# mass of planet expressed as multiple of earths mass

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?

http://ift.tt/1kCwrSf