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

In summary, doubling the mass of the Earth while maintaining the same density and spherical shape would result in a doubling of the gravitational force. This is because the gravitational force is directly proportional to the mass, as seen in the equation Fg=Gm1m2/r^2. However, the weight of objects at the Earth's surface would not double, but instead increase by a factor of 1.26 or 2^1/3. This is due to the radius of the Earth also doubling, as mass and radius have a direct relationship for a sphere. This can be seen by rearranging the equation for gravitational force to solve for radius (r=√(Gm/g)). By doubling both the mass and the radius,
  • #1
StaticWaffles
8
0

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.
 
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  • #2
If you double the mass, but keep the same density, what happens to the radius?
 
  • #3
It would increase?
 
  • #4
Did you increase the radius in your calculation?
 
  • #5
No I didn't. So it would double as well?
 
  • #6
Would it?
What is the relationship between mass and volume? volume and radius for a sphere?
 
  • #7
I get it now. My Physics teacher explained it to me after school. Thank you!
 
  • #8
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...?
 

1. What would happen to the Earth's gravitational pull if its mass were doubled?

If the mass of the Earth were doubled, its gravitational pull would also double. This means that objects on the Earth's surface would feel twice as much gravitational force pulling them towards the center of the Earth. This would also affect the orbits of objects around the Earth, as they would need to travel faster to maintain their orbits.

2. How would doubling the Earth's mass affect its size and density?

Doubling the Earth's mass would not change its size significantly. The Earth's size is primarily determined by its distance from the sun and its own internal structure. However, its density would increase since density is directly proportional to mass. This means that the Earth would become more compact and its gravitational pull would also increase.

3. Would the Earth's rotation and revolution be affected by a doubled mass?

Yes, the Earth's rotation and revolution would be affected by a doubled mass. The increase in mass would cause a slight decrease in the Earth's rotation speed, resulting in longer days. This change in rotation would also affect the Earth's orbit around the sun, causing it to take longer to complete one revolution around the sun.

4. How would doubling the Earth's mass impact the tides?

Doubling the Earth's mass would have a significant impact on the tides. The gravitational pull between the Earth and the moon is what causes the tides, so with a doubled mass, the Earth would have a stronger gravitational pull on the ocean waters. This would result in higher and stronger tides, which could have significant effects on coastal areas.

5. What would happen to the Earth's atmosphere if its mass were doubled?

If the Earth's mass were doubled, the force of gravity would be stronger, which would make it more difficult for gases to escape the Earth's atmosphere. This could lead to a thicker atmosphere, trapping more heat and potentially leading to a warmer climate. However, other factors such as the Earth's positioning in relation to the sun would also play a role in the Earth's overall climate.

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