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Silly Gravity / Radius Question

  1. Sep 30, 2004 #1
    I think this is pretty basic, but I'm obviously missing something. Here's the ?:

    A planet has the same mass as earth, but it's gravitational acceleration is g/2. What is the radius of the planet?


    What's the relationship here? -AT77A
     
  2. jcsd
  3. Sep 30, 2004 #2

    Pyrrhus

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    Homework Helper

    Well, let me see (correct me if i'm wrong)

    [tex] \vec{F} = G \frac{m_{1}m_{2}}{r^2} \vec{r} [/tex]

    [tex] m_{2} \vec{g} = G \frac{m_{1}m_{2}}{r^2} \vec{r} [/tex]

    [tex] \vec{g} = G \frac{m_{1}}{r^2} \vec{r} [/tex]

    so, if g/2

    [tex] \frac{\vec{g}}{2} = \frac{G \frac{m_{1}}{r^2}}{2} \vec{r} [/tex]
     
  4. Oct 1, 2004 #3

    mathman

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    Science Advisor

    For a constant mass, to cut g in half, you have to increase the radius by 1.414... (sqrt(2)).
     
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