I've got this question that I just can't seem to answer. The question is as follows:
A comet approaches the solar system with velocity v and would, if the sun would not attract the comet, pass the sun at a distance d. What is in reality the shortest distance between comet and sun? (Hint: use conservation of angular momentum and energy).
I've tried a few things, but apparently they are all wrong. I thought about getting a formula for the distance to the sun, and then finding where the derivative is 0. Is that the right approach? I just can't get to a correct formula. I've also tried equating the total energy and momentum with gravity to the total energy and momentum without gravity, but that becomes a complete mess. Any help or pointers would be greatly appreciated!