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!

Orbit of a star in a sherical potential

  1. Sep 8, 2009 #1
    1. The problem statement, all variables and given/known data
    A star is at radius r = 10kpc with v_t=100km/s and v_r=50km/s. The spherical potential is
    \phi = V^2ln(r) with V=200km/s
    1. what is r_min r_max?
    2. Integrate the orbit numerically

    3. The attempt at a solution

    1.
    at r_min and r_max v_r is 0 therefore I can write

    E_min = E_max = L^2/(2r^2) + V^2ln(r) = E

    but how can I solve this to r = ??

    I thought actually I can use angular momentum conservation and say L^2/(2r_min^2) = L^2/(2r^2) which does not really work out? But I think I have to include angular momentum conservation somehow...

    2.
    I tried numerical integration with the following equation

    dr/dt = sqrt(2*(E-\phi) - L^2/(2r^2))

    but the value below the root is negative ???

    I also found

    (dr/r^2d\theta)^2 = 2E/L^2 - 1/r^2 + 2V^2ln(r)/L^2

    but here I have a very similar problem.
    So my question concerning the numerical integration is actually which equation should I use and how to integrate it. I would like to do the integration in a C/C++ for loop by myself instead of using mathematica or other tools... is that possible?
    thanks and best regards
    florian
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Orbit of a star in a sherical potential
  1. Orbital Energy Problem (Replies: 0)

Loading...