Change in the Earth's orbit radius from changing mass of the Sun

In summary, the conversation discusses a problem involving the Earth's orbit around the sun and the change in mass of the sun. The final answer is supposed to be M1R1/R2, but the person is having trouble relating the two equations and figuring out what is conserved in the situation. They believe they need another equation to solve the problem.
  • #1
Rwindsor1
6
0

Homework Statement


Consider the Earth's orbit around the sun orbit as circular. Suppose the sun slowly loses mass from mass M1 to mass M2. Suppose that the initial orbit is R1 and the final orbit is R2. Express R2 in terms of the other parameters.
2. The attempt at a solution
The problem I'm having here is relating the two equations for the gravitational force initially and finally. I can't think what is conserved in this situation. The final answer is supposed to be M1R1/M2. Looks like something to do with moments but I can't figure out what.
 
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  • #2
Rwindsor1 said:
I can't think what is conserved in this situation.
Are there any unbalanced external torques?
The final answer is supposed to be M1R1/R2.
You seem to have mis-quoted the answer.
 
  • #3
jbriggs444 said:
Are there any unbalanced external torques?

You seem to have mis-quoted the answer.

Apologies, corrected now. And I don't believe there is, but when I tried moments I was always left with one too many variables to solve the equation
 
  • #4
Rwindsor1 said:
Apologies, corrected now. And I don't believe there is, but when I tried moments I was always left with one too many variables to solve the equation
If you have too many variables then likely you need more equations. But you have not shown any equations. There was a place on the homework template for them.
 
  • #5
jbriggs444 said:
If you have too many variables then likely you need more equations. But you have not shown any equations. There was a place on the homework template for them.
This is what I meant by I feel there is something else that must be conserved. I know I need another equation, I just don't know what that is.
 
  • #6
Rwindsor1 said:
This is what I meant by I feel there is something else that must be conserved. I know I need another equation, I just don't know what that is.
Something else? What thing have you decided is conserved so far?
 

1. How does the change in mass of the Sun affect the Earth's orbit radius?

The mass of the Sun directly affects the gravitational pull it exerts on the Earth. As the mass of the Sun increases, the gravitational force between the two bodies also increases, resulting in a smaller orbit radius for the Earth. Conversely, a decrease in the Sun's mass will result in a larger orbit radius for the Earth.

2. Can the change in the Earth's orbit radius have an impact on our climate?

Yes, the Earth's orbit radius plays a significant role in determining the amount of solar radiation the planet receives. A change in the orbit radius can result in variations in the Earth's climate, such as changes in temperature and precipitation patterns.

3. How does the Earth's orbit radius change over time?

The Earth's orbit around the Sun is not a perfect circle, and it experiences small variations over time due to gravitational interactions with other planets and celestial bodies. These changes are known as orbital eccentricity and occur on a cyclical basis.

4. Could a significant change in the Sun's mass cause a shift in the Earth's orbit?

Yes, a significant change in the Sun's mass could potentially result in a shift in the Earth's orbit. However, these changes would be gradual and would not happen overnight. The Earth's orbit is also stabilized by the gravitational pull of other planets, which helps to maintain its relatively stable path around the Sun.

5. Is the change in the Earth's orbit radius a concern for the future?

While natural variations in the Earth's orbit radius do occur, they are typically small and have minimal impact on our planet. However, some scientists are concerned that human activities, such as burning fossil fuels and releasing greenhouse gases, could lead to more significant changes in the Earth's orbit radius, which could have detrimental effects on our climate. It is essential to continue monitoring and understanding these processes to mitigate any potential impacts.

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