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

[Rwindsor1]

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.

 

[jbriggs444]

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.

 

[Rwindsor1]

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

 

[jbriggs444]

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.

 

[Rwindsor1]

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.

 

[jbriggs444]

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?