# Mass of planet expressed as multiple of earth's mass

1. Apr 11, 2014

### toothpaste666

1. The problem statement, all variables and given/known data
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?

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

3. 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?

2. Apr 11, 2014

### 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.

3. Apr 11, 2014

### 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.

4. Apr 11, 2014

### 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.