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Question: an asteroid of mass m is in a perfectly circular...

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An asteroid of mass m is in a perfectly circular orbit of radius d about a planet of mass M. You may assume that M>>m so that M is completely stationary.

a. Determine an expression for the orbital period of the asteroid.

(I already completed this step. Answer is T=2pi(r^3/2)/sqrt(GM)

b. The asteroid is suddenly stopped in its tracks and allowed to fall freely towards the planet. Determine the time it takes to collide with the planet (assumed to have a radius of zero) and express that time in terms of your answer to part a. (Hint: you will need to determine dr/dt (r) and ultimately trigonometric substitutions will be useful.)

I am stuck on part b. The answer is supposed to be t=T/(4sqrt(2)) but I can't get there. I don't have any trig stuff to substitute with.

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