How Do You Calculate the Mass of Planet Z?

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To calculate the mass of Planet Z, which has a diameter of 13,700 km and a free-fall acceleration of 8.79 m/s², the relevant equation is a = G*M/r². The user initially struggled to connect concepts and attempted to use potential energy but realized that the correct approach involves recognizing the relationship between gravitational force and acceleration. After correcting the diameter to radius and ensuring proper squaring in calculations, the user arrived at a mass of 2.47 x 10²⁵ kg, but faced issues with the answer being marked incorrect. The discussion highlights the importance of using the radius instead of diameter and correctly applying the gravitational formula. Accurate calculations are crucial for determining the mass of celestial bodies.
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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?
 
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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.
 
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?
 
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.
 
You didn't square the radius either in your post, a typo or a genuine mistake?
 
Typo as well as forgetting to turn it into the radius
 
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