How Do You Calculate the Mass of Planet Z?

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Homework Help Overview

The problem involves calculating the mass of Planet Z, given its diameter and the free-fall acceleration. The subject area relates to gravitational physics and the application of Newton's law of universal gravitation.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster expresses uncertainty about how to approach the problem and questions which equations are relevant. Some participants suggest using the relationship between gravitational force and acceleration to derive the mass. Others raise questions about the consistency of gravitational equations with force.

Discussion Status

Participants are actively engaging with the problem, with some providing guidance on how to manipulate the gravitational equation. There is a recognition of potential errors in calculations, particularly regarding the use of diameter versus radius.

Contextual Notes

There are indications of confusion regarding the correct application of the gravitational formula and the need to convert diameter to radius. The original poster's repeated calculations suggest a struggle with the underlying concepts.

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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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