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Universal Gravitation w/ Earth & Moon

  1. Oct 20, 2014 #1
    1. The problem statement, all variables and given/known data
    The acceleration of gravity on the Moon is 1/6 what it is on Earth. The radius of the Moon is 1/4 that of the Earth. What is the Moon's mass compared to the Earth's?

    2. Relevant equations
    [itex]F_g = \frac{GMm} {r^2}[/itex]
    [itex]=> mg = \frac{GMm} {r^2}[/itex]
    [itex]=> g = \frac{GM} {r^2}[/itex]
    [itex]=> M = \frac{gr^2} {G}[/itex]

    3. The attempt at a solution
    gravity on the Moon is 1/6 what it is on Earth => g => g/6
    radius of the Moon is 1/4 that of the Earth =>r^2 => (r/4)^2 = r^2 / 16
    [itex]M = \frac{(\frac{g}{6}\frac{r^2}{16})} {G} = \frac{(\frac{gr^2}{96})} {G} = \frac{gr^2}{96G}[/itex]

    The Moon's mass compared to the Earth's is 1/96.

    Did I divide and bring the G up correctly?

    Thank-you
     
  2. jcsd
  3. Oct 20, 2014 #2

    BvU

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    You can google the moon fact sheet to check :)

    All the ratios you want are also there !
    Considering you only have these numbers 4 and 6 to begin with, you have done just fine.
     
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