Question

Compute the gravitational acceleration on the moon and on Mars, given the following data:
mass of moon= 0.0123 mass earth
mass of Mars= 0.107 mass earth
R of moon= 0.272 R earth
R of Mars= 0.530 R earth
Please help, I am really struggling to understand Physics this year.
Thank you

Answer 1

\[\frac{ g_{moon} }{ g_{earth} }=\frac{ 6.672\times10^{-11}\frac{M_{moon} }{ R_{moon} } }{ 6.672\times10^{-11}\frac{M_{earth} }{ R_{earth} } }\]

You can cancel out 6.672 x 10^-11

Then substitute Mmoon with 0.0123 mass earth (Mearth)
substitute R moon with 0.272 R earth

Do the same to find the gravitation acceleration of Mars

Answer 2

firstly, it's an **inverse square** law..

\[\large \frac{ g_{moon} }{ g_{earth} }=\frac{ 6.672\times10^{-11}\frac{M_{moon} }{ R_{moon}^\color{red}{2} } }{ 6.672\times10^{-11}\frac{M_{earth} }{ R_{earth}^\color{red}{2} } }\]

but mostly (!!) the question doesn't say do it by comparing values with earth

and so if you're allowed to Google earth's radius and mass then you're presumably allowed also to google the universal gravitation constant G.....

all of which amounts to suggesting using this instead,...., for a given planet p:

\(\large mg_p = \dfrac{GM_pm}{r_p^2}\)

\(\implies \large g_p = \dfrac{GM_p}{r_p^2}\)

not that there's anything wrong with doing it the other way...

https://en.wikipedia.org/wiki/Gravitational_constant