- #1
KBriggs
- 33
- 0
Homework Statement
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.
Homework Equations
[tex]\frac{d^2u}{d\theta^2} + u = \frac{-mF(u^{-1})}{L^2u^2}[/tex]
[tex]u=r^{-1}[/tex]
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: