Universal Gravitation w/ Earth & Moon

[logan3]

Homework Statement

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?

Homework Equations

$F_g = \frac{GMm} {r^2}$
$=> mg = \frac{GMm} {r^2}$
$=> g = \frac{GM} {r^2}$
$=> M = \frac{gr^2} {G}$

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
$M = \frac{(\frac{g}{6}\frac{r^2}{16})} {G} = \frac{(\frac{gr^2}{96})} {G} = \frac{gr^2}{96G}$

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

Did I divide and bring the G up correctly?

Thank-you

 

[BvU]

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.