Interesting question about gravitational attraction,accleration and time of collision

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SUMMARY

The discussion centers on calculating the time taken for two bodies with masses M1 and M2, separated by a distance D, to collide due to gravitational attraction. The gravitational acceleration is defined by the equation a = G*M/x², where G is the gravitational constant, M is the mass of the other body, and x is the distance between them. The challenge lies in the fact that acceleration varies with distance, complicating the integration process needed to determine the time of collision. The user expresses difficulty in converting time differentials to distance differentials for integration.

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Homework Statement


There Are two bodies with mases M1 and M2 placed in space separated by a distance D. They attract each other due to gravitational forces and hence acclerate towards each other.The problem is to Find out the time taken before their collision?

Homework Equations


I know that, the acceleration is provided by the gravitational force so,
a=G*M/x^2 for each body where M is the other body's mass and x is the distance from other body at that instant.

The Attempt at a Solution


I am hopless at attemting a solution.
Had my equation of accelartion, dependent on time (like a = Kt^2 + Ct ... etc) I could integrate with respect to time and find instanteneus velocity with respect to time. Then I could Integrate V.dt for a certain time to get distance, and etc. But here acceleration varies with distance,
I tried to convert dt to dx but failed.
So, please Help
 
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