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