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!

Find force lawa from orbit equation

  1. Oct 13, 2009 #1
    1. The problem statement, all variables and given/known data
    The orbit of a particle moving on a central field is a circle passing through the origin, namely, [tex]r = r_0cos(\theta)[/tex]. Show that the force law is inverse fifth power.


    2. Relevant equations

    [tex]\frac{d^2u}{d\theta^2} + u = \frac{-mF(u^{-1})}{L^2u^2}[/tex]
    [tex]u=r^{-1}[/tex]

    3. The attempt at a solution

    I keep getting that it is inverse third power....

    [tex]u = \frac{1}{r_0cos(\theta)}[/tex]
    then
    [tex]\frac{d^2u}{d\theta^2} = u + \frac{tan^2(\theta)}{u}[/tex]

    so

    [tex]F(u^{-1}) = \frac{-1}{m}\left(L^2u^2\left(u + \frac{tan^2(\theta)}{u}\right) + L^2u^2\right)[/tex]

    [tex]=\frac{-2L^2}{m}\left(u^3+utan(\theta)\right)[/tex]

    so [tex]f(r) = \frac{-2L^2}{m}\left(\frac{1}{r^3}+\frac{tan(\theta)}{r}\right)[/tex]

    Where am I going wrong?
     
    Last edited: Oct 13, 2009
  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: Find force lawa from orbit equation
Loading...