# Comet's distance with and without gravity [closed]

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!

• The Sun will ALWAYS attract the comet, even if the comet doesn't end up hitting the Sun. Your question is really confused: what is it you'd like to know or understand? – Gert Nov 18 '15 at 3:38
• I think you should consider changing the title of your question. Its not so much about having/not having gravity. The parameter, $d$, is the impact parameter, which defines the initial angular momentum to be $L=mv_0d$. You can also consider your system's total energy at this point to be $E_{tot} = 1/2mv_0^2$. – tmwilson26 Nov 18 '15 at 4:30
• Hi and welcome to the Physics SE! Please note that this is not a homework help site. Please see this Meta post on asking homework questions and this Meta post for "check my work" problems. – John Rennie Nov 18 '15 at 7:24
• – BowlOfRed Nov 18 '15 at 7:51