Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    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
  2. jcsd
  3. Sep 28, 2006 #2


    User Avatar

    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

    User Avatar
    Science Advisor
    Homework Helper

    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]

  5. Sep 28, 2006 #4

    Chi Meson

    User Avatar
    Science Advisor
    Homework Helper

    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]


    [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:


    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! :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook