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Correct use of is proportional to symbol (alpha)

  1. Sep 28, 2006 #1
    Correct use of "is proportional to" symbol (alpha)

    Hello, I am facing a problem that can be solved quite easily using the proportional symbol ( I think ), so I would like to try to use it! Only problem is.. I don't know exactly how to use it correctly...

    The question is :An astronaut weighs 882N on Earth, determing the weight of the astronaut on Planet X, which has a mass 95.3 times that of Earth and a radius 8.9 times that of Earth.

    So, [tex]g=\frac{Gm}{r^{2}}[/tex] and thus [tex]g\alpha\frac{m}{r^2}[/tex]

    So I wrote down
    [tex]g\alpha\frac{m}{r^2}[/tex]
    [tex]g\alpha\frac{95.3}{79.21}[/tex]

    But of course this false... g is not proportional to 95.3/79.21.. lol. Can someone show me how to correctly show my work? Thanks. This would allow me to simply use this ratio to calculate his new weight.
     
    Last edited: Sep 28, 2006
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  3. Sep 28, 2006 #2

    J77

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    Remember that G is the gravitational constant, ie. it always takes the value 6.67ishe-11

    This constant turns the proportionality into an equality.
     
  4. Sep 28, 2006 #3

    Andrew Mason

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    Saying [itex]g \propto m/r^2[/itex] is equivalent to saying that [itex]g = Gm/r^2[/itex] where G is a constant (the proportionality constant) ie. g is a linear function of m and r2. If you want to perform mathematical operations you have to use the equality sign and the constant.

    [tex]g_1 = \frac{GM_1}{r_1^2}[/tex]

    [tex]g_2 = \frac{GM_2}{r_2^2}[/tex]

    dividing, the constant falls out:

    [tex]\frac{g_2}{g_1} = \frac{M_2}{M_1}\frac{r_1^2}{r_2^2}[/tex]

    AM
     
  5. Sep 28, 2006 #4

    Chi Meson

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    g is proportional to [tex]\frac{m}{r^2}[/tex]
    but when cramming in the values you did, you get a comparison to Earth's "g." Multiply (95.3/79.21) by 9.81, and you get the "g" of the other planet.
     
  6. Sep 28, 2006 #5
    If you want to use the proportionality sign, then say

    [tex]g_{e}\propto \frac{M_e}{r_e^2}[/itex]

    and

    [tex]g_{x}\propto \frac{M_x}{r_x^2}[/itex]

    where [itex]g_{e/x}[/itex] refers to earth or planet x etc. Now you can say:

    [tex]\frac{g_x}{g_e}=\frac{M_xr_e^2}{r_x^2M_e^2}[/tex]
    [tex]g_x}=g_e\frac{M_xr_e^2}{r_x^2M_e^2}[/tex].


    By the way, the "proprtional to" symbol isn't alpha. In tex it's "\propto"... heres the difference:

    [tex]\alpha \ldots \propto[/tex]

    The first is alpha, the second is proptional to.
     
    Last edited: Sep 28, 2006
  7. Sep 28, 2006 #6
    Thanks alot guys! :)
     
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