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

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The discussion focuses on the mathematical analysis of when two bodies in free space will collapse due to gravity. The user presents an equation involving gravitational force and attempts to integrate it, seeking clarification on their calculations. They express confusion about the next steps after reaching a specific integral form. Participants encourage the user to elaborate on their initial approach and the steps taken to derive the current equation. The conversation emphasizes the need for clear communication of the mathematical process to facilitate understanding and assistance.
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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?
 
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Hi Sobi, welcome to PF :smile: !

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 ?
 
a=(GM*r^-2)=(dv*dt^-1)*M*(m+M)^-1
 
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.
 
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.
 
Can someone answer my question
 
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