- #1
logan3
- 83
- 2
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
[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]
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