1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Distance of Closest Approach

  1. Jan 26, 2012 #1
    1. The problem statement, all variables and given/known data
    A particle, unknown mass, has velocity v0 and impact parameter b. It goes towards a planet, mass M, from very far away. Find from scratch (? i'm not sure why it says from scratch), the distance of closest approach.


    2. Relevant equations
    I believe this equation is relevant: Veff(r)=L2/2mr + V(r)


    3. The attempt at a solution
    I haven't attempted this problem because I have no idea what distance of closest approach is. I looked throughout my book and haven't found anything.
     
  2. jcsd
  3. Jan 26, 2012 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    This question really doesn't make sense to me. The "distance of closest approach" is just what it says- the distance a which the particle is closest to the planet as it flies by. Of course, it it hit the planet, that would be 0. But to calculate such a thing you would have to compute its trajectory which would involve knowing not only its initial distance and speed but also it initial direction of travel. when you said "velocity [itex]v_0[/itex], is that a velocity vector? That would help buit then your formula would be adding a number ([itex]L^2/2mr[/itex]) to a vector (V(r)). In any case, I don't see how the "impact parameter" would be relevant if the partical does not "impact" the planet.
     
  4. Jan 26, 2012 #3
    Maybe i should have written the equation as Ueff(r) = (angular momentum)2/2mr2 + U(r). Where U(r) is the potential energy. I also should have mentioned that part b says to use the section in my book about hyperbolas to show that the distance of closest approach is k/(ε + 1) where k and ε are some ridiculous constants that I'm certain would waste your time if I gave them to you. I'm sorry about that :frown:
     
  5. Jan 26, 2012 #4

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Draw a line through the center of the planet, parallel to v0. The particle is a distance b from this line initially. Use this information to calculate the angular momentum L of the particle.

    Once you have that, you can use energy considerations to figure out what the minimum value of r the particle can achieve is.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Distance of Closest Approach
  1. Semiclassical approach (Replies: 0)

Loading...