Understanding the Collapse of Two Bodies in Free Space: Gravity Question

[Sobi]

I have seen a question about two bodies left in a free space and the question ask when shall they collapse.
For solving this I reached this step:(GM)*r^-2)*dr=(M*(m+M)^-1)*v*dv
For the left side,the lower bound of the integral is R and the upper bound is 0.after calculating it the answer of the left side is:1*0^-1-(GM*R^-2),what can we do with it?

 

[BvU]

Hi Sobi, welcome to PF !

Interesting question, but assume that I don't know how you got here. Could you tell a little more about what you started with, what steps you did to get here ?

 

[Sobi]

a=(GM*r^-2)=(dv*dt^-1)*M*(m+M)^-1

 

[Vanadium 50]

Are we going to have to wring this out of you one line at a time? "Could you tell a little more about what you started with, what steps you did to get here?" was a very good question, and pretty much what we need to know to help you.

 

[Sobi]

Continuing the question:I then multiplex the right side of it with dr*dr^-1.then bringing dt to the left side of the equation then it became the integral I talked about first.

 

[Sobi]

Can someone answer my question