TheTourist
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I have derived the following equation for the velocity of a collapsing shell of a collapsing star.
I now need to integrate this to find the free-fall time, and the hint is to manipulate the equation into a form where you can use a standard integral: substitute x=r/R and then use the standard integral [tex]\int[/tex][[tex]\frac{x}{1-x}][/tex]1/2 dx=[tex]\pi[/tex]/2
I am completely stuck on how to do this
[tex]\frac{dr}{dt}[/tex]=-[GM([tex]\frac{1}{2}[/tex]-[tex]\frac{1}{R}[/tex])]1/2
I now need to integrate this to find the free-fall time, and the hint is to manipulate the equation into a form where you can use a standard integral: substitute x=r/R and then use the standard integral [tex]\int[/tex][[tex]\frac{x}{1-x}][/tex]1/2 dx=[tex]\pi[/tex]/2
I am completely stuck on how to do this
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