- #1

OONeo01

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## Homework Statement

A binary system consists of two stars of equal mass m orbiting each other in a circular orbit under the influence of gravitational forces. The period of the orbit is τ . At t = 0, the motion is stopped and the stars are allowed to fall towards each other. After what time t, expressed in terms of τ , do they collide?

## Homework Equations

T

^{2}=4

^{∏}(r1+r2)

^{3}/G(M1+M2)

^{2}

F=GMm/R

^{2}

## The Attempt at a Solution

I tried using Kepler's law(T²=(4π²/GM²)(r1+r2)^3)

Assuming r1+r2=R is the distance between them, how do I use it in a force equation(Say like GMm/R^2) and end up getting the required time in terms of τ. (I figure there is an integration somewhere but I can't set up any justifiable equations to begin with !)

I am confused. Any help would be appreciated. Even better if somebody can actually solve this or at least give helpful mathematical hints instead of purely descriptive ones.

Thanks a lot in advance for your time :-)