other major assumptions that you make concerning the densities and shapes of the planets.


    my attempt solution:
    a = Gm/r
    for earth a = GM/R
    volume of sphere is ⁴/₃πr
    Assuming both have the same density
    M = kR
    a = GM/R
    a = GkR/R = GkR

    The ratio of the two values of a = 9.81/3.59 = 2.73
    then the radius of mercury is 3.59=9.81*2.73R
    gives R=0.13

    is this incorrect? thx
    Last edited by hazeleyes; May 5th 2011 at 08:56 AM.
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  2. #2
    MHF Contributor Unknown008's Avatar
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    Wait, for the last step, I'm not sure what you did exactly.

    We have:

    a_{E} = GkR_{E}

    a_{M} = GkR_{M}

    Then the ratio becomes:

    \frac{a_{E}}{a_{M}} = \frac{GkR_{E}}{GkR_{M}}

    This simplifies to:

    \frac{9.81}{3.59} = \frac{R_E}{R_M}

    You have to get R_M

    R_M = \frac{3.59R_E}{9.81}

    I don't know where your radius of the Earth went in your problem... I only see "radius of the Earth is approximately m"

    EDIT: And why is latex not working again
    EDIT2: seems okay now.
    Last edited by Unknown008; May 5th 2011 at 11:14 AM.
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  3. #3
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    thanks for your replied.
    sorry for the mistype. The radius of the Earth is approximately 6.38*10^(-6) m

    therefore to find Rm=[3.59*6.38]/9.81 = 2.34*10^(-6)m
    is this correct? thanks!!
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  4. #4
    MHF Contributor Unknown008's Avatar
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    The figures are correct... but you got the wrong sign

    10^-6 is in the realm of the micro world
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  5. #5
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    sorry for the mistype AGAIN..lol The radius of the Earth is approximately 6.38*10^(6) m

    therefore to find Rm=[3.59*6.38*(10^6)]/9.81 = 2335780.836m
    thanks!!
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