# Homework Help: Finding the mass of a planet using gravitational acceleration and radius

1. Nov 22, 2008

### PrometheuSIT

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

Planet Z is 5000 km in diameter. The free-fall acceleration on Planet Z is 7.00 m/s^2. What is the mass of Planet Z?

2. Relevant equations

Well Newton's gravitational law G(M1M2)/R^2
And I cannot think of much else

3. The attempt at a solution

On one of the earlier homeworks we were given a table in which there were fictional planets and their ratios of mass and radius to earth so I tried using

gG M(earth)/(R(earth))^2 = gG M(z)/(R(z))^2
Where the "g"s are each planet's free fall acceleration.
so that the Gravitational constant would cancel and I'd have the Mass of planet Z

For the mass of the earth I used 5.97E34, for the radius of the earth I used 6387.1 km
I know that the radius needs to be in meters and would be correctly notated as 6.3871E6

I don't know how to figure this one out

2. Nov 22, 2008

### LowlyPion

Welcome to PF.

F = ma = GMm/r2

a = GM/r2

3. Nov 22, 2008

### PrometheuSIT

Thank you very much