How Do You Calculate the Mass of Planet Z?

[talaroue]

Homework Statement

Planet Z is 13700 km in diameter. The free-fall acceleration on Planet Z is 8.79 m/s2.
What is the mass of Planet Z?

Homework Equations

Gm₁m₂/r²

The Attempt at a Solution

I am not sure how this problem is suppose to be worked at all, any of these kind I am having a problem connecting things together. I thought I would use potential energy which would be -G*M1*M2/r but that won't work because I am not given another weight. So my questions are...

Where do I start?

What equations do I have to use?

 

[LowlyPion]

You have the equation. Simply recognize that

G*M*m/r² = F

But you know that F = m*a

... so the acceleration part of that expression should be ...

a = G*M/r²

They have given you a and r and you can look up G, so ... solve for M.

 

[talaroue]

FML. You are a genious I was missing the relationship that my equation was equal to force. Now that brings up another question when dealing with gravity will that equation always equal the force?

 

[talaroue]

so i solved for M...and got M=aR^2/g with numbers is 8.79 m/s^2*1.37x10^7 m/ 6.67x10^-11 which comes out to be 2.47x 10^25 correct? It is saying my anwser is worng. I have done it 5 times and it keeps coming up with the same anwser on my calculator.

EDIT: I was rushing and forgot to make it radius instead of Diameter.

 

[Cyosis]

You didn't square the radius either in your post, a typo or a genuine mistake?

 

[talaroue]

Typo as well as forgetting to turn it into the radius