# Gravitational Acceleration given mass and radius

1. Apr 9, 2014

### EliteCodexer

1. The problem statement, all variables and given/known data
If you lived on a planet with five times the mass of Earth and twice the radius, what would be the gravitational acceleration at the surface of your planet?

2. Relevant equations
GM/r^2
Mass of Earth = 6.00*10^24 kg
Radius of Earth = 6.38*10^3 km

3. The attempt at a solution
So, when I started out doing this, I quickly plugged in earth's radius (in m), mass (in kg) and the gravitational constant just to make sure it came out at 9.8 because I know that's what Earth's gravitational acceleration from the surface is, but none of the answer I get are even close. I can't even get this right and I still have to do the actual problem (using 5x the mass and 2x the radius).

2. Apr 9, 2014

### SteamKing

Staff Emeritus

3. Apr 9, 2014

### BiGyElLoWhAt

it does work. we did it the other day sitting around.
try
GM/r^2
Mass of Earth ≈ 5.97*10^24 kg
Radius of Earth ≈ 6.38*10^3 KM = 6.38*10^6 m
G≈ 6.67 × 10^-11

$\frac{M_{earth}}{r_{earth}^2}G ≈ \frac{5.97*10^{24}}{6.38*10^{12}}*6.67*10^{-11}$
$=\frac{5.97*6.67*10}{6.38} ≈9.805$

4. Apr 9, 2014

### haruspex

It's worth persevering to get that right, but you don't need it for this question.
You can solve it just by taking g = 9.8m/s2 for Earth and adjusting it. What effect will 5 times the mass have on that? What effect will twice the radius have?