Suppose the mass of the Earth were doubled (Physics 12)

AI Thread Summary
Doubling the mass of the Earth while maintaining the same density and shape results in an increase in radius. The gravitational acceleration at the surface is affected by both mass and radius, leading to a new value of g that is not simply double. The correct calculation shows that the new gravitational acceleration is approximately 1.26 times that of Earth's current value. Understanding the relationship between mass, volume, and radius for a sphere is crucial to solving this problem. The discussion emphasizes the importance of reasoning through the problem rather than relying solely on external solutions.
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Homework Statement


Suppose the mass of the Earth were doubled , but it kept the same density and spherical shape. How would the weight of objects at the Earh's surface change?


Homework Equations


Fg=Gm1m2/r^2


The Attempt at a Solution


g=G2m/r^2
g=19.59817612

g/g(on Earth - 9.8)
=2

I know this is wrong because the textbook says the answer is 1.26 or 2^1/3.
I have no idea how to get this answer. I did find an online solution but they used equations that I have not been taught.

Here is a link to the online solution:
http://archives.evergreen.edu/webpages/curricular/2005-2006/PhyAstro/0506/HW/G6solns.pdf

If anyone can explain how to get this answer step by step that would be great.
 
Physics news on Phys.org
If you double the mass, but keep the same density, what happens to the radius?
 
It would increase?
 
Did you increase the radius in your calculation?
 
No I didn't. So it would double as well?
 
Would it?
What is the relationship between mass and volume? volume and radius for a sphere?
 
I get it now. My Physics teacher explained it to me after school. Thank you!
 
Cool. Of course it would have been better if you'd reasoned it out yourself.
If you posted the answer here, you'd help someone else stuck on the same problem...?
 

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