Mass of planet expressed as multiple of earth's mass

[toothpaste666]

Homework Statement

On the surface of Planet X, the gravitational acceleration is 2g. If the diameter of Planet X is 1/3 that of Earth's, what is the mass of Planet X, expressed as a multiple of Earth's mass?

Homework Equations

$F=G\frac{m1m2}{r^2}$

The Attempt at a Solution

let Mx = mass of planet x, Me = mass of earth, Rx = radius of planet x and Re = radius of planet earth. the diameter of planet x is 2Rx and the diameter of Earth is 2Re.
$2Rx = \frac{2Re}{3}$
$Rx = \frac{Re}{3}$

we have

$a = \frac{GMx}{Rx^2} = \frac{GMx}{(\frac{Re}{3})^2} = \frac{9GMx}{Re^2} = 2g$

since 2g = $\frac{2GMe}{Re^2}$ we have

$\frac{9GMx}{Re^2} = \frac{2GMe}{Re^2}$

$GMx = \frac{2GMe}{9}$


$Mx = \frac{2Me}{9}$

Is this correct?

 

[electricspit]

Everything looks fine, I recommend using subscripts with $Rx$. In LaTeX it is just an underscore followed by the letter:

R_x is $R_x$.

But the problem you have done correctly.

 

[dauto]

Agreed. The solution is correct. I also second the need to use subscripts correctly. This kind of thing is more important than what most people realize. Skipping the use of subscripts in an equation is like omitting proper punctuation. People might still understand what you mean, but it's wrong nevertheless.

 

[toothpaste666]

Ahh ok thanks guys. Sorry about the subscript thing I usually do them when i write it on paper i just didn't know how to do it here.

 

[HalfLostAndSearching]

Yes, your solution is correct. The mass of Planet X is 2/9 times the mass of Earth. This means that Planet X is significantly less massive than Earth, as it would take approximately 9 Planet Xs to equal the mass of Earth. This information would be valuable for further studies on the composition and formation of Planet X, as well as its potential habitability for life forms.