1. Not finding help here? Sign up for a free 30min 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!

Impact parameter of a photon in Schwarzchild metric

  1. Oct 19, 2015 #1
    Hi, I'm having trouble answering Question 9.20 in Hobson's book (Link: http://tinyurl.com/pjsymtd). This asks to prove that a photon will just graze the surface of a massive sphere if the impact parameter is [tex]b = r(\frac{r}{r-2\mu})^\frac{1}{2}[/tex]

    So far I have used the geodeisic equations [tex](1-\frac{2\mu}{r})\dot{t} = k[/tex] and [tex]r^2\dot{\phi} = h[/tex] to give [tex]\frac{d\phi}{dt} = \frac{b(1-\frac{2\mu}{r})}{r^2}[/tex] and b = h/k due to the argument given here http://www.physicspages.com/2013/06/13/photon-equations-of-motion/

    This is extremely close to the actual result but I can't figure out why [tex]\frac{d\phi}{dt}=\frac{1}{b}[/tex].

    Any help? Thank you!
     
  2. jcsd
  3. Oct 24, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
  4. Oct 28, 2015 #3
    I solved it myself. The metric for lightlike separation implies [tex] g_{00}\dot{t}^2 +g_{11}\dot{r}^2+g_{22}\dot{\phi}^2 =0[/tex] and we have expressions for phi dot and t dot from the OP. Just plug them in and since the expression is true everywhere we evaluate it on the surface of the star i.e where motion is purely tangential -> r dot is zero. So we just arrange the above equation for b = h/k to get the required answer.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Impact parameter of a photon in Schwarzchild metric
  1. GR - Impact Parameter (Replies: 5)

Loading...